## SPRING 2018 SCHEDULE

**Cool Mathematics**

*Abstract: *I will in fact talk about some unsolved, or recently solved, problems in Mathematics.
The main purpose of the meeting, however, will be to organize the Undergraduate Colloquium
for those interested in taking it for credit (1 hour credit/no credit). For many participants
this will be the first class in which they have to write a technical report. This
is a complicated yet gratifying task. I will discuss some of the issues involved and
also give a first introduction to the use of LaTeX.

**What's the deal with being a high school teacher?**

*Abstract:* Are you thinking about maybe teaching middle or high school math someday? Maybe as
a career or even as a bridge to graduate school or some other career? Perhaps you’ve
thought about it as a profession after you retire from something more lucrative?
There is a shortage of math teachers in Utah (and across the country); teaching is
incredibly rewarding, but also challenging because there is a lot to know to be successful
in a classroom. This colloquium will focus on three questions: 1) What is *mathematical knowledge for teaching?* 2) What’s in the “Common Core”? and, 3) What are the paths into teaching secondary
math?

Tim Jones, Ph.D.

**The Joy of Teaching Kids Math**

*Abstract*: My career has taken me from particle physics at CERN to defense work at Lockheed Martin
to start ups in Silicon Valley. I have worked with tremendous people on some amazing
projects – but nothing has been more rewarding to me than the past decade I have spent
teaching math to secondary kids (7^{ }– 12). When we teach math at our school, we teach kids that math is hard – it is
not built-in and requires a significant effort on the part of the student to learn
math. We teach kids how to do math – that it is not guess-work. Math, to us, is
a language – a language that is used to communicate ideas and to communicate logical
reasoning. Not surprisingly, our algebra standards are therefore quite high. We
do not use gimmicks to teach math – we do not need to. Students get the same intrinsic
rewards as scientists, engineers, and mathematicians when they can do math – when
they can solve problems. When students are taught at a level that is appropriate
to them as an individual, they can learn math efficiently. All students – independent
of socio-economic background can be successful – when given a chance. Teaching math
requires teachers that have a drive to change the world – a willingness to invest
in kids – a willingness to do the right thing. Math teachers, however, must be smart
in math. Not x + 3 = 5 smart, but Fourier Series smart.

*If you would like to talk to Tim about trying out teaching, you can contact him at
tjones@apamail.org*

**Sequences and Differential Equation**

*Abstract*: You learned arithmetic sequences and geometric sequence in an elementary algebra class. In this talk, I will talk about another type of sequence which is little bit more complex than arithmetic/geometric sequences. We will find its n-th term by solving a corresponding differential equation. That means we will use differentiation, integration, taylor expansion, linear differential equation etc, to understand the sequence.

**Cupid's Identity: Valentine's Day = pi Day - One Month = e Day + One Week**

*Abstract*: On this day of love, can we quell the recent antagonism between pi and e, as documented in an infamous recent debate at Williams College? Let's meditate away the irrational differences (and sums and products) between these transcendental numbers and instead toast the innumerable occasions on
which they work together in harmony.

Rebecca Hardenbrook

**A Knot-vice’s Guide to Untangling Knot Theory**

*Abstract*: Consider a single piece of string. Now, knot it using a variety of twists and turns,
finishing by combining the two ends together so that the string is one continuous
loop. Is it possible to untangle this into the trivial knot? Although it may seem
impossible to tell for the most complicated of knots, much work has been done over
the past century to determine such an answer. This work has led to the development
of a new field in mathematics: knot theory. In this talk, we will explore the history
and basics of knot theory and, hopefully, won’t find ourselves too tangled up along
the way.

**Spot the Math!**

*Abstract:* Spot It! is a pattern recognition game. There is a deck of 55 cards. Each card shows eight different symbols. Any two cards have exactly one symbol in common. I will explain the rules of the basic version of the game during the talk, then I will answer the following two questions:

1) How can we generate such a deck?

2) In particular, what's the total number of symbols in the whole deck?

Both questions turn out to be quite difficult. However, they become simpler if we use a little bit of geometry. The only prerequisite for this lecture is to know that the equation of a line is y=a+bx.

Yuri Tschinkel, New York University

**Rational points**

*Abstract:* The Gauss circle problem asks about the number of vectors with integer coefficients in a circle of growing radius. More generally, one can consider this problem in spaces of higher dimension, and impose polynomial conditions of the vectors. In many cases, this problem can be solved, applying a range of tools from harmonic analysis and analytic number theory. I will discuss a general conjecture concerning the distribution of lattice points satisfying polynomial conditions, in spheres of growing radius, as well as some recent results establishing this conjecture.

Nicholas Cahill

**Bias and Threat: Understanding Sexism in STEM**

*Abstract:* One of the largest ongoing projects in American education has been the attempt to
understand the role sexism plays in gaps in performance and achievement between men
and women in the sciences. While it may at first have seemed like a simple attitude
problem, the gap has proven to be a complicated challenge, with many subtle and less
subtle factors at play in the minds of educators and students, and in the broader
environment where learning takes place. As the tenacity of this problem has become
clear, it is more important now than ever for mathematicians to be understand the
threat! This talk will be a brief overview of some of the most important concepts
we use to understand what sexism is and how it operates in the sciences.

** The Infinite Monkey Theorem**

*Abstract:* Would you be surprised to learn that, given an infinite amount of time, a monkey sitting
at a typewriter hitting keys at random will almost surely type the complete works
of William Shakespeare (or any other given string of letters)? Maybe not, since after
all a lot can happen in an infinite amount of time. But how long would you have to
wait? Surprisingly, low long you'd have to wait depends on more than just the length
of the string. We'll discuss and prove these facts. No monkeys or advanced mathematics
required, just some basic probability (which I will review).

Anna Nelson

**On the rheology of cats: are cats fluid?**

*Abstract: *In this talk we will determine whether the claim that cats are liquid is solid! Using
principles of rheology and fluid mechanics, we will study the flow and deformation
of cats in different time scales. No prior knowledge of fluid mechanics is required!

**The scallop theorem**

*Abstract:*Bacteria and other small swimming organisms can't coast. Once they stop moving their flagella, they come to a complete stop instantaneously. They live in a world where inertia doesn't matter. We, on the other hand, live and swim in an inertia dominated world. The scallop theorem is a beautiful and simple geometric argument explaining why if inertia does not matter, you can't swim with a single hinge or via reciprocal motion. While the scallop theorem tells us what does not work, it does not explain the rich swimming behavior observed in nature. To answer this question, applied mathematicians use a combination of model, analysis and simulation starting from the famous Navier-Stokes equations.

**Stein's Paradox and Shrinkage**

*Abstract:*** **Suppose we want to compute the batting average of Adam Eaton. Then, our natural estimator
would be Hits/At Bats. Now suppose, we want to compute a batting average for each
of the top 10 MLB players. Our natural estimator is no longer the best choice. In
fact, the moment you are interested in 3 or more players, you are better off not using
the natural estimator.

Charles Stein pointed out this paradox much to the horror of the statistical community in 1955. Today, a host of shrinkage estimators owe their origins to his result.

## Math 3000 (Receive Credit for Attending)

The Undergraduate Colloquium is open to anyone to attend; however, if students would
like to receive credit, you may register for **Math 3000**.

This is a 1 credit hour CR/NC course. To receive credit:

- You may not miss more than 2 of the colloquia
- You will need to write a short paper on one of the topics presented during the semester. (Report Specifications)

Course Coordinators

Peter Alfeld | |

Course Instructor | Administrative Coordinator |

pa@math.utah.edu | ugrad_services@math.utah.edu |