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MATH43011/63011 Computation and Complexity


Quite a lot of the mathematics you have studied so far involves using algorithms to solve computational problems. For example, you have probably used Euclid's algorithm to solve the problem of finding the greatest common divisor of two integers. In this course, we abstract a level further, and study the properties of problems and algorithms themselves. The kind of questions we ask are "is there an algorithm to solve every problem?" and "what problems can be solved by an efficient algorithm?".

Compared with most of mathematics, this area is in its infancy, and many important things remain unknown. The course will take you to the point where you understand the statement of, and some of the issues surrounding, one of the most important open questions in mathematics and computer science: the "P vs NP" problem, for which the Clay Mathematics Foundation is offering a $1,000,000 prize. And who knows, perhaps one day you will be the one to solve it!

(Note that this is a proof-based course about the theory of computation, and not a practical computational course.)


The course has minimal formal prerequisites, and is taken by quite a range of students: All students should be aware that it is a rigorous proof-based course (not a course in practical computation), and that it contains some philosophical content which requires stronger English language skills than most mathematics courses.

Course Materials

Materials for the 2020-21 presentation are available on Blackboard.

Further Links

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