Outline of Set Theory

A problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work on projects in groups and present their solutions to the class. With all necessary assistance from the instructor, students complete their weekly assignments, write short papers for their classmates, and lecture on their results. This method offers a deeper understanding of the material, as well as a clearer view of what it means to do mathematics. An Outline of Set Theory is organised into three parts: the first presents definitions and statements of problems, the second offers suggestions for their solutions, and the third contains complete solutions. Topics include standard undergraduate set theory, as well as considerations of nonstandard analysis, large cardinals, and Goodstein's theorem. Drawn from the author's practical experience as Professor of Mathematics at Smith College, this text offers a novel and effective approach to teaching and learning the fundamentals of set theory.