Computability theory is a branch of mathematical logic that studies the limits of computation.

A Turing machine is a theoretical model of computation that defines an abstract machine that can be used to simulate any computer algorithm.

The Halting Problem is a fundamental problem in computer science that asks whether there exists an algorithm that can determine whether any given program will halt or run forever.

The Church-Turing Thesis is a widely accepted conjecture in computer science that states that any computation that can be carried out by a Turing machine can also be carried out by a human computer.

Complexity theory is a branch of computer science that studies the computational resources required to solve a given problem.

The P versus NP problem is one of the most important unsolved problems in computer science. It asks whether the class of problems that can be solved in polynomial time (P) is equal to the class of problems that can be verified in polynomial time (NP).

Information theory is a branch of mathematics that studies the measurement, transmission, and storage of information.

The Shannon-Hartley theorem is a fundamental theorem in information theory that states the maximum rate at which information can be transmitted over a noisy channel.

Algorithmic theory is a branch of mathematics that studies the design and analysis of algorithms.

The time complexity of a linear search algorithm is O(n), where n is the number of elements in the list.

The time complexity of a binary search algorithm is O(log n), where n is the number of elements in the list.

The space complexity of a linear search algorithm is O(1), meaning that it does not require any additional space beyond the space required to store the list itself.

The space complexity of a binary search algorithm is O(log n), meaning that it requires additional space proportional to the logarithm of the number of elements in the list.

Quantum computing theory is a branch of mathematics that studies the relationship between computation and physics, particularly the use of quantum-mechanical phenomena to perform computation.

Bioinformatics is a branch of mathematics that studies the relationship between computation and biology, particularly the use of computational methods to analyze biological data.