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Problem Books in Mathematics

An Excursion through Elementary Mathematics, Volume I

Real Numbers and Functions

Authors: Caminha Muniz Neto, Antonio

  • Combines an in-depth overview of the theory with problems presented at several Mathematical Olympiads around the world.
    Offers a comprehensive course on problem-solving techniques
    Presents a coherent development of mathematical ideas and methods behind problem solving
    Brings several classical, relevant results of various fields in mathematics

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-53871-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-53870-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Antonio Caminha M. Neto received his PhD from the Federal University of Ceará, Brazil in 2004. In the same year he joined the University as a Professor of Mathematics, where he is now a member of the Differential Geometry Research Group. The author of several research papers, Caminha is distinguished by a CNPq Research Grant on Differential Geometry. He is also an Affiliate Member of the Brazilian Academy of Sciences. Prior to his academic career, Caminha was himself an Olympic competitor, who has placed 4th in the 1990 Brazilian Mathematical Olympiad. Subsequently, as a high school teacher in the 1990s, he coached Brazilian students in preparation for various mathematical competitions, from regional meets to the Iberoamerican Mathematical Olympiad and the International Mathematical Olympiad, where several of them were medalists. He was also a Leader of the Brazilian Team at the 1996 and 1999 South Cone Mathematical Olympiad, and Deputy Leader of the Brazilian Team at the 1995 and 2001 International Mathematical Olympiads. In 2012, Caminha published a six-volume book collection entitled Topics in Elementary Mathematics with the Brazilian Mathematical Society, which gave rise to this book.

Reviews

“This book develops several basic concepts in elementary mathematics and which are needed in the preparation of mathematical Olympiads around the world. … Throughout the book, the author puts great emphasis on explaining the issues discussed. … The presentation is pedagogical and coherent throughout with emphasis on concepts and underlying ideas … . The author has succeeded in crafting a comprehensive book to give a well-rounded picture of the role of real numbers and functions in elementary mathematics.” (Teodora Liliana Rădulescu, zbMATH 1371.97002, 2017)


Table of contents (11 chapters)

  • The Set of Real Numbers

    Caminha Muniz Neto, Antonio

    Pages 1-18

  • Algebraic Identities, Equations and Systems

    Caminha Muniz Neto, Antonio

    Pages 19-59

  • Elementary Sequences

    Caminha Muniz Neto, Antonio

    Pages 61-86

  • Induction and the Binomial Formula

    Caminha Muniz Neto, Antonio

    Pages 87-110

  • Elementary Inequalities

    Caminha Muniz Neto, Antonio

    Pages 111-141

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-53871-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-53870-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Excursion through Elementary Mathematics, Volume I
Book Subtitle
Real Numbers and Functions
Authors
Series Title
Problem Books in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-53871-6
DOI
10.1007/978-3-319-53871-6
Hardcover ISBN
978-3-319-53870-9
Series ISSN
0941-3502
Edition Number
1
Number of Pages
XIII, 652
Number of Illustrations and Tables
73 b/w illustrations
Topics