University of Toronto Mathematics Competition (2001–2015)

1. Front Matter

   Pages i-viii

   PDF

2. Problems of the Contests

   • Edward J. Barbeau

   Pages 1-22

3. Algebra

   • Edward J. Barbeau

   Pages 23-48

4. Inequalities

   • Edward J. Barbeau

   Pages 49-57

5. Sequences and Series

   • Edward J. Barbeau

   Pages 59-73

6. Calculus and its Applications

   • Edward J. Barbeau

   Pages 75-84

7. Other Topics in Analysis

   • Edward J. Barbeau

   Pages 85-106

8. Linear Algebra

   • Edward J. Barbeau

   Pages 107-132

9. Geometry

   • Edward J. Barbeau

   Pages 133-148

10. Group Theory

    • Edward J. Barbeau

    Pages 149-151

11. Combinatorics and Finite Mathematics

    • Edward J. Barbeau

    Pages 153-170

12. Number Theory

    • Edward J. Barbeau

    Pages 171-185

13. Back Matter

    Pages 187-207

    PDF

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.

• Putnam competition preparation
• Toronto math competition
• undergraduate problems mathematics
• university mathematics competition
• single-variable calculus
• linear algebra
• advanced algebra
• analytic geometry
• combinatorics
• fundamental group theory
• differential equations
• ordinary differential equations

“The book under review is mainly intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay among applied analysis, mathematical physics, and numerical analysis.” (Teodora-Liliana Rădulescu, zbMATH 1357.97001, 2017)

“This book is the compilation of the problems from those competitions from 2001 to 2015, along with their solutions, an appendix of notation and key results, and an appendix listing the top ranking students. … This books seems most useful as a supplementary resource for a problem solving or Putnam prep group, class, or math club.” (Megan Patnott, MAA Reviews, maa.org, August, 2016)

• University of Toronto, Toronto, Canada

  Edward J. Barbeau

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 Institutefor 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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