Topics in algebra and analysis : preparing for the Mathematical Olympiad
著者
書誌事項
Topics in algebra and analysis : preparing for the Mathematical Olympiad
Birkhäuser, c2015
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注記
Includes bibliography (p. 307-308) and index
内容説明・目次
内容説明
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.
目次
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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