Exploring Mathematics Problem-Solving and Proof /

• Main Author: Grieser, Daniel (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Mathematics-Study and teaching .; Mathematics, general.; Mathematics Education.; Popular Science in Mathematics.

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 p...

Table of Contents:

• Introduction
• 1 First explorations
• 2 Recursion - a fundamental idea
• 3 Mathematical induction
• 4 Graphs
• 5 Counting
• 6 General problem solving strategies
• 7 Logic and proofs
• 8 Elementary number theory
• 9 The pigeonhole principle
• 10 The extremal principle
• 11 The invariance principle
• A A survey of problem-solving strategies
• B Basics on sets and maps
• List of symbols
• Glossary
• Lists of problems, theorems and methods
• Hints for selected exercises
• References.