A list of fun talks that Mathematics and Computer Science faculty have prepared for undergraduate audiences.
- Anneke Bart (firstname.lastname@example.org), Associate Professor, Research Area: low-dimensional topology, geometric topology
- Mathematics in ancient Egypt
Abstract: Ancient Egyptian mathematics seems to have been more experimental than theoretical in nature. We have some knowledge of what was known through inscriptions and papyri. A survey of some egyptian mathematics will be given. The pyramids were developed through intermediate stages and there is some evidence of experimentation. Pharaoh Djoser had a step pyramid constructed, and this later developed into a true pyramimd. Snefru, the father of king Khufu (owner of the great pyramid at Giza), has several pyramids - the bent pyramid and the collapsed pyramid at Meidum - that show signs of experimentation. Inscriptions showing us something about the methods of constructing temples and tombs that were used. The stretching of the cord was a sacred ritual used in laying the foundation of a temple. Other inscriptions show some of the tools used in the construction of the egyptian monuments. We have ancient papyri that give us a glimpse of the knowledge the ancient egyptians may have had. The famous Rhynd (sometimes spelled Rhind) and Moscow papyri explain the arithmetic used as well as some problems from geometry familiar to the educated. This talk is accessible to undergraduates and strong high school students.
- Geometry and Art
Abstract: The graphical artist MC Escher used geometry to develop some of his patterns. Several of his prints show different types of wallpaper patterns. Escher also created artwork that demonstrates properties of Non-Euclidean geometry. We will discuss the methods used for creating wallpaper patterns and the non-euclidean works. If time permits works by other artists such as Dali, Picasso, Duchamp, etc will also be discussed. This talk is accessible to undergraduates and strong high school students.
- Bryan Clair (email@example.com), Associate Professor, Research Area: topology and graph theory
Abstract: Folding a map is always a challenge - maybe mathematics can help? From puzzles to permutations to open problems, folding has never been this much fun.
Abstract: Look at tic-tac-toe through a mathematicians eyes, and see that a simple game can lead to some interesting questions.
- How to eat as much pizza as possible
Abstract: Order some pizza, and observe how people select their slices. Of course, they want as much as possible. This turns into an abstract mathematical game with subtle strategy.
- Other Possible titles: Drilling Square Holes; Soap Bubbles; 100 Prisoners; How to win your football pool.
- Brody Johnson (firstname.lastname@example.org), Assistant Professor, Research Area: applied harmonic analysis
- The nonholonomy of the rolling sphere
Abstract: The goal of this talk is to provide a positive answer to the question: Given a pair of orientations for a sphere resting on a plane, is there a closed path along which one can roll the sphere (without slipping or twisting), starting with the first orientation, which ends with the sphere in the second orientation? The proof of this old result involves material from a standard course on differential equations.
- How good bowlers stay off the straight and narrow
Abstract: This lecture uses basic physics and differential equations to explain the curved trajectories of a bowling ball under spin.
- The hat problem
Abstract: This talk explores the subject of algebraic coding theory with the goal of solving the well circulated "hat problem" for 2n-1 players.
- David Letscher (email@example.com), Associate Professor, Research Area: geometric topology, normal surface theory
- Can you tell if a knot is knotted or not?
Abstract: Under construction.
- Strategies for sports betting pools
Abstract: Under construction.
- Julianne Rainbolt (firstname.lastname@example.org), Associate Professor, Research Area: group representation theory
- Mathematical fallacies
Abstract: We will prove several impossible facts such as an elephant weighs the same as a mouse, -1 is a positive number, and everyone in Saint Louis is the same age. Each of these proofs only uses facts from college algebra, calculus and/or an introductory proofs course. Come see if you can discover the mistakes in each argument.
- Kevin Scannell (kscanne "at" gmail "dot" com), Professor, Research Area: hyperbolic geometry, low-dimensional topology; computational linguistics
- What is the shape of the universe?
Abstract: We present some recent results that constrain the possible "shapes of space", under assumptions that only a mathematician could love: (1) the universe is closed and (2) the universe contains no mass or energy. Accessible to undergraduates and bright high-schoolers.
- Saving languages with statistics
Abstract: Well over half of the 7000 languages spoken in the world today are expected to die out before the year 2100. Learn how researchers in the field of Natural Language Processing are using statistics to develop resources that help revitalize endangered languages.
- Christine Stevens (email@example.com), Professor, Research Area: topological groups, history of mathematics
- Ham sandwiches and hairy coconuts - an algebraic topologist's feast
Abstract: Everyone knows how to make a ham sandwich: You put a piece of ham between two slices of bread, and you cut it in half. If the piece of ham and the slices of bread are square, then it's easy to cut the sandwich so that each half contains exactly half of the ham and exactly half of each slice of bread. But what if the ham and the bread aren't square, or even symmetrical? What if the ham is unevenly cut, one slice of bread is in the corner of the room, and the other slice is down the hall somewhere? Using just one swing of the knife, can you still cut the sandwich so that each half contains exactly half of the ham and exactly half of each slice of bread? The Ham Sandwich Theorem says that the answer is "yes." In the course of explaining why this is true, I'll discuss some concepts from the branch of mathematics that is called topology. (Level of talk: I will assume that the audience knows what the graph of a function is; familiarity with the idea of a continuous function is helpful, but not essential.)
- Math, college students, and opera
Abstract: For over forty years, Jerome Hines (1921-2003) was a major singer at the Metropolitan Opera in New York. He was also a math major who retained a lifelong interest in mathematics. He published six mathematical papers, including one that presents a method for approximating the solutions of equations that was based on work that he did as an undergraduate. After describing his method of approximation, I will explore the question of what mathematics meant to Hines and why, in the midst of a demanding musical career, he felt it important for him to develop and publish his mathematical ideas. (Level of talk: I will assume that the audience knows enough calculus to find derivatives; familiarity with Newton's method is helpful, but not essential.)
- Mathematical ways and congressional means
Abstract: Many of the issues that confront local, state, and national governments ranging from how to conduct a census to what to do with toxic waste have a significant mathematical and scientific component. Our success in dealing with these issues depends on our ability to integrate their technical and political aspects. How do Members of Congress - whose background is usually in law, not science - deal with issues like these? Drawing upon my own experience working in a Congressional office, I will offer an answer to this question. I will also explore the implications of that answer for society at large, but especially for students majoring in mathematics, science, and engineering. (Level of talk: This talk makes no explicit use of mathematics beyond arithmetic and percentages.)
- Mathematical inequalities, social inequities, and science education
Abstract: Everyone knows that more men than women go into careers in mathematics, science, and engineering. Somewhat less well known are the important consequences that this inequality in men's and women's participation in technical fields has for society as a whole. We will explore some of those consequences and discuss their implications for the future of science and engineering education. (Level of talk: This talk contains makes no explicit use of mathematics beyond an understanding of percentages.)