What can be inferred by the phrase recruiting on beer soaked beaches?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

What does freshly minted mean (Passage I)?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

The author s tone in passage II can be described as _________.

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

What does the author mean by the term anecdotal evidence (Passage II)?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

Based on the Passage II, we can infer which of the following ______________.

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

The main idea of this story is that (Passage I) _______________.

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

What does Cheryl Allmen-Vinnidge mean when she says students have done their homework (Passage I)?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

Which of the following didn't happen in the four years when the class of 2003 was in college (Passage I)?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

Which of the following is not the view expressed by the author with respect to union of Slovak with Hungary?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following misleadingly appears as a desire of Slovak people for a connection with Poland as against the others which depict the actual prevalent conditions?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following is not a view of the author with respect to Slovakia?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following facts actually identifies the objective behind the Polish pretensions to Slovakia?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following does not connote the word Incipient?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following did not advocate the administrative reform instituted in 1927 to tide over the difficulty of developing a federal state structure during the first half of the 20^th century?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Consider the following random Fibonacci sequence, in which the first two terms are 1,1 and the subsequent terms are generated as, A coin is tossed, if it is a head the previous two terms are added, if it is a tail the last term is subtracted from the one before that. The following are the results of the coin tosses: HHTHHTTHH. Which of the following denotes the random Fibonacci sequence?

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

Which of the following applications is not listed that could benefit directly or indirectly as a result of Viswanath's experiments on random Fibonacci sequences?

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

What was the difference between the concept Viswanath had discovered in the mathematical context involving so-called random matrix multiplication by Furstenberg and Kesten?

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

In a standard Fibonacci series, the hundredth power of the Golden Ratio is equal to the _____________.

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

Which of the following best describes the relationship between the two passages?

Passage – I

College graduation brings both the satisfaction of academic achievement and the expectation of a well-paying job.But for 6000 graduates at San Jose State this year, there's uncertainty as they enter one of the worst job markets in decades. Ryan Stewart has a freshly minted degree in religious studies, but no job prospects. "You look at everybody's parents and neighbors, and they're getting laid off and don't have jobs," said Stewart. "Then you look at the young people just coming into the workforce... it's just scary." When the class of 2003 entered college the future never looked brighter. But in the four years they've been here, the world outside has changed dramatically. "Those were the exciting times, lots of dot-com opportunities, exploding offers, students getting top dollar with lots of benefits," said Cheryl Allmen-Vinnidge, of the San Jose State Career Center. "Times have changed. It's a new market." Cheryl Allmen-Vinnidge ought to know. She runs the San Jose State Career Center. It is sort of a crossroad between college and the real world. Allmen-Vinnidge says students who do find jobs after college have done their homework. "The typical graduate who does have a job offer started working on it two years ago. They've postured themselves well during the summer. They've had several internships," she said. And they've majored in one of the few fields that are still hot -- like chemical engineering, accounting, or nursing -- where average starting salaries have actually increased over last year. Other popular fields (like information systems management, computer science, and political science) have seen big declines in starting salaries. Ryan Stewart (he had hoped to become a teacher) may just end up going back to school. "I'd like to teach college some day and that requires more schooling, which would be great in a bad economy," he said. To some students a degree may not be ticket to instant wealth. For now, they can only hope its value will increase over time.

Passage – II

After years of barely any activity, the job market for college seniors and graduate students finally appears to be picking up. Firms are interviewing more, giving more offers and even bumping up pay a bit.

While the market is nowhere near as strong as in the late 1990s — when the job market was so hot, firms were recruiting on beer-soaked beaches during spring break — a turnaround definitely appears to be taking shape. "It is starting to pick up," says Carol Lyons, dean of career services at Northeastern University in Boston. "Not in any drastic way; in a slow, hopefully steady, way. ”Andrew Ferguson, director of the career development center at the University of Richmond, calls this market more "normal," unlike the late 1990s. "It's actually been a decent year." The same appears to be true for graduate students. "This year is a definite improvement than earlier in this decade," says Dan Poston, director of the business school at the University of Washington in Seattle. The number of second-year MBAs at the University of Washington with job offers is up 20% from last year. Megan Wasserman, 22, hasn't even gotten her diploma from Northeastern University but she has already started work as a production assistant at the Dr. Phil show, where the journalism student interned in the fall. With enough credits to skip the final semester, Wasserman jumped at the chance for a full-time job with the show in Los Angeles when it was offered to her late last year.” I’m one of the lucky ones," she says. Although there is little solid data about the current job market for college students, anecdotal evidence suggests things are getting better: 

• Booz Allen Hamilton expects as many as 400 recent college graduates will start work in its government and technology group this fiscal year, which began April 1. Last year, 300 were hired, while the year before, 220 new college grads started work, says Judy Merkel, director of recruiting at the McLean, Va.-based consulting firm.

