Objectives

This course provides students with the basic terminology and tools used in a formal presentation and development of mathematical concepts and proofs. It provides a transition from more computational lower-division courses to the more conceptual activities found in most upper- division courses.

Topics

Mathematical reasoning, logic, sets, equivalence relations, one-to-one and onto functions, cardinality, mathematical induction, divisibility in the integers, the real number system (arithmetic, order, least upper bound axiom), sequences, limits.

Possible Texts

1. Schumacher, Chapter Zero: Fundamental Notions of Abstract Mathematics, Addison-Wesley, 1996.

2. Gerstein, Introduction to Mathematical Structure and Proof, Springer-Verlag, 1996.

Students develop computational skills in lower division mathematics courses, but often do not acquire the basic terminology and tools used in a formal presentation and development of mathematical concepts and proofs. These additional skills are needed for the more conceptual activities found in most upper division mathematics courses. Curricular efficiency is gained by organizing this material into a single course to be taken by students at a particular point in their studies.