Monday, May 7

Monday, May 7

**Reception 4:00, King 203**

**Lecture 4:30, King 239**

**Nicholas Wilcox `18**

**Topic: Elliptic Curve Cryptography: A Computational Introduction**

At its core, cryptography relies on problems that are simple to construct but difficult to solve unless certain information (the key") is known. One such problem is that of computing the discrete logarithm in finite groups. In order to implement cryptographic protocols based on the discrete logarithm problem, we must obtain very large groups that have an easily computable operation. Fortunately, we can derive groups from the set of points on an algebraic curve, that is, the set of points*(x; y)*satisfying a polynomial equation *p(x; y)*= 0, where *p*is a polynomial in *x*and *y*.

This presentation will describe the basic algebra behind fundamental cryptographic protocols, such as Diffie-Hellman Key Exchange, and then show how a certain class of algebraic curves, elliptic curves, can be used to implement those protocols.

The mathematics Honors lectures Series

The mathematics Honors lectures Series

**Monday, April 30**

**Reception 4:00, King 203**

**Lecture 4:30, King 239**

**Hannah Pieper `18**

**Topic: Comparing Two Thickened Cycles**

Complex networks play an important role in a variety of disciplines, ranging from computer science, physics, sociology, and biology. One of the most significant classes of graphs are those that demonstrate ``small-world" phenomenon; meaning that they are highly connected and display local clustering but have a relatively small diameter. The most famous example of this is the concept of six degrees of separation; meaning that on average, any two people can be connected via a sequence of five or fewer mutual friends.

In this talk, we will give an overview of the standard mathematical tools used to analyze networks. We will also discuss a variation of a known small-world random graph model, as well as some novel results that arose from our explorations.

**Thursday, April 26**

**he Mathematics Pizza Lunch**

### With Professor Bob Bosch

**Pizza will be served at 12:15 p.m. in King 203**

**Lecture to follow at 12:30 p.m. in King 241**

**Topic: Report from the Gathering**

I recently returned from G4G13, the thirteenth Gathering for Gardner, a biennial conference held in honor of Martin Gardner. Gardner has been called "the greatest friend mathematics has ever had." For more than 25 years, he wrote the Mathematical Games column for Scientific American magazine. In his columns, he introduced the general public to topics like Conway's Game of Life, the artwork of M.C. Escher, Penrose tiles, the logic puzzles of Raymond Smullyan (knights and knaves, for example), and much more. Gardner also

wrote over 100 books, the last one when he was 95! Some of his books were collections of his columns, but others were about magic tricks (he is revered by the magic community), and still others were on puzzles.

G4G13 was my ninth Gathering. I've been attending since G4G5, which was held in 2002. G4G13 was the largest Gathering, with over 280 participants (mathematicians, magicians, puzzle enthusiasts, artists, authors, and more). I'll talk about what I saw there, show numerous pictures, and answer questions.

Wednesday, April 25

Wednesday, April 25

** **

**The Mathematics Department**

*Welcomes Speaker*

*Welcomes Speaker*

* ***Jonathan Webster**

**Associate Professor**

**Butler University**

**Reception at 4 p.m. in King 203**

**Lecture at 4:30 p.m. in King 239**

**Topic: Searching for Patterns in Primes**

How do you quickly find certain patterns in prime numbers? Certain patterns in prime numbers are famous in mathematics. One example is twin primes where two primes differ by 2. Another example is Carmichael Numbers of the form (6k+1) (12k+1)(18k+1) where each factor is a prime number. We will review the Sieve of Eratosthenes and show it is used to find all prime numbers up to some bound. We conclude by demonstrating an asymptotically faster algorithm for finding prescribed patterns in the primes.

