Set Theory and Logic

An excellent summary of basic set theory and logic can be found inChapter 1, Set Theory and Logic, in the following textbook :

"Topology, a first course.", James R. Munkres, Prentice-Hall, Inc., 1975

This textbook was used in an undergraduate course which I had the goodfortune of taking at my undergraduate college. It determined the courseof my career as a mathematician.

Munkres is an excellent author who is very thorough and clear in all ofhis expositions of mathematics. I highly recommend his textbooks.

A second edition of this textbook was published more recently:

"Topology, second edition.", James R. Munkres, Prentice-Hall, Inc., 2000

I particularly recommend reading the following sections of Chapter 1 ofeither edition of this textbook:

Chapter 1 Set Theory and Logic 1 Fundamental Concepts 2 Functions 3 Relations 4 The Integers and the Real Numbers 5 Cartesian Products 6 Finite Sets

The concepts discussed in these sections of Chapter 1 are thefoundations of mathematics. The later sections in Chapter 1 get into deeper issues related toinfinite sets (e.g. countability, well-ordering, etc..) These are alsopart of the foundations of mathematics, but we shall probably not haveoccasion to deal with them at any length in this class.