Topics in Algebra and Analysis

Preparing for the Mathematical Olympiad

Authors: Bulajich Manfrino, Radmila, Gómez Ortega, José Antonio, Valdez Delgado, Rogelio

  • Illustrates mathematical Olympiad topics with exercises
  • Explains the theory of algebra and analysis as used in mathematical contests
  • Provides key observation on how to attack functional equations
  • Presents interesting ways to tackle known problems such as double counting arguments to find sums of natural numbers
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eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-11946-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-319-11945-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world.

In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in recent years, and solutions to all exercises and problems presented in the book.

It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university. It will be of interest to teachers in college and university level, and trainers of the mathematical Olympiads.

About the authors

Radmila Bulajich Manfrino and Rogelio Valdez Delgado are professors at the Universidad Autónoma de Mexico in Cuernavaca, Mexico, and José Antonio Gómez Ortega is professor at the Universidad Nacional Autónoma de México in Mexico City. They are the co-authors of the previously published Birkhäuser book: Inequalities - A Mathematical Olympiad Approach.

Reviews

“The subtitle of this book is ‘Preparing for the Mathematical Olympiad’, and its value lies in the wealth of examples and exercises (with solutions). … it came across as enjoyable and hard to put down, surely the best of all reasons for anyone, whether student, teacher or mathematics aficionado, to find a copy. … I can well imagine an inquisitive pupil being drawn in and fired up by some of the cleverly constructed problems and solutions.” (Stephen Rout, The Mathematical Gazette, Vol. 100 (547), 2016)

“A very enjoyable collection of high school mathematics competition problems in algebra and analysis, the level of which ranges from local contests to the International Mathematical Olympiads. … The book is extremely useful for high school students preparing for competitions. … Essential for libraries used by high school students. Summing Up: Highly recommended. Lower-division undergraduates through researchers/faculty.” (M. Bona, Choice, Vol. 53 (2), October, 2015)


Table of contents (10 chapters)

  • Preliminaries

    Manfrino, Radmila Bulajich (et al.)

    Pages 1-29

  • Progressions and Finite Sums

    Manfrino, Radmila Bulajich (et al.)

    Pages 31-42

  • Induction Principle

    Manfrino, Radmila Bulajich (et al.)

    Pages 43-62

  • Quadratic and Cubic Polynomials

    Manfrino, Radmila Bulajich (et al.)

    Pages 63-74

  • Complex Numbers

    Manfrino, Radmila Bulajich (et al.)

    Pages 75-88

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-11946-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-319-11945-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Algebra and Analysis
Book Subtitle
Preparing for the Mathematical Olympiad
Authors
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-11946-5
DOI
10.1007/978-3-319-11946-5
Softcover ISBN
978-3-319-11945-8
Edition Number
1
Number of Pages
IX, 311
Number of Illustrations and Tables
39 b/w illustrations, 1 illustrations in colour
Topics