**Thursday, April 19**

**The Mathematics Department**

*2018 Honors Examiner Lecture*

*2018 Honors Examiner Lecture*

*Please help us welcome*

*Please help us welcome*

**Kate Petersen**

**Associate Professor**

**Florida State University**

**Reception at 4 p.m. in King 203**

**Lecture at 4:30 p.m. in King 239**

** **

**Topic: Uniform Distribution on the Circle**

Roughly, a sequence of numbers in the interval I=[0,1] is said to be uniformly distributed on I if for every closed subinterval, the proportion of the elements lying in that subinterval equals the length of the subinterval. This notion has many interesting connections, including the following. If we consider the powers of 2:

1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8092, …

there are more integers starting with a 1 than, say, a 3. Uniform distribution can also be used to differentiate rational and irrational numbers. Specifically, the sequence 0, x, 2x, 3x, 4x, … of all multiples of x is uniformly distributed mod 1if and only if x is irrational. (We say that a sequence of real numbers is uniformly distributed modulo 1 if their fractional parts are uniformly distributed on I.)

I’ll discuss some classical problems about uniform distribution, and then discuss the uniform distribution of rational points on the circle. I’ll relate these points to “visible points” on the integer lattice and discuss how the distribution of these points connects to properties of the Riemann zeta function.

**Tuesday, April 17**

**The Mathematics Department**

*Welcomes Speaker*

*Welcomes Speaker*

**Judy Holdener**

**Professor of Mathematics**

**Kenyon College**

Reception at 4 p.m. in King 203

**Lecture at 4:30 p.m. in King 239**

** **

**Topic: Homage to Emmy Noether: The Ideal Woman**

In 1953 American painter Jackson Pollock created the diptych “Portrait and a Dream,” which is generally believed to be a self-portrait of the artist. On the right-hand side of the work is a Picasso-esque depiction of Pollock’s head, rendered with black line intersecting and enclosing regions of black, red and yellow. On the left-hand side is Pollock’s dream illustrated as an abstract black-and-white drip painting. The drips evoke movement and confusion, suggestive of the subconscious mind at work. In this way the two panels of the painting represent the inner and outer self of Pollock, displaying** **an interplay – or perhaps even an identification – between the subconscious and conscious minds of the artist.

Similar to Pollock’s artwork, the creation of mathematical theory also involves a rich interplay between the conscious and the subconscious minds, and I portray this interplay in my digital portrait of the German mathematician Emmy Noether (1882-1935). Inspired by Pollock’s “Portrait and a Dream,” my artwork is also a diptych, displaying a portrait of Noether alongside mathematical writing on a chalkboard reflecting the conceptual, axiomatic way in which she approached her groundbreaking work relating to ideals.

Monday, April 9

Monday, April 9

**The Mathematics Department**

*2018 Fuzzy Vance Lecture*

*2018 Fuzzy Vance Lecture*

*Please help us welcome*

**Craig Guilbault **

**Professor of Mathematical Sciences**

**University of Wisconsin-Milwaukee**

**Lecture at 7:30 p.m. in King 306 **

**Reception following in Lobby**

**Topic: Proof or Swindle? The surprising effectiveness of a sketchy technique**

More than fifty years ago Samuel Eilenberg and Barry Mazur proved unrelated theorems using similar techniques which, to many, seemed too good to be true. Both proofs were completely rigorous, but their method was so magical that it has become known as the "Eilenberg-Mazur Swindle". In this talk, we will introduce the audience to this technique by using it to prove a variety of interesting theorems. Examples will be chosen from topics understandable to the average undergraduate student; in particular, infinite series, set theory, and the topological study of knots.

