Robert Toft. Aural Images of Lost Traditions: Sharps and Flats in the Sixteenth Century. Toronto: University of Toronto Press, 1992. viii, 199 pp. ISBN 0-8020-5929-5

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION In Memory of Robert Barrington Leigh

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION In Memory of Robert Barrington Leigh

6. Two competitors play badminton. They play two games, each winning one of them. They then play a third game to determine the overall winner of the match. The winner of a game of badminton is the first player to score at least 21 points with a lead of at least 2 points over the other player. In this particular match, it is observed that the scores of each player listed in order of the games fo...

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION In Memory of Robert Barrington Leigh

1. Determine the supremum and the infimum of (x− 1)x−1xx (x− (1/2))2x−1 for x > 1. 2. Let n and k be integers with n ≥ 0 and k ≥ 1. Let x0, x1, · · ·, xn be n+1 distinct points in R and let y0, y1, · · ·, yn be n + 1 real numbers (not necessarily distinct). Prove that there exists a polynomial p of degree at most n in the coordinates of x with respect to the standard basis for which p(xi) = yi ...

Programming in Haskell by Graham Hutton, Cambridge University Press, 2007, 184 pp., ISBN 0-521-69269-5

The proposed solution runs entirely against the orthodoxy that compositionality is necessary for modularity, but it is persausive. Much to their credit, the authors have robustly defended this view and others in several online forums, and have shown they are prepared to accept and develop viewpoints distinct from their own. In closing, I must ask the inevitable rhetorical questions: would CTM h...

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION In Memory of Robert Barrington Leigh

7. Let G be a group of finite order and identity e. Suppose that φ is an automorphism of G onto itself with the following properties: (1) φ(x) = x if and only if x = e; (2) φ(φ(x)) = x for each element x of G. (The mapping φ has the property that it is one-one onto and that φ(xy) = φ(x)φ(y) for each pair x, y of elements of G.) (a) Give an example of a group and automorphism for which these con...