# Mathematics Colloquia

# The Basics of Neural Networks

### UW Fox Math Associate Professor Alex Lavrentiev

### Wednesday, April 3, 2019, 4:10 – 5:10 pm

### Swart 217

abstract

# November 28, 2018, Colloquium: Number Talks

### UW Oshkosh Math Professor Jen Szydlik & Associate Professor Amy Parrott

### Wednesday, November 28, 2018, 4:10 – 5:10 pm

### Swart 217

abstract

# April 16 Colloquium: Math in German Schools and Museums

### UW Oshkosh Math Professors Eric Kuennen & John Beam

** Monday, April 16, 2018, 3:00 – 4:00 pm**

**Swart 217**

In Spring Interim 2017, we took a group of fourteen UW Oshkosh students to Germany for three weeks to study mathematics education from an international perspective. We visited German schools, observed math classes and talked with teachers, and paired with a class for pre-service mathematics teachers at Marburg University. We also visited many outstanding museums that feature some really neat mathematics.

In this presentation, we will present and discuss several of the demonstrations and exhibits that we experienced in these German museums, including an “Infinity Clock”, how to multiply using a parabola, and other interactive experiments at the Mathematikum in Giessen, some early calculating machines from the Arithmeum in Bonn, and solving a problem from an ancient Egyptian mathematics text at the Neues Museum in Berlin. We will also show photos and discuss our experiences in German schools and at Marburg University, and underscore the rich learning experiences available to students and their professors alike through study-abroad programs.

# March 5 Colloquium: A Modular Mathematical Mystery

### Dr. David Penniston

### UW Oshkosh Mathematics Professor

**Monday March 5, 2018, **4:10-5:10 pm

**Swart 217**

In the last twenty-five years modular forms have held a prominent place in number theory research. Most famously they played a central role in Andrew Wiles’ proof of Fermat’s Last Theorem, a problem that remained unsolved for over 300 years. In this talk we will explore how modular forms were used to answer a question that arose in my own research, a process that involved a good bit of detective work and offered some interesting twists and turns. The talk will be aimed at a general audience, and no knowledge of modular forms will be assumed - the only prerequisite is an interest in mathematics.

# November 10 Colloquium: Mathematical Models in Blood Clotting

**Dr. Tyler Skorczewski**

### UW Stout Assistant Professor and UWO Math & Physics graduate

**Friday November 10, 2017, ****3:00 – 4:00 pm**

**Swart 217**

Blood clotting, or hemostasis, is a vital process in the human body. Bleeding disorders, such as hemophilia, arise when hemostasis occurs on too slow of a timescale or not at all. On the other end of the spectrum, if clotting occurs too rapidly (thrombosis), pathological clots, or thrombi, can form, leading to heart attacks and strokes. Understanding how blood clotting occurs requires knowledge of biophysical and biochemical processes which take place over multiple scales in both time and space. Fluid flow is an integral component of the blood clotting system. Blood flow brings platelets and chemical reactants required for clot growth to a vascular injury site. In addition this flow imposes mechanical stresses that affect the formation and breaking of molecular bonds. In this talk we will discuss how the immersed boundary method can be used as a mathematical modeling framework to study both the fluid structure interactions of platelets moving in a blood vessel and how the platelets bind to the vessel wall in response to injury.

# October 24 Colloquium: Creating Research Projects In and Out of the Classroom

### UW Milwaukee Mathematical Sciences Professor Gabriella Pinter

**Tuesday, October 24, 2017, 4:10 – 5:10 pm**

**Swart 217**

Finding just the right research project for students can be challenging at all levels. However, working on one’s own project could provide powerful motivation, and can turn out to be a transformative experience, so we strive to have more and more students participate in some form of research.In this talk we are going to present a few different research projects that grew out of a mathematical modeling class, an undergraduate bio-math program and some Math Circles. We illustrate ways of finding/creating projects and show how simple-looking problems could go further and further and lead to surprising connections and results.

# October 24 Colloquium: Dynamical Systems and your Car Odometer

**Monday, October 24, 4:10 -- 5:10 pmSwart 127**

One device that we take for granted within our cars is the odometer. The function is simple: for every mile that is driven, the odometer increases by 1. Since we work in a base ten world, if our car has 99,999 miles, when we add one, we say it "rolls over" to 100,000 miles. It turns out that this action of "addition by one with carry" appears frequently within dynamical systems.

