Polynomials like \(x^4 + y^4\), which don't change when we exchange the variables, are called symmetric. We will show how a small number of basic symmetric polynomials (like \(x + y\) and \(xy\)) can be used to describe all possible symmetric polynomials. As an application, we will see how to generalize the discriminant \(b^2 - 4ac\) of a quadratic polynomial to higher-degree polynomials.


Note: Free refreshments. The talk starts at 5:45.

Game theory is the study of strategic interactions. The fate of every person in a "game" will usually depend on the decisions of all "players". Nash Equilibrium, developed by Nobel Prize Winner John Forbes Nash, says that in any finite game with a finite number of players, each player has a "best response", or best strategy, for that player to win the game. This week, together we will explore many different types of games, discuss possible strategies, and try some problems to help you start thinking about these interactions like a game theorist.

Note: Cookies will be provided.

The probabilistic method is a technique for showing a mathematical object exists by considering a construction like it at random and showing the random construction has a positive probability of being the type of object you seek. The positive probability tells us the object has to exist, because if it did not exist then it could not have a positive probability of occurring. Examples of the probabilistic method will be shown from combinatorics and geometry.


Note: Free refreshments. The talk starts at 5:45.

The famed mathematician Gauss allegedly once said "Mathematics is the queen of the sciences and number theory is the queen of mathematics."

Number theory is a branch of mathematics that deals primarily with the integers. Many problems in number theory are easy to state, yet have solutions that require deeper concepts with rich connections to other branches of mathematics. This week, together we will solve some problems in number theory. We will also play a number theory version of "Simon Says'' and learn about open problems in the field.

All are welcome. Problems of varying levels, as well as cookies, will be provided.

What do coloring, polynomials and some cancer treatments have in common? They are all related to knots! In this talk, we will introduce the mathematical subject of Knot Theory. We will see how to use simple techniques like counting and coloring to tell some knots and links apart. This doesn't always give us enough information, however. We will also learn how to find special polynomials from knot diagrams and what these polynomials can tell us about the knots. We will touch on some knot history and current applications of knot theory.

This talk is a preview for the spring semester Math 3094 topics course on Knot Theory.


Note: Free refreshments. The talk starts at 5:45.

A job interviewer might use logical puzzles to test the problem solving abilities of an applicant. In this meeting, we will discuss such problems of varying levels, and a few other things that may come up in an interview. All are welcome.


Note: Pizza will be provided.

There are three things one can watch forever: fire burning, water falling, and humanity computing more and more digits of \(\pi\) (the current record is 62.8 trillion digits).

The fundamental constant \(\pi = 3.1415\ldots\) has played a significant role in mathematics, science, and most world cultures for over 4000 years. Once, the number \(\pi\) was even a subject of political debates in the state of Indiana where they wanted to pass a bill that would define \(\pi\) as a rational number.

The constant interest in the nature of \(\pi\) has left us with a lot of unusual, intriguing, and surprising formulas for \(\pi\). They are a source of delight for many of us. In this talk we are going to review a few such formulas. We'll explain why some of the formulas hold true (on the level of Calculus 2). Finally, we’ll see some of them in action and how they help to compute more and more digits of \(\pi\).


Note: Free refreshments. The talk starts at 5:45.

Can you escape? In a mansion haunted by several bored logicians, you will encounter perilous situations where one’s life depends on common knowledge and quick
thinking.

Don’t worry, your life won’t actually be in danger. You will work through the
puzzles in small groups and learn how to survive if you ever find yourself in a situation
where your life depends on figuring out the color of your hat.
All are welcome.

Come solve some riddles and win some candy!

Geometry is about shapes and number theory is about integers. These might seem unrelated, but over 100 years ago Minkowski discovered many interesting links between them and he called his ideas "the Geometry of Numbers." It allowed him
to use geometry to prove theorems in number theory and number theory to prove theorems in geometry. We'll see some examples relating the geometric properties of shapes on grids of points in the plane (and in higher dimensions) to number-theoretic properties of primes, integers, and rational numbers.


Note: Free refreshments. The talk starts at 5:45.

The math club is hosting a panel discussion on undergraduate mathematics research opportunities. The panelists will discuss how to become involved in mathematics research as an undergraduate and what the research process is like.

A set \(S\) is convex if, for any two points in \(S\), the line segment connecting them is also in \(S\). Given a set of points \(P\), we define their convex hull as the smallest convex set that contains \(P\).

Sometimes, we want to shrink the convex hull of a set of points in a non-uniform manner. This gives rise to the more general concept of a "reduced convex hull." Such objects originated in binary classification problems in machine learning, and have been studied further in the field of computational geometry. We will explore various properties of reduced convex hulls, and how these properties behave as the number of points in our set gets large.

Note: Free refreshments. The talk starts at 5:45.

The idea that math and music are related to each other goes back to the ancient Greeks, and the relations found since then can get quite sophisticated. This talk will describe how the tasks of tuning instruments, playing instruments, hearing music, and (digitally) recording music are connected with a broad range of mathematics, including infinite series, differential equations, linear algebra, and number theory.


Note: Free refreshments. The talk starts at 5:45.