Mathematics

Professor Gareth Roberts (College of the Holy Cross) discusses how the connections between mathematics and music are numerous, deep, and fun to investigate. Early educational traditions (e.g., Plato and Boethius) grouped music with arithmetic and geometry. A “music first” approach will reveal hidden connections, encouraging a greater appreciation and desire for mathematical thinking. For example, many composers use transpositions, retrogrades, and inversions in their compositions to develop a short theme or motif into a longer, more intricate section of music.

Lauren Vollmer.’10 of the Mathematica Policy Research group will give a presentation in the STEM Alumni series on mathematical applications to public policy and discuss career opportunities in the field.

Tom Perera, one of the world’s leading experts on cipher machines, will present a talk on “The Real Story of ‘The Imitation Game’ and the Enigma of Alan Turing”. Dr. Perera is an emeritus professor of psychology at Columbia, Barnard and Montclair. The author of the book “Inside ENIGMA:The Secrets of the Enigma and other Historic Cipher Machines,” Dr. Perera is the founder of the Enigma Museum. He has been collecting, restoring, and preserving antique scientific cipher and telegraph instruments for more than six decades.

Kelsey will discuss Cayley Digraphs. Could you pass through every vertex in this graph exactly once? Could you then return to the starting point? Cayley digraphs are a fun way to visualize groups, and Hamiltonian paths and circuits are ways to navigate these digraphs. In this talk I will examine some Cayley digraphs and a few proofs on the existence on Hamiltonian paths and circuits.

The Department of Mathermatics presents a talk by Tom Perera on “Inside Enigma: The Story of the Enigma and Other Historic Cipher Machines”

Graham will discuss “Branching and Bounding Through the Knapsack Problem.” The classic Knapsack Problem asks how to choose among a set of items, each with a given weight and value, so that the total weight is less than or equal to a given capacity and the total value is as large as possible. This talk will contain an overview of some algorithms available that can help us intelligently enumerate a solution space for variations of the Knapsack Problem.

Library instruction for FYSE 1280 - “Breaking the Code: Alan Turing” Bryan Carson/ Mike Olinick

Caitlin will speak about “Rational Points on Elliptic Curves.” Elliptic curves are projective algebraic curves whose rational points have the unique property of forming an additive abelian group. We will build a basic understanding of elliptic curves including background on projective geometry and algebraic curves. We investigate the structure and function of the group law that allows us to move among the rational points on an elliptic curve.

Brenda will discuss “Extreme Value Theory: Tears, Earthquakes and Puppet Shows.” Extreme Value Theory (EVT) is a branch of probability and statistics concerned with the probability of rare events.  From biology and engineering, to information technology and finance, EVT is used in a variety of real-world applications.  She will examine the Fisher-Tippet-Gnedenko Theorem, exploring examples of the theorem in use and overview the Block Maxima method, a statistical approach used to apply EVT to sets of observed data.  She will use EVT and earthquake data collected between 1

“Markov Chain Monte Carol Methods”: MCMC methods offer a solution to simulating from intractable probability distributions. By constructing a positive recurrent Markov chain that converges to the desired probability distribution, this method allows us to sample from the distribution. We examine why MCMC works, and how long it takes to converge. We start by exploring the Strong Law of Large Numbers for Markov chains, which explains how a constructed Markov chain can allow resampling from the desired probability distribution.