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## 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 Citation Click for BibTeX citation

### 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 Citation Click for BibTeX citation

### 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 Citation Click for BibTeX citation

### 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 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-author with Stanley R. Huddy and is forthcoming in the July 2018 issue of The Mathematical Gazette. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

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