University of Toronto mathematics competition (2001-2015)

Description

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. Front Matter....Pages i-viii Problems of the Contests....Pages 1-22 Algebra....Pages 23-48 Inequalities....Pages 49-57 Sequences and Series....Pages 59-73 Calculus and its Applications....Pages 75-84 Other Topics in Analysis....Pages 85-106 Linear Algebra....Pages 107-132 Geometry....Pages 133-148 Group Theory....Pages 149-151 Combinatorics and Finite Mathematics....Pages 153-170 Number Theory....Pages 171-185 Back Matter....Pages 187-207