Pizza Lunch & Talk

Thursday, April 5, 2018

Pizza Lunch & Talk

Thursday, April 5, 2018

**Pizza at 12:15 in King 203**

**Talk at 12:30 in King 241**

### Associate Professor Kevin Woods

*will be speaking on*

### "Untangling Escher with Complex Arithmetic"

**In 1956, M.C. Escher produced a lithograph entitled “Prentententoonstelling” (translation: “Print Gallery”). The first thing we notice is the wonkiness of the curvy lines. Then we start exploring: starting with the man in the lower left corner, we follow his eyes into the painting, follow the painting to the right as it explodes into a cityscape, follow the cityscape down and we’re at street level looking into a galley with a man standing inside, follow his eyes into the painting, …**

**Egads! With a little bit of complex arithmetic, we’ll be able to understand what’s happening here, leading to some amazing animations. We’ll also be able to figure out what’s going on with the hole in the middle, where Escher seems to have shrugged his shoulders and called it a day.**

Monday, April 2, 2018

Monday, April 2, 2018

**Nate Carlson **

**Associate Professor of Mathematics **

**California Lutheran University**

**Reception at 4:00 p.m. in King 203**

**Lecture to Follow at 4:30 p.m. in King 239**

**Topic: A Surprising Connection Between Two Proofs of the Infinitude of Primes**

In Book IX of his foundational work *The Elements*, written in 300BC, the Greek mathematician Euclid included his celebrated proof that there is an infinite number of primes. While this is the most well-known proof and has been studied by students of mathematics throughout the centuries, many other proofs of the infinitude of primes have been found. These include a classic proof by Euler and very recent proofs by Pinasco and Whang.

In 1955 Furstenberg gave an unusual topological proof involving arithmetic progressions. After dispensing with the topological language, the essential number theory in this proof was recently uncovered by Mercer. On the surface neither version seems to bear much resemblance to Euclid’s original proof.

In this talk, the speaker gives a variation of the Furstenberg/Mercer proof that in fact looks much like that classical proof. (This variation appeared as a short note in the American Mathematical Monthly in 2014). This demonstrates that while Furstenberg’s proof seems unusual, at its core it is in fact quite similar to the first and most well-known. Basic topological and number-theoretic background will be given.

**Thursday, March 1, 2018**

*Please help us welcome speaker*

Jonathan Brown

**Assistant Professor**

**Mathematics Department**

**University of Dayton, Ohio**

**Reception at 4 p.m. in King 203**

**Lecture to follow at 4:30 p.m. in King 239**

**Topic: ****Move Over SAS**

High school geometry is littered with triangle congruence theorems: Side-Angle-Side, Side-Side-Side, etc. Is that the end of the story? Are there any congruence theorems using other measurements of a triangle, like area and perimeter? It is well known that two triangles can have the same area and different perimeters or the same perimeter and different areas, but what about triangles that have the same area and the same perimeter: must they be congruent? An elementary education student asked me this question and it lead me on quest exploring such topics as triangle growth and transformational geometry. In this talk, I will share some of these explorations and pose some new questions.

Thursday, February 22, 2018

Thursday, February 22, 2018

**The Mathematics Pizza Lunch**

*With Speaker*

**Rudd Crawford**

**Former chair, Department of Mathematics Oberlin High School**

**Former Associate Professor of Mathematics, Oberlin College**

**Pizza will be served at 12:15 p.m. in King 203**

**Lecture to follow at 12:30 p.m. in King 241**

**Topic: ****Is There a Math Teacher Somewhere Inside of You?**

There are the technical how-to-do-it issues, and there are the human-development-of-teenagers issues, and there are the you issues—what might you have to bring to any of this? Come with your questions, wonderings, fears, hopes, wildest dreams—we'll talk.

Wednesday, February 21, 2018

Wednesday, February 21, 2018

**The Mathematics Department**

*Welcomes Colloquium Lecture Speaker*

*Welcomes Colloquium Lecture Speaker*

**Harald Andrés Helfgott**** **

**Alexander von Humboldt Professor**

*at the***University of Göttingen in Germany**

**Reception at 4 p.m. in King 203**

**Lecture follows in King 239**

**Topic: Voronoi, Sierpinski, Eratosthenes**

Eratosthenes of Cyrene (3rd century BCE) showed how to produce a list of all primes up to N in a rather efficient fashion -- much more rapidly than if one were to test each integer up to N individually for primality. His procedure -- the first in an entire family of such methods -- is known as a *sieve.*

We show how to carry out a sieve of Erastosthenes up to N in space O(N^(1/3)) and essentially linear time. The procedure here improves upon the usual versions of the same sieve, which generally take space about O(N^(1/2)) and essentially linear time. Our basic algorithm -- which, like the one in (Galway, 2000), is ultimately related to approximating real numbers by rationals -- can also be used to factorize integers n, and thus to give the values of arithmetical functions that depend on factorization.

