Chapter Zero: Fundamental Notions of Abstract Mathematics is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help students as they develop their proof writing skills. This book is most successful in a small, seminar style class.
Features
1.NEW! Coverage of Isomorphisms and Graph Theory.
2.Exercise sections have been improved by smoothing out the grade of difficulty.
3.Proof Sketches. Woven throughout the early chapters of the text, these sketches assist students with proof techniques.
4.Logic is used as a tool for analyzing the content of mathematical assertions and for constructing valid mathematical proofs.
5.Rigorous axiomatic treatment of set theory is introduced in Appendices A and B (which are written in the same style as the text's chapters.)
About the Author
Professor of Mathematics
Kenyon College
Table of Contents:
Chapter 1. Logic
Chapter 2. Sets.
Chapter 3. Induction
Chapter 4. Relations
Chapter 5. Functions
Chapter 6. Elementary Number Theory
Chapter 7. Cardinality
Chapter 8. The Real Numbers
Appendix A. Axiomatic Set Theory
Appendix B. Constructing R
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