4:15 pm

Swart Hall 217

Title: Quadratic forms and partition numbers

Abstract:

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).

Trail, and he would like to talk to us about it:

Monday, Oct 19, 4:10-5:00

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.

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Beam, who joined the faculty of the mathematics department at UW Oshkosh in 2002, teaches a variety of problem-based mathematics courses for pre-service elementary and middle grades students, as well as upper-level courses in the mathematics major.

According to the nomination statement by UWOshkosh Professor of Mathematics Jennifer Szydlik: “[Beam] is known for his focus on modeling mathematical practices (conjecturing, exploring, defining, finding counterexamples, and making arguments) for his students, and for his creative – sometimes wacky – classroom activities (e.g., hands-on probability experiments involving noodles; newspaper critiques; radio critiques; lots of logic puzzles; statistics activities that make use of current data; motion experiments involving toy cars; and so on).”

Szydlik’s nomination statement goes on to say: “His peers characterize his teaching style as mathematically rich, empowering for students, relaxed, and encouraging of individual ideas and opinions.”

]]>Tim Maruna, McGraw-Hill Education local representative

10:20-11:20 am

Tuesday April 28, 2015

Swart 13

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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 their scores, from lowest to highest. But this seemingly straightforward process can yield surprising and counterintuitive outcomes. In this presentation, 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!

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**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.

Listen to the WTMJ radio interview of John at http://www.jrn.com/wtmj/shows/wisconsins-afternoon-news/Running-to-the-Olympic-Trials-279056061.html

Results of the Chicago Marathon are reported here: http://www.usatf.org/News/Americans-impressive-in-Chicago-Marathon-elite-rac.aspx

]]>**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.

Please click on the image of the poster for more information

]]>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.

Wednesday, October 16 4:10 - 5:00 pm Swart 217

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.

“My motivation to invent arrowgrams was to find a way to communicate some aspects of my scholarship to people besides mathematicians,” Price said. “I was looking to have people do math that was fun.”

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“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.

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