• The number of firms recruiting students at Georgetown University's business school is up 24% from a year ago. Half of second-year students have job offers, up from 40% at this time a year ago, says John Flato, director of MBA career management at the Washington, D.C., school.

• Enterprise Rent-A-Car plans to hire 6,500 college seniors for its management training program this year, up from about 6,000 last year.

Viswanath's Ratio of 1.1319... is _____________.

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

Which of the following is not an inference that can be drawn from Viswanath's experiments on random Fibonacci series?

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

Which of the following is not analogous to the introduction of an element of randomness in a Fibonacci sequence?

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.

Go through the following tabular column and identity which of the statements in left column corresponds with the author's views on the state of Slovakia. A. Slovak representatives in the Czechoslovakian Government at London.| E. Not in favour of either the destruction of Czechoslovakia or the independence of Slovakia. | | B. 1939 Declaration of Czechoslovak National committee.| F. Study of various projects for decentralisation within the restored Republic. | | C. US, Great Britain, France.| G. Upholding tenets of liberty, equality and fraternity striving to establish an infallible republic founded on equal rights and duties.| | D. Four Slovaks in the Czechoslovak Government at London.| H. Acknowledgment of Czechoslovak Government in London keen on restoring Czechoslovakia as a State.|

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

Which of the following renders least support to the author's narration?

Four possible settlements may be envisaged for the Slovak problem: union with Poland, union with Hungary, independence, or restoration of Czechoslovakia under some sort of decentralized constitution structure.

I. UNION WITH POLAND

For years there have been Polish pretensions to Slovakia, resting on vague historical arguments which in reality apply only to the district of Spi. There were only 7,000 Poles in Slovakia according to the census of 1930. The Poles assert, for example, that some dialects in northern Slovakia differ very little from the local Polish dialect spoken across the Polish frontier. There is also a Polish contention that Polish Catholicism, strong in its support of the Vatican and never called into question like Czech Hussitism, is more akin to the Slovak spirit than is the Czech, spirit.

Back of the Polish pretension, however, has been the desire to establish a common frontier with Hungary, for purposes of alliance and defense, as was demonstrated in the period of the partition of Czechoslovakia from September 1938 to March 1939, when Poland encouraged the separatist movement in Slovakia.

There is no evidence of any real desire whatsoever on the part of the Slovak people for a connection with Poland, though there has been agitation on the part of irresponsible propagandists at times for such a union in order to frighten the Czechoslovak Government into concessions. The economic conditions of Slovakia are unfavorable to its incorporation into Poland. While Poland is an agricultural country with a substantial industrial development, Slovakia is overwhelmingly agricultural in character. Commerce between Poland and Slovakia has never been of significance. Union of Poland and Slovakia, moreover, might serve to stifle the incipient industrial development of Slovakia.

II. UNION WITH HUNGARY

Union with Hungary is another possible alternative solution which the Magyars within Slovakia and Hungary have desired ever since the separation in 1918. It is extremely doubtful, however, that more than a very few Magyarone Slovaks have desired to return to Hungary since 1918, after the experience of several centuries of Magyar rule. Before 1918 economic relations between the Slovak region and the central areas of the unitary Hungarian kingdom were close; the possibility has been suggested more than once that more Slovaks would be prepared to accept some kind of federal arrangement with Hungary, under which Slovakia would form an economic unity with Hungary but would enjoy cultural autonomy. On the other hand, it may be pointed out that no responsible Slovak representatives, even those of the Slovak populist Party, ever advocated reunion with Hungary; even under the "autonomous" and "independent" governments of Slovakia – despite the general orientation of the regime – Slovak troops have twice fought against Hungarian invasions.

