2017-2018 Academic Year Colloquium Schedule

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September 7, 2017

Title: Ergodic Theory and Normal Numbers.
Speaker:Drew D. Ash
Adjunct Assistant Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
Abstract: The purpose of this talk is to expose the audience to subfield of dynamical system called ergodic theory. To do so, we will consider the following question. How many numbers in $[0,1)$ are there when we look at their base-10 decimal expansion have the following property: The asymptotic (or expected) frequency of seeing the digit $d$, $d\in\{0,1,\dots,9\}$, is $1/10$? Can you even think of a number that has this property? We will show, using ergodic theory, that a surprising amount of numbers have this property! If time allows, we will discuss another interesting transformation called the Gauss map. The Gauss map has connections with continued fractions!
Location: Palenske 227
Time: 3:30 PM
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September 14, 2017

Title: Planning for Graduate Study in Mathematics and Computer Science
Speaker:David A. Reimann
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
Abstract: A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation.
Location: Palenske 227
Time: 3:30
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September 21, 2017

Title: How to Become An Extremal Graph Theorist
Speaker:Lauren Keough
Assistant Professor
Mathematics
Grand Valley State University
Allendale, Michigan
Abstract: Graph theory is the study of relationships that come in pairs. There are many such relationships occurring naturally, think of matching medical students to residencies, friendship on social networks, or even pairing animals with the regions in which they live. From these relationships we can draw graphs. For example, for each person on a social network draw a dot, and draw a line segment between two dots if the people are "friends". Graph theory is, broadly, the study of these pictures with these dot lines. So, what could extremal graph theory be? Unfortunately extremal graph theory is not doing graph theory while snowboarding. Think of "extremal" more like you may have in Calculus 1 — perhaps you remember finding "local and absolute extrema." By the end of the talk you'll be able to ask and answer extremal questions and perhaps even know a new card trick.
Location: Palenske 227
Time: 3:30 PM
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September 28, 2017

Title: The Black-Scholes- Merton Equation and Option Pricing
Speaker:Darren E. Mason
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
Abstract: The Black-Scholes option pricing formula is a 1997 Nobel Prize winning result in economics (& mathematical finance) that provides a framework for rational pricing of a large class of stock options. In this talk we will discuss the basic idea of an option on an asset as well as the problem of fair valuation of such a financial object. Then, assuming that the stock price St follows a geometric Brownian motion, we will discuss a rough hedging argument that results in the Black-Scholes partial differential equation as a necessary condition for risk-free portfolio evolution. Using changes of coordinate systems and integrating factors, the Black-Scholes partial differential equation will be transformed into the classic heat (or diffusion) equation, for which a standard integral solution form is known. Finally, we will use this integral solution to derive the celebrated Black-Scholes option pricing formula. Some limitations of this model will also be discussed.
Location: Palenske 227
Time: 3:30 PM
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October 19, 2017

Title: Symmetry: A mathematical approach using group theory and linear algebra
Speaker:David A. Reimann
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan
Abstract: Symmetric patterns are used in many situations to decorate an object with a repeating motif that is translated, rotated, or reflected without changing size. We will see examples of several symmetry types and look at these from the vantage point of group theory. In particular, we will study rosette patterns, frieze patterns, wallpaper patterns, and patterns on the sphere. We will then see how we can create all these pattern types with a unified framework based on the vectors and matrices of linear algebra.
Location: Palenske 227
Time: 3:30 PM
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October 26, 2017

Title: Graduate Studies in Survey Methodology and Biostatistics at the University of Michigan
Speaker:Michael R. Elliott
Professor Biostatistics, Research Professor, Survey Methodology
Biostatistics/Survey Methodology 1415 Washington Heights
University of Michigan
Ann Arbor, Michigan
Abstract: I will talk about the opportunities available for graduate study in survey methodology and/or biostatistics at the University of Michigan. Undergraduate majors in mathematics, computer science, biology, economics, political science, or related fields who are considering graduate school are welcome to attend and learn about the exciting opportunities these programs offer. The Program in Survey Methodology degree combines aspects of psychology, sociology, statistics, and information and data science to provide training in topics relevant to the understanding of human populations. Students who graduate from this program can pursue careers in public health, business, public policy, consulting, and academics. Everyone is familiar with political polling, but survey methodologists also help with understanding the spread of disease, the risk of transportation injuries, the lifetime antecedents to a healthy old age, the marketing for new and existing products, among many, many care er paths. Biostatistics is an equally interesting field; biostatisticians work to unravel genetic basis of human health and disease, design and analyze data from clinical trials for new drugs, and design life-saving systems to prioritize who gets organ transplants, among many other opportunities. I have appointments in both programs and will compare and contrast the fields and the graduate programs at the University of Michigan.
Location: Palenske 227
Time: 3:30 PM
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November 2, 2017

Title: All Parabolas Through Three Non-collinear Points
Speaker:Michael A. Jones
Associate Editor
Mathematical Reviews
Ann Arbor, MI
Abstract: There are an infinite number of parabolas through any three non-collinear points. In this talk, I'll explain how solving a system of three equations and three unknowns and applying rotation matrices can be used to find the parabolas. The parabolas form a one parameter family. Geometric intuition about when a parabola doesn't exist for three specific values of the parameter is verified by recognizing when the equation for the parabola is undefined. Looking at the family from a calculus perspective, one can find the parabola with the widest mouth through the three points. We will use Desmos online software to visualize all the parabolas for an example. This talk is based on an article of the same title that is co-authored with Stanley R. Huddy and is forthcoming in the July 2018 issue of The Mathematical Gazette.
Location: Palenske 227
Time: 3:30 PM
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