## University of Toronto Mathematics Competition (2001–2015)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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

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 |

### Other editions - View all

University of Toronto Mathematics Competition (2001–2015) Edward J. Barbeau No preview available - 2018 |

University of Toronto Mathematics Competition (2001–2015) Edward J. Barbeau No preview available - 2016 |

### Common terms and phrases

angle appears in Chap arctan assume bulb Cauchy–Schwarz Inequality circuit coefficients colour column convex coprime denote desired result follows Determine diagonal digits distinct divides E.J. Barbeau eigenvalues elements ellipse entries equal equation finite graph greatest common divisor Hence heptagon hyperbola induction inequality inner product space Intermediate Value Theorem International Publishing Switzerland invertible least least common multiple length Let f(a linear linearly independent Mathematics Competition 2001–2015 matrix modulo multiple nonnegative integer nonzero open interval pairs parabola permutation plane points polynomial positive integer exceeding problem appears Prove Publishing Switzerland 2016 rational rational function real numbers real-valued function defined roots segment sequence side ſº Solution square subsets Suppose supremum tangent teams Toronto Mathematics Competition triangle University of Toronto Value Theorem vanishes vector vertex vertices whence Wolog