This text records the problems given for thefirst 15 annual undergraduate mathematics competitions, held in March each yearsince 2001 at the University of Toronto. Problems cover areas ofsingle-variable differential and integral calculus, linear algebra, advancedalgebra, analytic geometry, combinatorics, basic group theory, and numbertheory. The problems of the competitions are given in chronological order aspresented to the students. The solutions appear in subsequent chaptersaccording to subject matter. Appendices recall some background material andlist the names of students who did well.  

The University of TorontoUndergraduate Competition was founded to provide additional competition experience forundergraduates preparing for the Putnamcompetition, 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 intermediatedifficulty and relate to the first two years of the undergraduatecurriculum. The problems presented may beparticularly useful for regular class  assignments.Moreover, this text contains problems that lie outside the regular syllabus and may interest studentswho are eager to learn beyond the classroom.