# GAUSS (Graduate and Undergraduate Students Seminar)

## Upcoming Seminars for Fall Semester

Unless otherwise noted, the Fall Semester GAUSS talks will be on Fridays at 4:00PM in S2 308.

**October 24, 2014; 4:00PM in S2 308**: Samuel Macneil (Fresno State student)**Title: How to Guard a Museum**

**Abstract:** Suppose the manager of a museum wants to make sure that at all times every point of the museum is watched by a guard. The guards are stationed at fixed posts, but they are able to turn around. How many guards are needed? The art gallery theorem gives us a maximum number of guards required for an n-walled convex polygon.

In this talk, we will go over the proof of this theorem as detailed in Proofs from The Book, by Aigner and Ziegler, as well as some variants of the art gallery problem.

**October 24, 2014; 4:30PM in S2 308**: Kelsey Friesen, Simerjit Kaur, and Thoa Tran (Fresno State students)

**Title: Exploring the Fibonacci Numbers**

**Abstract:** The Fibonacci numbers can be used to model or describe a variety of phenomena in mathematics, art, and nature, even the human body!

In this talk, we will go over some history of the Fibonacci numbers and where in the real world they pop up. As funny as it sounds, we’ll start off by discussing how Leonardo of Pisa (who nicknamed himself Fibonacci) related these numbers to the reproduction of rabbits . Another application of the numbers is to use them to create beautiful equiangular spirals.

We will wrap up exploring the Fibonacci numbers by investigating how they are related to the “golden ratio”, the ratio deemed most aesthetically pleasing to the human eye when used in architecture and art.

**October 31, 2014; 4:00PM in S2 308**: Marat Markin (Fresno State)

**Title: Free AC check: The Axiom of Choice, its equivalents, and applications**

**Abstract:** The Axiom of Choice (AC), formulated by Ernst Zermelo in 1904 and considered controversial for a few decades after that, is now a basic assumption used in many parts of mathematics. A vast number of important mathematical results require AC for their proofs.

In this talk, we are going to formulate AC and its equivalents and see how it can be applied to proving the existence of a basis in any vector space and a set of real numbers that is not Lebesgue measurable.

Consider our discussion a "free AC check" making no pretense to be an in-depth treatment of such a fundamental principle of mathematics.

**If you need a disability-related accommodation or wheelchair access information, please contact the Mathematics Department at 559.278.2992 or e-mail** math.office@csufresno.edu. **Requests should be made at least one week in advance of the event.**