An Excursion through Elementary Mathematics, Volume I

Real Numbers and Functions

  • Antonio Caminha Muniz Neto

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Antonio Caminha Muniz Neto
    Pages 1-18
  3. Antonio Caminha Muniz Neto
    Pages 19-59
  4. Antonio Caminha Muniz Neto
    Pages 61-86
  5. Antonio Caminha Muniz Neto
    Pages 87-110
  6. Antonio Caminha Muniz Neto
    Pages 111-141
  7. Antonio Caminha Muniz Neto
    Pages 143-200
  8. Antonio Caminha Muniz Neto
    Pages 201-244
  9. Antonio Caminha Muniz Neto
    Pages 245-273
  10. Antonio Caminha Muniz Neto
    Pages 275-345
  11. Antonio Caminha Muniz Neto
    Pages 347-445
  12. Antonio Caminha Muniz Neto
    Pages 447-510
  13. Back Matter
    Pages 511-652

About this book


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 first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, 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.


Functions Real numbers Real functions Elementary algebra Problem solving Mathematics Olympiad IMO

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-53870-9
  • Online ISBN 978-3-319-53871-6
  • Series Print ISSN 0941-3502
  • Series Online ISSN 2197-8506
  • Buy this book on publisher's site
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