Chapter Zero: Fundamental Notions of Abstract Mathematics

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Chapter Zero 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.

Author(s): Carol Schumacher
Series: Featured Titles for Transition to Advanced Mathematics
Edition: 2
Publisher: Pearson
Year: 2000

Language: English
Pages: 256
City: Boston

Chapter Zero : Fundamental Notions of Abstract Mathematics
Title Page
Copyright
Preface
A Note to the Student: What This Book Expects from You
Contents
0 Introduction-An Essay
1 Logic
2 Sets
3 Induction
4 Relations
5 Functions
6 Elementary Number Theory
7 Cardinality
8 The Real Numbers
Appendix A Axiomatic Set Theory
Appendix B Constructing R
Index