Level: BSc, MSci, MSc
Title: Combinatorial game theory
Supervisor:

Dr Alex Fink
Research Area: Algebra
Description:

A combinatorial game is one in which there is no chance or hidden information, so that in theory, with enough computation, you could work out who would win if both players played perfectly. Familiar examples range from noughts and crosses to chess and go. In this project, you will learn about the algebraic structures which arise in analysing these games, such as the surreal numbers, a field containing the real numbers as well as diverse infinities and infinitesimals.

Several different specializations of this could be developed as MSc projects. One involves proving some observations about growth rate of misère quotients (misère games are those where the last player loses) while another has a measure of coding theory: it would be to investigate how lexicodes behave as the string grows in both directions.

 
Further Reading:
  • E. Berlekamp, J. H. Conway and R. K. Guy, Winning ways for your mathematical plays. Second edition. A K Peters Ltd., 2001–2004.
  • A. Siegel, Combinatorial game theory. Graduate Studies in Mathematics, Vol. 146, American Mathematical Society, 2013.
Key Modules:

MTH5100 Algebraic Structures I

MTH6104 Algebraic Structures II
Other Information:
Current Availability: Yes