An Invitation to Abstract Mathematics /
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approach...
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2020.
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| Edition: | 2nd ed. 2020. |
| Series: | Undergraduate Texts in Mathematics,
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
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?
- A Ten Famous Conjectures.-B Ten Famous Theorems
- II The Foundations of Mathematics
- 5 Let's Be Logical!
- 6 Setting Examples
- 7 Quantifier Mechanics
- 8 Let's Be Functional!
- C The Foundations of Set Theory
- III How to Prove It
- 9 Universal Proofs
- 10 The Domino Theory
- 11 More Domino Games
- 12 Existential Proofs
- D Ten Famous Problems
- IV Advanced Math for Beginners
- 13 Mathematical Structures
- 14 Working in the Fields (and Other Structures)
- 15 Group Work
- 16 Good Relations
- 17 Order, Please!
- 18 Now That's the Limit!
- 19 Sizing It Up
- 20 Infinite Delights
- 21 Number Systems Systematically
- 22 Games Are Valuable!
- E Graphic Content
- F All Games Considered
- G A Top Forty List of Math Theorems.