You can view event details by clicking here.

**Friday, February 16**

**Reception 4 p.m., King 203**

Lecture 4:30 p.m., King 239

Lecture 4:30 p.m., King 239

### Please help us welcome Assistant Professor of Mathematics and Computer Science Pamela Pyzza of Ohio Wesleyan.

**Her topic: Modeling Insect Olfaction**

Olfaction, or the sense of smell, is arguably the most primitive sense, and thus the mechanisms by which odors are detected and identified are shared across many animals, from insects to mammals.

We formulate a mathematical model to describe these mechanisms by considering the structure and behavior of individual neurons, then we analyze the activity generated by a network of these neurons.

Results from numerical simulations of this network, along with a simplified firing-rate analysis utilizing phase-plane techniques, present a biologically plausible picture of the two main mechanisms that characterize insect olfaction.

**The Mathematics Department**

*Invites you to attend the*

**2018 Lenora Lecture Series**

*with*

**Tristram Bogart `01**

**Assistant Professor of Mathematics**

**Universidad de los Andes**

**Bogotá, Colombia**

** **

**Determinants vs. Permanents**

Two of the most important invariants of a square (nxn) matrix are its

*determinant* and its *permanent*. The definitions of the two are very

similar, differing only by signs. Yet in other ways they are

profoundly different. The determinant is geometric in nature: it

measures area, volume, or in general n-dimensional volume. It can be

efficiently computed by the Gaussian elimination algorithm. The

permanent is not geometric but combinatorial: it can be used to solve

a wide range of counting problems. Indeed, in the power of the

permanent lies its very weakness: so many problems can be solved this

way that there is strong reason to believe that there is no efficient

algorithm to compute permanents.

** **

**Monday, January 8, 2018**** **

**Reception at 4 p.m. in King 203**

**Lecture follows in King 239**

Student Summer Research Experiences

Student Summer Research Experiences

**Pizza Lunch**

Thursday, November 30, 2017

King 203 at 12:15

Thursday, November 30, 2017

King 203 at 12:15

**Dominic Bosco**

**Modeling Collective Motion and Spontaneous Unjamming**

**Hannah Pieper**

**Generalized Catalan Numbers**

**Miranda Schaum**

**Studying Harmonic Measure Through Brownian and ****Teleportation**

**The Mathematics Department**

### **Colloquium Lecture**

** ***with Speaker*

**Caroline Turnage-Butterbaugh**

**Elliott Asst. Research ProfessorDepartment of MathematicsDuke University**

**Gaps between zeros of the Riemann zeta-function**

**The Riemann zeta-function is a ubiquitous yet mysterious function in number theory. The location of its so-called nontrivial zeros gives us information on the behavior of the primes. It is from this connection the Riemann Hypothesis arose. In this talk we will investigate the gaps between “critical" zeros of the Riemann zeta-function and provide a missing proof of an old result of Selberg.**

