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  • Textbook
  • © 2015

Methods of Solving Nonstandard Problems

Birkhäuser
  • Ideal resource for students preparing for a mathematical competition or for those looking to improve their problem-solving abilities

  • Contains over 300 problems covering most important topics of elementary mathematics with hints, answers, and detailed solutions

  • Includes important and sometimes overlooked topics on functions, polynomials, and inequalities

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-19887-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 49.99
Price excludes VAT (USA)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xxi
  2. Solving Problems Using Properties of Functions

    • Ellina Grigorieva
    Pages 1-48
  3. Polynomials

    • Ellina Grigorieva
    Pages 49-158
  4. Problems from Trigonometry

    • Ellina Grigorieva
    Pages 159-238
  5. Unusual and Nonstandard Problems

    • Ellina Grigorieva
    Pages 239-322
  6. Back Matter

    Pages 323-327

About this book

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad.

Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, answers, and detailed solutions. 

Methods of Solving Nonstandard Problems will interest high school and college students, whether they are preparing for a math competition or looking to improve their mathematical skills, as well as anyone who enjoys an intellectual challenge and has a special love for mathematics.  Teachers and college professors will be able to use it as an extra resource in the classroom to augment a conventional course of instruction in order to stimulate abstract thinking and inspire original thought.

Keywords

  • Elementary Functions
  • Math Problem Solving
  • Mathematical Skills
  • Mathematics Competitions
  • Mathematics Olympiad

Reviews

“Students with an interest in problem-solving (particularly students who like to take Olympiad-style contests) will find suggestions, techniques and examples here that will serve them well. Students who are studying, or want to brush up on, basic algebra or trigonometry should also find material of interest here. Instructors of basic algebra, trigonometry, calculus, and even number theory or combinatorics may also find some interesting problems in this book to present to this class either in lecture or as homework.” (Mark Hunacek, MAA Reviews, maa.org, December, 2015)

Authors and Affiliations

  • Mathematics and Computer Science, Texas Woman's University, Denton, USA

    Ellina Grigorieva

About the author

Ellina Grigorieva, PhD, is Professor of Mathematics at Texas Women's University, Denton, TX, USA

Bibliographic Information

  • Book Title: Methods of Solving Nonstandard Problems

  • Authors: Ellina Grigorieva

  • DOI: https://doi.org/10.1007/978-3-319-19887-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-19886-6

  • Softcover ISBN: 978-3-319-36901-3

  • eBook ISBN: 978-3-319-19887-3

  • Edition Number: 1

  • Number of Pages: XXI, 327

  • Number of Illustrations: 9 b/w illustrations, 2 illustrations in colour

  • Topics: Algebra, Analysis, Geometry, Number Theory, Mathematics Education

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-19887-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 49.99
Price excludes VAT (USA)