We will show how the concept of the car odometer can be generalized into an interesting collection of dynamical systems called "odometers" or "adding machines." We will then talk about how these dynamical systems can change if we "speed them up" by considering "addition by X with carry" where X is allowed to be larger than one. This is joint work with Drew Ash (Davidson College) and Nic Ormes (University of Denver).

# Matters of State: The Mathematics of Power in the Electoral College

### Dr. Stephen Szydlik

**Mathematics Department ColloquiumTuesday October 11, 2016, 3:00 – 4:00 pm Swart 217**

“Power is a lot like real estate. It’s all about location, location, location.”

-Frank Underwood, *House of Cards *

Your vote counts. Of course it does. But does it count as much as a vote in California or Alaska? Issues of power and control in our government have been a part of the national conversation since our country’s inception, and the Electoral College has been a focus of much of that controversy. In this presentation, we will take a brief tour of the Electoral College and examine some of the mathematics behind its complexities. We’ll consider the question of whether any states have unfair advantages when it comes to power in the College, and we’ll work on answering one of the fundamental questions in any democracy: how much does my vote really matter?

# Numbers in Nature: the Mathematics on Exhibit at the Chicago Museum of Science and Industry

### Amanda Roberts, Sophie Gresens, and Jenna Duchow

**(UWO Math Majors)**

**Thursday April 14 at 4:00 pm **

**Swart 127**

The UWO Math Club visited the new *Numbers in Nature* exhibit at the Chicago Museum of Science and Industry this Spring. They will share with us some of the mathematics featured in the exhibit, including fractal branching, spirals, the golden ratio, and Voronoi patterns.

## Describing Baseball's Managers: A Clustering Exercise

### Dr. Chris Edwards

UWO Associate Professor

Thursday, March 31, 2016, 4:00 – 4:50 pm

Swart 127

We collect information about athletes constantly, to evaluate their performance for almost every aspect of the games. Can we do the same for managers? Specifically in baseball, what strategies or actions does a manager take that differ from other managers? Can we describe managers’ tendencies with just a few clusters? I will explore these ideas and introduce the statistical technique of clustering.

## Quadratic Forms and Partition Numbers

### Eric Boll

UWO Mathematics and Computer Science graduate

**Monday, Feb 22, 2016**

** ****4:15 pm**

**Swart 217**

For a number *n,* the partition function *p*(*n*) counts the number of non-increasing sequences of positive integers (partitions) whose sum is *n*. For example, 3 = 2 + 1 = 1 + 1 + 1, so *p*(3) = 3. The great Indian mathematician Ramanujan proved that *p*(5*n* + 4) is always divisible by 5, and others have shown that the partition function has many intriguing divisibility properties of this form. Part of the allure of studying *p*(*n*) comes from how hard-won such results are; despite its elementary definition, no simple closed formula has been found.

Given a positive integer ℓ, the ℓ-regular partition function *b*ℓ(n) counts the number of partitions of *n* with no terms divisible by ℓ. In this talk, I present some of the machinery of modular forms and binary quadratic forms and show how it can be used to get a particularly good handle on the 3-divisibility of *b*13(n).

The Appalachian Trail, by the Numbers

### Dr. David Penniston

Professor of Mathematics, UW Oshkosh

**Monday, Oct 19, 2015**

** ****4:10-5:00 pm**

**Swart 217**

The Appalachian Trail is perhaps the best known long distance hiking

trail in the world, and has been the subject of many books and articles.

The most famous of these is Bill Bryson's "A Walk in the Woods",

which was recently made into a motion picture. Because of the trail's

unique place in the natural world, there is much about it that is

interesting - from the ecology of the trail and its surroundings to the

psychology of those who hike it. This talk will present one

mathematician's take on the trail.

## May the Best Team Win:

The Mathematics of Scoring a Cross-Country Race

### Dr. Stephen Szydlik,

**Professor of Mathematics, UW Oshkosh**

**Thursday, April 2, 2015**

**4:15 PM**

** ****Swart Hall 217**

**Abstract: **Scoring a cross-country running race seems simple: essentially, a team's score is determined by finding the sum of the placings of its runners, with teams ranked in the order of th

eir scores, from lowest to highest. But this seemingly straightforward process can yield surprising and counterintuitive outcomes. In this presentatio

n, we will explore some of the dilemmas associated with determining the team winner of a race, and we will consider alternative scoring schemes.

