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Birkhäuser - Birkhäuser Mathematics | Topics in Algebra and Analysis - Preparing for the Mathematical Olympiad

Topics in Algebra and Analysis

Preparing for the Mathematical Olympiad

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

2015, X, 307 p. 37 illus., 1 illus. in color.

A product of Birkhäuser Basel
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ISBN 978-3-319-11946-5

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  • 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

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.

Content Level » Lower undergraduate

Keywords » algebra - complex numbers - functional equations - polynomials - sequences

Related subjects » Birkhäuser Mathematics

Table of contents 

​1. Preliminaries.- 2 Progressions and finite sums.- 3 Induction principle.- 4 Quadratic and cubic polynomials.- 5 Complex numbers.- 6 Functions and functional equations.- 7 Sequences and series.- 8 Polynomials.- 9 Problems.- 10 Solutions of the exercises and problems.- Notation.- Bibliography.- Index.

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