Table of contents

  1. Front Matter
    Pages i-xiii
  2. Mark Joshi
    Pages 1-9
  3. Mark Joshi
    Pages 11-17
  4. Mark Joshi
    Pages 19-23
  5. Mark Joshi
    Pages 25-31
  6. Mark Joshi
    Pages 33-41
  7. Mark Joshi
    Pages 43-51
  8. Mark Joshi
    Pages 53-64
  9. Mark Joshi
    Pages 73-80
  10. Mark Joshi
    Pages 81-95
  11. Mark Joshi
    Pages 97-103
  12. Mark Joshi
    Pages 105-108
  13. Mark Joshi
    Pages 109-118
  14. Mark Joshi
    Pages 137-141
  15. Mark Joshi
    Pages 143-145
  16. Mark Joshi
    Pages 147-150
  17. Mark Joshi
    Pages 151-172

About this book

Introduction

This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity.

The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Keywords

Combinatorics Euclidean Geometry Game Theory Mathematics Education Patterns Proof Pure Mathematics

Authors and affiliations

  • Mark Joshi
    • 1
  1. 1.Centre for Actuarial StudiesUniversity of MelbourneMelbourneAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16250-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16249-2
  • Online ISBN 978-3-319-16250-8
  • About this book
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