Math M114S: General Course Outline
M114S. Introduction to Set Theory. (Formerly numbered M112.) (Same as Philosophy M134.) Lecture, three hours; discussion, one hour. Prerequisite: course 110A or 131A or Philosophy 135. Axiomatic set theory as framework for mathematical concepts; relations and functions, numbers, cardinality, axiom of choice, transfinite numbers. P/NP or letter grading.
General Information Math 114S covers the basic facts about abstract sets, including the axiom of choice, transfinite recursion, and cardinal and ordinal arithmetic. It also makes a serious effort to explain how axiomatic set theory can be viewed as a "foundation of mathematics'' --- and, in particular, what this means.
Math 114S is especially useful for:
Undergraduate students who are preparing for graduate study in pure mathematics and graduate students in mathematics who have not had an opportunity to learn set theory in their undergraduate work. Real analysis, in particular, looks a lot more real if you know cardinal arithmetic and understand the meaning and uses of the axiom of choice.
Undergraduate students in mathematics or computer science who are preparing for graduate study in theoretical computer science, and CS graduate students who are veering towards theory and need to understand the mathematical justification of fixpoint theorems and the like.
Philosophy students with an interest in the philosophy of mathematics and a good mathematical background.
There is a strong tradition of research in logic --- especially set theory --- at UCLA, and both the Mathematics and Philosophy Departments offer a rich graduate program of study in the field.
Moschovakis, Y., Notes on Set Theory, 2nd Ed., Springer.