# Exploring Mathematics

## Problem-Solving and Proof

• Daniel Grieser
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

1. Front Matter
Pages I-XXI
2. Daniel Grieser
Pages 23-39
3. Daniel Grieser
Pages 41-70
4. Daniel Grieser
Pages 71-81
5. Daniel Grieser
Pages 83-105
6. Daniel Grieser
Pages 107-137
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Pages 139-156
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Pages 157-179
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Pages 181-194
10. Daniel Grieser
Pages 195-217
11. Daniel Grieser
Pages 219-251
12. Daniel Grieser
Pages 253-280
13. Back Matter
Pages 281-320

### Introduction

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics.

Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book.

Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

### Keywords

MSC (2010): 00-01, 00A07, 00A09, 97D50 problem solving mathematical proofs mathematical problem solving mathematical exploration problem solving strategies mathematics extremal principle invariance principle pigeonhole principle counting principles mathematical induction logic proofs elementary number theory

#### Authors and affiliations

• Daniel Grieser
• 1
1. 1.Institut für MathematikCarl von Ossietzky Universität OldenburgOldenburgGermany

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