Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Math Club

Math Club - Francesco Cellarosi (Queen's University)

Thursday, April 4th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Francesco Cellarosi (Queen's University)

Title: The irrationality of $\zeta(3)$.

Abstract:  This talk will discuss the famous theorem by R. Apéry who showed in 1978 that $\zeta(3)$ is irrational.
We will see a proof of this fact, due to F. Beuker in 1979, which only uses calculus.

Math Club - Ivan Dimitrov (Queen's University)

Thursday, March 21st, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Ivan Dimitrov (Queen's University)

Title: Why 0.499999999992646 does not equal 12.

Abstract:  We will see why

  • $\int_{0}^\infty \frac{\sin x}{x} \,dx = \pi/2,$
  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3}\, dx = \pi/2, $

… and so on all the way to

  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13}\, dx = \pi/2, $

However,

  • $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13} \cdot \frac{\sin x/15}{x/15} \,dx < \pi/2, $

Math Club - Richard Gottesman (Queen's University)

Thursday, March 14th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Richard Gottesman (Queen's University)

Title: Gaussian Integers and Sums of Two Squares.

Abstract:  The Gaussian integers consist of the set of all complex numbers whose real and imaginary parts are both integers. We begin by exploring the number theory of the Gaussian integers. For example, we shall see why $3$ is a Gaussian prime but $5 = (2 +i)(2 - i)$ is not.

We will then show how to use the Gaussian integers to prove that if $p$ is a prime number which is one more than a multiple of $4$ then $p$ is a sum of two perfect squares. This proof is very striking and it generalizes to other number systems, such as the Hurwitz quaternions.

In honor of $\pi$ day, we must also mention that $\pi$ is equal to the average number of ways to write an integer as a sum of two squares.

Math Club - Neha Prabhu (Queen's University)

Thursday, February 28th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Neha Prabhu (Queen's University)

Title: The one-sentence proof.

Abstract:  Which primes can be written as a sum of two squares? The answer to this classical question has been known for centuries and many different elaborate proofs have been discovered. In this talk, we present Don Zagier's sensational "one-sentence" proof.

Math Club - Ram Murty (Queen's University)

Thursday, February 14th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Ram Murty (Queen's University)

Title: The Basel Problem.

Abstract:  In 1650, Pietro Mengoli posed the problem of explicitly evaluating $$1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots $$ and this had come to be known as the Basel problem. The solution is $\pi^2/6$ and it was discovered by Euler almost a century later in 1734, when Euler was 28 years old.

Euler's proof, though correct, was far from rigorous and had to await further developments in complex analysis to put it on a sure footing. We will give a slick proof that uses only ideas from first year calculus.

Math Club - Emine Yildirim (Queen's University)

Thursday, February 7th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Emine Yildirim (Queen's University)

Title: Cluster Algebras.

Abstract:  We will talk about how a fundamental, simple, and old mathematical notion from the 2nd Century called the “Ptolemy relation” reappears in modern mathematics.

Cluster combinatorics is a very interesting, powerful, and one might even say miraculous technical tool studied in many different areas of mathematics, and even discovered in some areas of physics.

For this talk, we will only focus on cluster combinatorics coming from triangulations of polygons.

Math Club - Peter Taylor (Queen's University)

Thursday, January 31st, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Peter Taylor (Queen's University)

Title: Is Bacon Shakespeare?

Abstract: We will look at a sampling of the cryptographic "proofs" that have been put forward for Francis Bacon's authorship of Shakespeare's plays, and then analyze these using Claude Shannon's fundamental ideas based on the information content of the English language.

Math Club - Mike Roth (Queen's University)

Thursday, January 24th, 2019

Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker: Mike Roth (Queen's University)

Title: The primes from analysis.

Abstract: The prime numbers are the multiplicative building blocks of the integers, and as such appear to be creatures of algebra. This talk will explain a way in which the prime numbers arise naturally out of a question in analysis.

Math Club - Jamie Mingo (Queen's University)

Thursday, March 29th, 2018

Time: 5:30 p.m.  Place: Jeffery Hall 118

Speaker: Jamie Mingo (Queen's University)

Title: Paradoxical Probabilities.

Abstract: Since the early days of probability theory there have been paradoxical statements, usually the result of implicit assumptions. The best known example is the Monty Hall problem. In this talk I discuss several examples, in particular the "bigger number paradox".

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