Basic Notions Seminar

Basic Notions Seminar

Welcome to the Basic Notions Seminar web-page! The seminar meets either on tuesdays from 2:15 to 3:15 and wednesdays from 1:30 to 2:30 in Wilson 405. Students or professors (from wsc or other colleges) will give interesting, fun, mathematical, interactive talks and of course there will be cookies :) So please come join us! The talks should be accessible for anyone interested in math.

1) Tuesday September 18 Volker Ecke, WSC: Origami Math Can you take a piece of paper and fold it in half? Easy, you say. OK. How about folding it into equal thirds? Can we tri-sect an arbitrary angle by folding? While we may commonly think of straightedge and compass when considering geometric constructions, Origami paper folding is another powerful way to explore geometry in two and three dimensions that is both beautiful, illuminating and tangible. Together, we will explore some Origami math in two and three dimensions. (Paper provided.)

2) Wednesday September 26 Molly Fenn, UMass Amherst: The Four Color Theorem and the Platonic Solids: An Introduction to Graph Theory Two problems with very interesting histories will be explored. The first states that when coloring a map so that adjacent regions have different colors, one needs at most 4 colors. The second has to do with regular polyhedra, 3 dimensional shapes that have congruent faces. The ancient Greeks showed that there are only 5 such objects, we will find all 5 and prove that there aren't any more. Both of these problems have to do with graph theory, a branch of math that requires very little introduction to begin working on lots of cool problems.

4) Wednesday October 10 Larry Griffith, Computer Science, WSC: Graph Theory Mathematics is a deeply interconnected subject. In this talk, I'll use some algebra (permutation groups) to shed light on an unsolved problem in topology: efficiently finding if a graph has a Hamiltonian circuit.

5) Wednesday October 17 Jessica Sidman, Mount Holyoke College: Geometry and the complexity of computation Algebraic geometers study curves, surfaces, and higher dimensional objects that are defined implicitly by systems of polynomial equations. Manipulating polynomial equations on a computer can reveal interesting geometric properties of their solution sets. The Mayr-Meyer examples show that such computations can be very costly in general. However, in nice geometric situations, computations are often quite manageable. Recent work shows that the complexity of computing lexicographically with a curve in generic coordinates is governed by the singularities of a generic projection. I will discuss joint work with Aldo Conca treating a special case of this phenomenon and remark upon the general situation.

6) Wednesday October 24 Joe Axenroth, WSC: The history of Logic In some various courses taken as either a Computer Science or Mathematics major as WSC, part (or all) of this course lies over a foundation of Boolean Algebra as a means to learn about logic. Due to the scope of these courses, however, we never really get to see its historical start. In 1854, George Boole published "An Investigation of the Laws of Thought" which sought "to investigate the fundamental laws of those operations of the mind by which reasoning is performed." This talk discusses chapters two and three of his work.

8) Friday November 16, 1:45 - 2:30 in Wilson 411 Christine von Renesse, Volker Ecke and Judah Hughes, WSC Mathematics in the public school system We will be discussing topics such as: What kind of teachers do we want to be? What do we believe is good teaching? What will your first day of teaching your own class look like? Ask Judah about what he thinks you really need to learn to be a good teacher. The MTEL and the MCAS Why is there a large turnover among teachers? What if a student asks me something and I don't know the answer? How can you get your students to become confident math thinkers? Any other questions you have!