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.
"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 Radulescu, 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)
