MATH 3274 Set Theory
Students who take this course will require knowledge of the basic concepts of Algebra. They will also be required to have a solid grounding in elementary set theory and basic logic. Thus, ABSTRACT ALGEBRA I is listed as a prerequisite.
The first part of the course involves axiomatic set theory, which includes philosophy of sets. The language of set theory is used to describe representations of relations and functions. A fundamental approach to concepts in set and the algebraic structures of groups, rings and fields is utilized to develop number systems. These systems include the natural numbers, integers, rationals, reals and complex numbers. The course proceeds onto a treatise on infinite sets and on the different cardinal numbers that lead to transfinite arithmetic. Axiom of Choice and its equivalent representations are then introduced, as well as point-set topology.
Since cogent communication of mathematical ideas is important in the presentation of proofs, the course will emphasize clear, concise exposition. This course will therefore be useful for all students who wish to improve their skills in mathematical proof and exposition, or who intend to study more advanced topics in mathematics.