MATH-4403 Set Theory
(Fall 2023)

Instructor / Office hours

Dr. Iian Smythe (i.smythe@uwinnipeg.ca) / TBD

Class meetings

Lecture: MW 2:30pm-3:45pm in 3M54 Manitoba Hall

Textbooks & Resources

Textbook: Herbert B. Enderton, Elements of Set Theory, Academic Press, 1977. This text is freely available as an eBook through the UW Library: https://uwinnipeg.on.worldcat.org/oclc/815470912

All course information and announcements will be posted on the course Nexus site the course Nexus site.

Course outline:

An introduction to axiomatic set theory, the foundations of mathematics, and the study of the infinite. Our course is divided into two parts:

• Set theory as foundations (Ch. 1-5 in Enderton): The Zermelo-Fraenkel axioms of set theory, algebra of sets, functions, relations, and the construction of number systems. We will see how set theory can be used as a common axiomatic foundation for all of mathematics. 

• Set theory proper (Ch. 6-8 in Enderton): Cardinals (“sizes” of infinity), ordinals (“lengths” of infinity), transfinite methods, and the Axiom of Choice. We will learn how to compute and compare sizes of sets across mathematics, develop tools for generalized (potentially uncountable) inductive constructions, and obtain a global picture of the set-theoretic universe.

Due to time constraints, some topics on the above list may not be covered.

Students will be expected to read, write, and understand mathematical proofs.

See the course syllabus (PDF) for more detailed information on course format, evaluation, and expectations.