The specific research areas of algebra covered at McMaster range from the study of general algebraic structures, general ring theory, representation theory of groups, and the theory of quadratic forms, to the related areas of number theory, logic, and combinatorics. Number theory was already prominent in Babylon and Classical Greece, and it remains a central area of mathematics to this day. It draws from and influences developments in algebra, analysis, and geometry. Testing integers to determine whether or not they are primes is a central problem of this subject, and the best current methods employ the theory of elliptic curves, the same theory from which the recent proof of Fermat's Last Theorem has sprung. There is also a lot of contemporary activity in this area, which includes much of the theory of prime numbers and their distribution among the integers.
Logic is an ancient subject whose tradition is carried on today mostly in philosophy departments.
Although mathematical logic is not divorced from philosophical issues, it differs from philosophical logic in that its goal is not the understanding of human reasoning but is the study of the language of mathematics and the way abstract mathematical objects are defined. This is often called metamathematics. At McMaster, there are several people who are active in logic and foundations. Their areas of interest include model theory and general algebraic systems, set theory and its history, and category theory. Combinatorial theory, with historical roots in mathematical recreations and games, has become an increasingly important branch of mathematics whose influence continues to grow.