III. AN INDEPENDENT SLOVAKIA

A third possible alternative envisages complete independence for Slovakia. Complete independence was never on the program of any of the Slovak parties, including the Slovak Populist Party, until it was proclaimed by the extreme elements of the Slovak Populist Party on March 14, 1939. It should be remembered, however that at the time that “independence” was proclaimed, the state was placed under the "protection" of National Socialist Germany.

The experience of the Slovaks under the "independent" regime of Father Tiso and Dr. Tuka- may not be conducive to further developments in that direction. Moreover, there is every evidence that complete independence is quite impracticable. It is extremely doubtful that an independent state would be either politically or economically viable.

IV. REUNION OF SLOVAKIA AND BOHEMIA-MORAVIA IN A RESTORED CZECHOSLOVAKIA

A final alternative is the reincorporation of Slovakia in a restored Czechoslovak Republic, under some kind of decentralized administrative and legislative regime.

While the Czechs and Slovaks had their difficulties under the Republic because of mistakes on the part of both these related Slavic peoples, and on account of the impossibility of developing a federal-state structure in the period between 1918 to 1938, the major difficulties appeared to be in process of solution by 1927, when an administrative reform was instituted. Under this reform Slovakia became one of the four provinces – the others being Bohemia, Moravia-Silesia, and Ruthenia. Slovakia had a provincial president and vice-president, and an assembly, with a small executive committee. The provincial assembly or diet had authority over economic and administrative affairs, questions of public health, provincial social, educational and communications questions, and the imposition of taxes concerning these matters.

Today, there are four Slovaks in the Czechoslovak Government at London, which are studying various projects for decentralization within the restored Republic. In its first proclamation in 1939. the Czechoslovak National Committee declared: "In the spirit of Masaryk and Tefanik, in the spirit of the founders and the martyrs of our nation, we enter the struggle united. Recognizing no difference of party, class or any other kind, we are determined to fight to the end and to assure a free, democratic Czechoslovak Republic, inspired by the spirit of justice for all its nationalities. We wish to have a republic socially just, founded on equal rights and equal duties for all its citizens. As regards the new organization of the State, the relationship of free Czechs to free Slovaks, the majority of free Czechs and the majority of free Slovaks will decide in democratic form and brotherly understanding, inspired by the principles of equality in rights and duties.”

The United States of America, Great Britain and France have never recognized the destruction of Czechoslovakia or the independence of Slovakia. The Soviet Union, however, did recognize the independent State of Slovakia. All the members of the United Nations, including the United States, Great Britain, the Soviet Union and China, have recognized the existence of the Czechoslovak Government in London and are committed to the restoration of Czechoslovakia as a state.

Despite the participation of Slovaks in the Czechoslovak Government-in-exile, there is some opposition among Slovaks living abroad to the program of the Government. This opposition centers around the personalities of Dr. Milan Hoda, former Prime Minister, and Dr. Tefan Osusk, former Czechoslovak Minister to France. Hoda seems to favour a definite statement from the Government favouring autonomy for Slovakia within a restored Republic of Czechoslovakia. President Bene and the Government refuse to commit themselves to any specific program on the ground that the internal constitutional structure of the Republic must be decided by the people at home after the war. Some Slovaks fear, however, that the electorate might  then be manipulated in favor of a centralist form of Government, even though autonomy might be preferred by a majority in Slovakia.

One could find Fibonacci sequences appearing in all the following instances except ____________________.

It all started out with imaginary rabbits. In a book completed in the year 1202; mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence gets closer and closer to a specific number, often called the golden ratio. It can be calculated as 1.6180339887.... For instance, the ratio 55/34 is 1.617647.... and the next ratio, 89/55, is 1.6181818…..

Now, computer scientist Divakar Viswanath of the Mathematical Sciences Research Institute in Berkeley, California, has taken a fresh look at Fibonacci numbers and unexpectedly discovered a new mathematical constant: the number 1.13198824.... He describes his result in a paper to be published in Mathematics of Computation.

Viswanath's research represents an intriguing gateway to heavy-duty mathematics, says mathematician Keith Devlin of Saint Mary's College of California in Moraga. It relies on powerful mathematical techniques that also are used, for instance, to elucidate the behavior of disordered materials.

