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An Excursion through Elementary Mathematics, Volume III

Discrete Mathematics and Polynomial Algebra

  • Antonio Caminha Muniz Neto

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Antonio Caminha Muniz Neto
    Pages 1-32
  3. Antonio Caminha Muniz Neto
    Pages 33-66
  4. Antonio Caminha Muniz Neto
    Pages 67-93
  5. Antonio Caminha Muniz Neto
    Pages 95-123
  6. Antonio Caminha Muniz Neto
    Pages 125-156
  7. Antonio Caminha Muniz Neto
    Pages 157-191
  8. Antonio Caminha Muniz Neto
    Pages 193-207
  9. Antonio Caminha Muniz Neto
    Pages 209-220
  10. Antonio Caminha Muniz Neto
    Pages 221-242
  11. Antonio Caminha Muniz Neto
    Pages 243-268
  12. Antonio Caminha Muniz Neto
    Pages 269-281
  13. Antonio Caminha Muniz Neto
    Pages 283-315
  14. Antonio Caminha Muniz Neto
    Pages 317-345
  15. Antonio Caminha Muniz Neto
    Pages 347-361
  16. Antonio Caminha Muniz Neto
    Pages 363-394
  17. Antonio Caminha Muniz Neto
    Pages 395-416
  18. Antonio Caminha Muniz Neto
    Pages 417-433
  19. Antonio Caminha Muniz Neto
    Pages 435-450
  20. Antonio Caminha Muniz Neto
    Pages 451-476
  21. Antonio Caminha Muniz Neto
    Pages 477-503
  22. Antonio Caminha Muniz Neto
    Pages 505-527
  23. Antonio Caminha Muniz Neto
    Pages 529-634
  24. Back Matter
    Pages 635-648

About this book

Introduction

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more.

As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.

The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Keywords

Discrete mathematics Counting Polynomials Graph theory Problem solving Mathematics Olympiad IMO

Authors and affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77977-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77976-8
  • Online ISBN 978-3-319-77977-5
  • Series Print ISSN 0941-3502
  • Series Online ISSN 2197-8506
  • Buy this book on publisher's site
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