Chases and Escapes: Virtue or Vertigo for the Lady in the Lake?
The ideas of pursuit and evasion pervade much of human existence and as a result have always been a huge part of human entertainment – it has been said that half of all fictional writing boils down to a single conflict between the hunter and the hunted. But more than just recreational, the study of chases and escapes is also mathematically interesting and has applications to computer science, surveillance, traffic control, and military strategy. After learning some fundamental concepts from game theory, we will discuss the classic pursuit-evasion problem, “The Lady in the Lake,” in which a woman finds herself in a rowboat in the middle of a circular lake while a pursuer waits for her along the shore. If the pursuer runs at four times the woman’s rowing speed, can the woman reach a spot on the shore before her purser does? We will uncover the woman’s optimal escape strategy in order to answer this question and much further, find the minimum speed relative to her pursuer’s that the woman must row to evade capture.
Everyone has heard about the number π, everyone who has taken calculus has heard
about the number e, but there’s a third important number in mathematics that fewer
people have heard about: γ (called gamma, or Euler’s constant). This number, whose
decimal expansion starts out as 0.5772156…, was discovered nearly three centuries
ago when Euler was investigating properties of the harmonic numbers
Hn=1+1/2+1/3+⋯+1/n. Despite its age, many basic questions about γ remain unsolved.
We will discuss the history of γ, how it can be computed, its connections to
different areas of mathematics, and a long-standing open question about its
“Before You Analyze, Know Y”
Michael Lavine, Professor and Department Head, Department of Mathematics and Statistics, will discuss why choosing a statistical analysis or statistical model without seeing the data is dangerous. He will present a few examples from linguistics, public policy, biology, and ecology that illustrate why.
Due to the weather, this talk has been cancelled.
Please join us for Math Club this Wednesday, 5:30-6:30 in LGRT 1528. This week, Professor Bill Meeks will speak on, “From soap films to minimal surfaces” (abstract below). As always, pizza and soda will be provided.
Title: From soap films to minimal surfaces
Abstract: I will present some basic minimization problems in the calculus
of variations. A key problem in this subject is the classical Plateau
problem that asks: Given a simple closed curve in three-space, is it the
boundary of a surface of least area? I will also discuss related problems
such as the Kelvin problem for minimizing perimeter in dimension 3 and
Fermat’s problem of constructing roads of least pavement that connect
three cities in a planar map. However, the focus of my talk will be on
Plateau’s problem and how it is related to the existence of soap films on
a closed wire contour. As an important aside, I will attempt to explain
how this problem leads to the mathematical theory of what are called
minimal surfaces and to applications like the solution of the Positive
Mass Conjecture in the theory of relativity. The talk will be visual with
many colorful slides that illustrate the concepts in nature and in real