** **

**Wednesday, November 29, 2017**

** ****Reception at 4 p.m. in King 203**

**Lecture follows in King 306**

*Please Help *

*Please Help*

**The Mathematics Department**

*Welcome*

*Welcome*

**Barry Cipra**

*Freelance Mathematics Writer*

*Freelance Mathematics Writer*

*Northfield, Minnesota*

*Northfield, Minnesota*

**Monday, November 13, 2017**

**Reception at 4 p.m. TO 4:30 in King 203**

**Lecture at 4:30 to 5:30 in King 239**

*Lecture Topic*

*Lecture Topic*

* ***In Praise of Not Paying Attention**

** **

**More about the speaker**

**Barry Cipra is a freelance mathematics writer based in Northfield, Minnesota. He has been a contributing correspondent for Science magazine and a regular writer for SIAM News, the monthly newsletter of the Society for Industrial and Applied Mathematics. He wrote the first five volumes of What’s Happening in the Mathematical Sciences (American Mathematical Society, 1993-2002), and is the author of Misteaks… and How to Find Them Before the Teacher Does: A Calculus Supplement (A.K. Peters, Ltd., 2000). He received a Ph.D. in mathematics from the University of Maryland, College Park.**

The Mathematics Department

The Mathematics Department

*Welcomes *

*Welcomes*

**Marian Frazier**

*Assistant Professor of Mathematics*

*Assistant Professor of Mathematics*

*The College of Wooster*

*The College of Wooster*

**Thursday, November 9, 2017**

**Reception at 4 p.m. to 4:30 in King 203**

**Lecture at 4:30 to 5:30 in King 237*** *

*Lecture Topic*

*Lecture Topic*

* ***A theologian, a statistician, and an environmentalist walk into a church...**

** **

**More about the speaker**

My research is in computer experiments, specifically the development of efficient sequential designs for computer experiments. I am particularly interested in improving upon existing sequential design techniques used on non-stationary surfaces, or data with non-stationary qualities. My research focuses on achieving an accurate global fit of such surfaces.

Additionally, I have an interest in statistics education research and curricular design. I believe in including high-impact practices at all levels of the curriculum and I am dedicated to continuously exploring new ways to improve my students' experience and learning.

**Degrees**

**A., Kenyon College 2002****S. The Ohio State University 2004****D. The Ohio State University 2013**

**Courses Taught**

**Calculus and Analytic Geometry I****Probability and Statistics I**

The Math Majors Committee Presents

The Math Majors Committee Presents

**Patrick Keebler and Taiyo Scanion-Kimura from the Career Center**

*TopicS…*

*TopicS…*

**Exploring Careers with a Math Major**

Making a Resume Branding Oneself and

Networking with Alumni

Making a Resume Branding Oneself and

Networking with Alumni

**Wednesday, November 1**

**Lecture at 4:30 p.m., King 239 with Pizza to Follow**

*Please help*

**The Mathematics Department**

*Welcome Alumnus*

**Samuel Cole `09**

*Welcome Alumnus*

**Ph.D. Student, University of Illinois**

** **

**for a Fun Filled Day**

**Thursday, October 26, 2017**

**Pizza Lunch at 12:15 in King 306 **

**Afternoon Lecture at 4 p.m. in 203**

*Pizza Lunch Topic*

*Pizza Lunch Topic*

**Graduate School in Mathematics and **

**Math-Related Fields**

*Lecture Topic*

*Lecture Topic*

**Community Detection in Random Graphs**

** **

**Reception at 4 p.m. to 4:30 in King 203**

**Lecture at 4:30 to 5:30 in King 239**

**Partially funded by Alumni in Service to Oberlin College**

**More about the speaker**

Sam Cole is a Chicago native and Oberlin alum (’09). After graduating from Oberlin, he worked as a software developer and is now working on his PhD in math at the University of Illinois at Chicago. He has diverse mathematical interests spanning across combinatorics, linear algebra, and theoretical computer science, and has worked on problems in random graph theory and algorithms. His favorite Oberlin pastimes include biking on the bike path, going to concerts at the Conservatory, and hanging out with friends at The Feve.

