MIT Women in Mathematics Lecture Series

Organizers: Mia Minnes, Gigliola Staffilani, Katrin Wehrheim

This lecture series is intended for an advanced undergraduate or beginning graduate student audience. The talks will begin in the late afternoon, usually at 5:30pm. There will be pizza available after each talk.

Mathematicians of all levels, areas, and genders are welcome!

The solicitation for applications and suggestions for lecture series speakers is here.
The "MIT: Women in Math, a Celebration" conference website is now located here.
For titles and abstracts from the 2008-2009 lecture series, visit the archive.

Wednesday September 16, 2009 5:30pm-6:30pm 2-135
Johanna Franklin (Fields Institute)
Defining Randomness.

What does it mean for an infinite binary sequence to be random? What does it mean for an infinite binary sequence to be nowhere near random? I will present three different approaches to defining randomness, show how they can be made to be equivalent, and describe some of the other properties that random binary sequences can have. Then I will present ways in which a real can be said to be "far from random," discuss whether or not these definitions are equivalent, and explore some of the other properties of these binary sequences.

Prerequisites for the talk: None.

Pizza after the talk.

Thursday October 22nd, 2009 5:30pm-6:30pm 2-135
Julia Wolf (Rutgers University)
What the Fourier transform can and cannot tell us about the integers.

It is surprisingly straightforward to count the number of solutions to simple equations such as x+y=2z (representing a 3-term arithmetic progression) or x-y=z2 (a square difference) in a "random-looking" subset of the integers. The discrete Fourier transform provides a natural way of quantifying what we mean by random-looking, but fails us once we start to consider longer arithmetic progressions and other more intricate structures. This failure opens the door to a rich and as yet largely unexplored theory of higher-degree Fourier analysis, which we shall try and catch a glimpse of in this talk.

Prerequisites for the talk: modular arithmetic, roots of unity and the Cauchy-Schwarz inequality; some familiarity with the Fourier transform is desirable but not essential.

Pizza after the talk.

Monday October 26th 5:30pm-6:30pm 4-145
Valentina Harizanov (George Washington University)
Priority methods.

In computable mathematics the existence of certain objects is often demonstrated by actually building them. We will present an example of a construction which will in a very simple setting illustrate the main ideas and give the flavor of a computability theoretic technique called the finite injury priority method. This method, which was invented in the 1950's and revolutionized computability theory, represents the first level in the hierarchy of priority methods. This intricate and powerful technique allows us to satisfy mutually conflicting requirements by fitting together opposite strategies.

Prerequisites for the talk: none

Pizza after the talk.

SPECIAL PRESENTATION

Wednesday December 2nd 5:30pm-6:30pm 2-135
Debra Borkovitz (Wheelock College )
Elementary Math is Not Elementary! Thoughts on Preparing Teachers.

For many years, it was commonly believed in the U.S. that future elementary school teachers learned all the math content they needed to know by the end of high school. Now it is widely recognized that for teachers to take school mathematics beyond calculation without understanding, they need to develop a much deeper understanding of elementary mathematics. There is a specialized body of math content knowledge for elementary teaching, just as there are such bodies of knowledge for engineering and other professions (and even people with Ph.D's in math have not necessarily mastered this math content).

In this talk we will look at some not so elementary examples of K-8 math to get a sense of some of the deeper issues involved for both elementary teachers and for those who prepare them. We will also look at some efforts to improve mathematics education in Massachusetts and beyond. I will also share a bit of my own path from a PhD in math from MIT to working primarily with future elementary teachers.

The talk will be participatory, so come prepared to think, to share experiences, and to take a fresh look at third-grade math.

Prerequisites for the talk: none

Pizza after the talk.