Surprisingly, this small encounter in a minor corner of the sporting world will lead us to one of the most significant ideas in twentieth-century mathematics: the mathematics of voting. During our short run through the subject, we will briefly look at the mathematics of social choice, and we will draw both connections and distinctions between reasonable ways to score cross-country invitationals and “fair” voting methods. Runners, mathematicians, math students, and especially running math students are welcome to attend – no calculus required. Lace up your shoes and join us!

## Differentiability at Infinity via Stereographic Projection (Feb. 12 Mathematics Colloquium)

### Dr. McKenzie Lamb, Ripon College

### February 12, 2015, 4:15 PM

### Swart Hall 217

**Abstract: **This talk will introduce stereographic projection along with the following question: If the graph of a differentiable function of 1-variable is wrapped around the sphere using inverse stereographic projection, the ends of the graph will meet up at the North Pole. For which functions will the resulting closed curve on the sphere be differentiable? This question leads to one possible notion of “differentiability at infinity” for real-valued functions. We will discuss a number of examples and some techniques that can be used to determine whether a function is or is not differentiable at infinity. If we have time, we will also consider higher-dimensional analogues. Most of the talk will be accessible to anyone with a Calculus I background.

## Compressions: A Tale of Love and Two Rings

### Dr. Kenneth Price, Professor, UWO Mathematics

### Wednesday, April 23, 2014 Swart 217 from 4:00 to 5:00 pm

** **

### Abstract:

With springtime come thoughts of love and gardens. These thoughts are linked in Louise Riottes gardening book, Carrots Love Tomatoes, which points out carrots tend to be healthier when planted near tomatoes. On the other hand, potatoes do not love tomatoes because they share diseases.

To design gardens with happy plants in mind, we use directed graphs to show love from plant to plant. If plant A loves plant B we draw an arrow pointing from A to B.

Even though potatoes love cabbages and cabbages love tomatoes, potatoes do not love tomatoes. Thus love is not always transitive and this must be accounted for in a garden plan. Many graph-lovers would add all arrows forced by transitivity, but here this would be a mistake: these extra arrows in the transitive closure of a garden may lie about love.

But do not despair. We present a transitive closure alternative, which may appeal to gardeners and, as well see, also has interesting applications to matrices.

# Provincial Polynomia

## Uncommon Excursions for the Seasoned Visitor

### Dan Kalman, American University

### Thursday April 3, 4:00 - 5:00

### Swart Hall 217

Please click on the image of the poster for more information

# Mathematics Learning in China: Observations from a Study Abroad

Presented by:

**Leah Christian, UWO Math Major**

**Sarah Roth, UWO Math Major**

**& Jen Szydlik, UWO Faculty Member**

In the spring of 2013, eleven UWO students and two faculty members traveled to the People’s Republic of China to study math education. In this presentation, we will tell you what we learned from Chinese teachers and students.

## Partitions, Pentagons and Patterns

A partition of a number is a non-increasing sequence of positive integers that add up to it. So, for example, 4+2+1 and 4+1+1+1 are partitions of 7. It turns out that 4 has 5 partitions, 9 has 30 partitions, 14 has 135 partitions, and Ramanujan proved the following beautiful result: the number of partitions of 5n + 4 is divisible by 5 for any nonnegative integer n. The study of partitions generates a multitude of deep connections to topics in geometry, group theory, analysis, and other fields of mathematics. In this talk, I will explore some of these connections and show how to prove partition results similar to those of Ramanujan.

## Basel and Beyond: An Incomplete History of a Famous Sum

### Benjamin Collins

### March 27, 2013

### Swart Hall 217, 4:30 - 5:30 PM

“If anyone finds and communicates to us that which thus far has eluded our efforts, great will be our gratitude."

With these words, published in 1689, Jacob Bernoulli brought to the attention of European mathematicians a problem first posed by Pietro Mengoli in 1644. The problem was to find an exact value for the infinite sum of reciprocals of squares: 1 + 1/4 + 1/9 + 1/16 + ...

The problem came to be known as the Basel Problem, after the Swiss university town where Bernoulli lived and worked. Fittingly, the problem was solved by Basel's finest mathematician, Leonard Euler, in 1735. In his long and productive career, Euler provided two separate proofs, as well as two efficient ways to calculate the value of the sum.

The Basel Problem continues to intrigue mathematicians. Dozens of proofs have been given, including two published within the last year. We will discuss Euler's first proof, as well as a few more recent proofs. We will also explore some of the many extensions and variations.