2017 Tamura/Lilly Lecture

2017 Tamura/Lilly Lecture

2017 Tamura/Lilly Lecture

**Henry Segerman**

**Assistant Professor of Mathematics**

**Oklahoma State University**

** **

**3D Shadows: **

**Casting light on the fourth dimension**

**Jun Li, Math Major 2017**

**Honors Lecture**

**Low-Dimensional Manifolds and**

**Open Book Decompositions**

**Wednesday, May 3**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

**Jad Salem, Math Major 2017**

**Honors Lecture**

**Dynamical Systems, Binary Expansions,**

**and Continued Fractions**

**Thursday, May 4**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

**Andrea Allen, Math Major 2017**

**Honors Lecture**

**Average Shortest Path Length in a**

**Novel Small-World Network**

**Thursday, April 27**

**Refreshments, 4:00 p.m. ~ King 203**

**Lecture, 4:30 p.m. ~ King 239**

The Mathematics Department

## WELCOMES

# Peter D Hislop

# 2017 Distinguished Visitor

Professor of Mathematics

University of Kentucky

## Wednesday, March 1, 2017

### Reception, 4:00 p.m., King 203

Lecture, 4:30 p.m., King 239

Resonances in Quantum **Mechanics**

Resonances in Quantum

Resonances are states of atomic systems with long lifetimes. They look like bound states on short time scales but eventually decay. It is diﬃcult to describe resonances in the mathematical theory of quantum mechanics. Resonant energies look like eigenvalues of the energy matrix, but have small imaginary parts that cause states to decay in time. However, the energy matrix is self-adjoint so has only real eigenvalues. The correct way to describe resonances is to go into the complex plane by meromorphically continuing certain functions. This talk will present some basic examples of resonances in quantum mechanics and show how resonances can be properly deﬁned and estimated. This talk will be accessible to students with a background in linear algebra, calculus, and basic analysis.

The Mathematics Department

## Welcomes

# Peter D Hislop

# 2017 Fuzzy Vance Lecture

###### Professor of Mathematics

University of Kentucky

## Thursday, March 2, 2017

### 7:30 p.m. - King 306

Reception following

# The Mathematics and Physics of Electrons in Solids

The propagation properties of electrons in solids have been studied since the beginnings of quantum mechanics. The quantum theory of a perfect crystal provides the basis of our understanding of insulators, semi-conductors, and conductors. However, for such a simple model, the conductivity is inﬁnite. When impurities are included in the model, the propagation properties of the solid are signiﬁcantly altered. This situation more closely models the ﬁnite conductivity properties of real solids. The mathematics needed to describe these properties is both fascinating and challenging, and draws from functional analysis and probability theory. This talk will concentrate on simple examples that illustrate and provide insight into Anderson localization and ﬁnite conductivity.

**mathematics pizza lunch**

**Professor Robert Bosch**

**OC students build bridges between math & art:**

** a report from Jyväskylä, Finland**

###### In August, four OC students --- Simon Ever-Hale,

###### Max Grusky, Hank Guss, and Sage Jensen (all

###### alumni of Bob Bosch's MATH 397 class) --- shared

###### some of their original mathematical artwork in

###### Jyväskylä, Finland at the Bridges conference, an

###### annual celebration of mathematical connections

###### to art, music, architecture, education, and culture.

###### Bob will talk about the conference, his students'

###### beautiful contributions, and identify upcoming

###### opportunities for combining math and art.

WEB SITES

Bob Bosch's Power Point Presentation

### Simon Ever-Hale '18

Max Grusky '16

Henry Guss '16

Sage Jenson '17

### Jeffrey Witmer

Professor of Mathematics

###### I spent a week in Kenya with my son Joel (OC class of 2003), who was there to shoot a documentary film on the East Africa Dairy Development, a project of Heifer International. We spent some time on safari in the Masai Mara National Game Reserve, which included the following memorable event, told here by Joel:

###### Our driver took us two hours out on as legitimate a road as you get in these parts, and then got onto what can generously be described as a path, and at this point I'm thinking unpleasant thoughts. Just how long is it going to take to get back now? And for what? We are headed deeper into the savannah. Everything is savannah. Going into the middle of it isn’t any better than seeing it from the road because there is no ‘middle of it’ in any real sense. It’s an open space. And now we’re just inconveniently situated in it. This was a mistake. That’s what I’m thinking.

