Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (11 chapters)
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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.
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Bibliographic Information
Book Title: An Excursion through Elementary Mathematics, Volume I
Book Subtitle: Real Numbers and Functions
Authors: Antonio Caminha Muniz Neto
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-319-53871-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-53870-9Published: 10 April 2017
Softcover ISBN: 978-3-319-85261-4Published: 08 May 2018
eBook ISBN: 978-3-319-53871-6Published: 31 March 2017
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XIII, 652
Number of Illustrations: 73 b/w illustrations
Topics: Real Functions, General Algebraic Systems, Linear and Multilinear Algebras, Matrix Theory