Topics in Algebra and Analysis: Preparing for the Mathematical Olympiad

ISBN-13: 9783319119458 / Angielski / Miękka / 2015 / 311 str.

Radmila Manfrino Bulajich

Opis

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.

Recenzje

"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)

Spis treści

​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.

O autorze

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.