###### An hour into the path we are in a narrow valley between two sizable hills and I see a bloody zebra carcass at eye level a few feet up one hill. It's slumped against the base of a tree. This is interesting because until now every carcass I've seen has been well worn, if not skeletal. This one is red with blood. This excursion is paying off.

###### We drive forward a few feet, eyes still on the zebra because, you know, it's black and white and red all over. It's hard to look away. That is, until you clear the tree and on the other side you see a lion, tired but regal, her cub playing a few feet up the hill. She too is eye level. The adrenaline rushes and instinctively I contemplate death. I don't know how else to put it. Here is a mom protecting both her very young child — the guide later estimated the cub was 2-3 months old — and dinner for the next week and I'm sitting in an open air vehicle, completely vulnerable, sitting 20 feet away. Measuring in distance almost seems laughable, actually. A more accurate measure would be Seconds Left Alive Should This Lion Pounce. I'm guessing 3-5.

###### We sit there quietly, mostly. Any sound we make catches the lion's attention. She greets it with a stare. We remain still. But after a few minutes I start hearing noises on the opposite side of the truck. Not stealthy noises either. Noises that suggest the creature making them does not care about the situation, or maybe does not know. Oblivious or indifferent, it's causing a stir. Now the lion is looking beyond me, through the truck, to the noise machine a few yards away. I turn and see an elephant. This just got more interesting. We are idling between a killing machine made of fast twitch muscle fiber and an animal made of battering rams.

###### Anyway, this is getting long and we didn’t die, obviously. But what a way to go if we had!

**MATHEMATICS DEPARTMENT**

*WELCOMES SPEAKER*

**Ilesanmi Adeboye**

###### Assistant Professor of Mathematics

###### Wesleyan University

### Friday, November 4, 2016

### Reception 4:00 p.m., King 203

### Lecture 4:30 p.m. , King 239

**Euler's Equation and the Philosophy of Numbers**

This talk will begin with the statement of Euler's equation: “the most remarkable formula in mathematics." We will then develop the number system from the natural numbers to the complex numbers, exploring why new numbers are defined and how basic operations are generalized. Next, calculus will be used to represent familiar functions in an unfamiliar way, in order to reveal a key relationship. Finally, our numbers and functions will be combined to give a proof of Euler's equation.

**Mathematics Department**

*Welcomes Speaker*

*Welcomes Speaker*

**Ken Kleinman**

**The University of Mass Amherst**

**Department of Biostatistics**** **

** ****Monday, October 10, 2016**

**Reception 3:30 pm – King 203**

**Lecture 4:00 pm King 343**

** **

**The life of a statistician in a medical school: ****three examples from practice**

In this talk I review one example from each of the three main elements of what statisticians in practice do: 1) educate about statistical methods and interpretation; 2) develop statistical methods needed for situations that arise; and 3) collaborate on projects my colleagues are pursuing. I begin with the problem of how to interpret odds ratios from logistic regression-- a seemingly simple issue that has actually generated errors, papers, and workarounds. I then talk about surveillance for bioterrorism using doctors' visits, and a statistical method I worked on to speed up a computationally onerous test. Finally, I discuss my colleagues' use of a specialized study design-- the cluster-randomized trial-- and how I worked with them to develop an approach to make their studies more robust.

Kevin Woods

### Associate Professor of Mathematics

Last summer, I visited the Universidad de los Andes, in Bogota, Colombia, to work with Tristram Bogart (Oberlin College '01) and John Goodrick. We've finished up a paper called "Parametrized Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior" which is available on my website http://www.oberlin.edu/faculty/kwoods/papers.html. Here's a picture of me in the cloud forests of Colombia.