Viswanath wondered what would happen to the Fibonacci sequence it he introduced an element of random-ness.

Here's one way to proceed: Start with the numbers 1 and 1, as in the original Fibonacci sequence. To get the next term, flip a coin to decide whether to add the last two terms or subtract the last term from the previous term.

Suppose that "heads" means add and "tails" means subtract. Tossing "heads" would result in adding 1 to 1 to get 2, and tossing "tails" would lead to subtracting 1 from 1 to get 0. According to this scheme, the successive coin losses H H T T T H, for example, would generate the sequence 1, 1, 2, 3, – 1, 4, – 5, – 1.

It's easy to write a short computer program to generate these random Fibonacci sequences, notes Lloyd N. Trefethen of the University of Oxford in England. Looking for patterns and trends among such sequences of numbers can be a fascinating pastime, he says. Indeed, infinitely many sequences follow Viswanath's rule. A few have special characteristics. In the coin always comes up heads, for instance, the result is the original Fibonacci sequence. Other strings of coin tosses can produce a repeating pattern, such as 1, 1, 0, 1, 1, 0, 1, 1, 0, and so on. Nonetheless, such special cases are sufficient rare among all possible sequences that mathematicians ignore them.

The standard Fibonacci sequence has an intriguing property. The hundredth Fibonacci number, for example, is roughly equal to the hundredth power of the golden ratio.

Despite significant fluctuations, the absolute values of the first 1,000 terms of a typical, computer-generated random Fibonacci sequence show a clear trend to larger values, fitting a pattern of exponential growth. By examining typical random Fibonacci sequences based on coin tosses, Viswanath uncovered a similar pattern. He ignored the minus signs, thereby taking the absolute value of the terms. He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824.... In fact, the higher the term, the closer its value gets to the appropriate power of 1.13198824....

Despite the element of chance and the resulting large fluctuations in value that characterize a random Fibonacci sequence, the absolute values of the numbers, on average, increase at a well-defined exponential rate.

It is not obvious that this should happen, Viswanath observes. Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponenstially.

Providing a rigorous proof of the result was a tricky business. To get the answer he required, Viswanath had to delve into several different areas of mathematics, including the intricacies of geometric forms known as fractals, and finish with a computer calculation.

Viswanath's achievement "showed persistence and imagination of a very high order," Trefethen remarks.

Now, Devlin adds, "Mathematics has a new constant. No one has yet identified any link between this particular number and other known constants, such as the golden ratio."

Surprisingly, Viswanath's constant provides one answer to a mathematical puzzle that arose several decades ago from the work of Hillel Furstenberg, now at Hebrew University in Jerusalem, and Harry Kesten of Comell University.

In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of random-ness, the value of the nth term of the sequence gets closer to the nth power of some fixed number. However, they provided no hint of what that fixed number might be for any particular sequence.

Because random Fibonacci sequences fit into this category of sequences, Viswanath's new constant represents an accessible example of these fixed numbers.

"It is a beautiful result with a variety of interesting aspects," Trefethen says. It's a nice illustration, for example, of how a random process can lead to a deterministic result when the numbers involved get very large.

Moreover, although Viswanath's result by itself has no obvious applications, it serves as an introduction to the sophisticated type of mathematics developed by Furstenberg, Kesten and others. That mathematical machinery has proved valuable in accounting for properties of disordered materials, particularly how repeated random movements can lead to orderly behavior, Devlin says.

Such mathematics underline explanations of why glass is transparent and how an electric current can still pass in an orderly fashion through a semiconductor laced with randomly positioned impurities.

Viswanath's original work was done at Cornell University, under Trefethen’s supervision. Trefethen and Oxford’s Mark Embree have recently studied slightly modified versions of the random Fibonacci sequence. If, for example, one combines the last known term with half the previous term, adding or subtracting according to the toss of a coin, the sequence’s numbers decease at a certain rate, displaying exponential decay.

By using fractions other than one-half, it's possible to find fractions for which one gets exponential decay, exponential growth, or merely equilibrium. "All this quickly gets under your skin when you start trying it on the computer,” Trefethen says, adding that it becomes an addictive pastime.

There's still plenty of room for mathematical exploration and experimentation in a problem that began centuries ago as a decidedly unrealistic model of a population of rabbits.