University of Toronto Mathematics Competition (2001–2015)

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Springer, Apr 13, 2016 - Mathematics - 207 pages
This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory. The problems of the competitions are given in chronological order as presented to the students. The solutions appear in subsequent chapters according to subject matter. Appendices recall some background material and list the names of students who did well.

The University of Toronto Undergraduate Competition was founded to provide additional competition experience for undergraduates preparing for the Putnam competition, and is particularly useful for the freshman or sophomore undergraduate. Lecturers, instructors, and coaches for mathematics competitions will find this presentation useful. Many of the problems are of intermediate difficulty and relate to the first two years of the undergraduate curriculum. The problems presented may be particularly useful for regular class assignments. Moreover, this text contains problems that lie outside the regular syllabus and may interest students who are eager to learn beyond the classroom.

 

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Contents

Chapter 1 Problems of the Contests
ix
Chapter 2 Algebra
23
Chapter 3 Inequalities
49
Chapter 4 Sequences and Series
59
Chapter 5 Calculus and its Applications
74
Chapter 6 Other Topics in Analysis
85
Chapter 7 Linear Algebra
107
Chapter 8 Geometry
133
Chapter 9 Group Theory
149
Chapter 10 Combinatorics and Finite Mathematics
153
Chapter 11 Number Theory
171
Appendix A Definitions Conventions Notation and Basics
186
Appendix B Top Ranking Students
201
Index
204
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About the author (2016)

Ed Barbeau is professor emeritus at the University of Toronto. Dr. Barbeau is a life member of the MAA, the AMS, and the CMS, and has served all three societies on various committees, particularly having to do with mathematics education. He has published a number of books directed to students of mathematics and their teachers, including "Polynomials" (Springer), "Pell's Equation" (Springer). Ed Barbeau has frequently given talks and workshops at professional meetings and in schools, has worked with high school students preparing for Olympiad competitions and has on five occasions accompanied the Canadian team to the International Mathematical Olympiad. He is currently associate editor in charge of the Fallacies, Flaws and Flimflam column in the College Mathematics Journal and education editor for the Notes of the Canadian Mathematical Society. He is a former chairman of the Education Committee of the Canadian Mathematical Society. Honors include the Fellowship of the Ontario Institute for Studies in Education, the David Hilbert Award from the World Federation of National Mathematics Competitions and the Adrien Pouliot Award from the Canadian Mathematical Society.

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