An Invitation to Abstract Mathematics
This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2013, 2013
|
| Edition: | 1st ed. 2013 |
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface to Instructors
- Preface to Students
- Acknowledgments
- I What's Mathematics
- 1 Let's Play a Game!
- 2 What's the Name of the Game?
- 3 How to Make a Statement?- 4 What's True in Mathematics?
- 5 Famous Classical Theorems
- 6 Recent Progress in Mathematics
- II How to Solve It?
- 7 Let's be Logical!
- 8 Setting Examples
- 9 Quantifier Mechanics
- 10 Mathematical Structures
- 11 Working in the Fields (and Other Structures)
- 12 Universal Proofs
- 13 The Domino Effect
- 14 More Domino Games
- 15 Existential Proofs
- 16 A Cornucopia of Famous Problems
- III Advanced Math for Beginners
- 17 Good Relations
- 18 Order, Please!
- 19 Let's be Functional!
- 20 Now That's the Limit!
- 21 Sizing It Up
- 22 Infinite Delights
- 23 Number Systems Systematically
- 24 Games Are Valuable!
- IV. Appendices
- A. Famous Conjectures in Mathematics
- B The Foundations of Set Theory
- C All Games Considered
- D Top 40 List of Math Theorems. - Index