Marie Snipes joined the Kenyon math department in 2009. Her research interests lie in the field of geometric measure theory, an area of math that uses measure theory to analyze geometric properties of sets and has its origins in the study of soap films. Prior to her doctoral studies at the University of Michigan, Marie spent four years in the Air Force conducting statistical analyses and developing mathematical models of personnel data. This applied math experience complements her academic perspective as a mathematics instructor.

Outside the classroom, Marie studies applied topology through a hands-on study of continuous deformations of phyllosilicate minerals (in other words, throwing pottery). She also enjoys playing racquetball, Scrabble and chess.

### Education

2009 — Doctor of Philosophy from University of Michigan

2005 — Master of Science from University of Michigan

1999 — Bachelor of Science from Harvey Mudd College

### Courses Recently Taught

INDS 100

## Data Analysis: Seeing w/ Data

#### INDS 100

In this course, students will gain experience analyzing, interpreting, and critiquing quantitative claims and communicating results and conclusions using graphical representations of data. Examples will be drawn from across the natural and social sciences, with context provided for each data set, so that students from any disciplinary background can participate in and benefit from this course. This course has no pre-requisites. It will be taught at a level accessible to all Kenyon students. Excellent preparation for further work on quantitative topics, this course will hone students' ability to apply mathematical techniques including graphing, statistics, linear and non-linear regression, and modeling the graphical behavior of mathematical functions to understanding and interpreting data. Students will practice these skills by engaging in critical reading of primary sources, oral presentation of quantitative data, and expression of analytic ideas in writing. Assessment will be based on in-class assignments, monthly quizzes, and oral reports on data-driven projects selected in consultation with the instructor.

MATH 106

## Elements of Statistics

#### MATH 106

This is a basic course in statistics. The topics to be covered are the nature of statistical reasoning, graphical and descriptive statistical methods, design of experiments, sampling methods, probability, probability distributions, sampling distributions, estimation and statistical inference. Confidence intervals and hypothesis tests for means and proportions will be studied in the one- and two-sample settings. The course concludes with inference regarding correlation, linear regression, chi-square tests for two-way tables, and one-way ANOVA. Statistical software will be used throughout the course, and students will be engaged in a wide variety of hands-on projects. No prerequisite. Offered every semester.

MATH 111Y

## Calculus/Elementary Functions

#### MATH 111Y

See MATH 110Y description.

MATH 112

## Calculus II

#### MATH 112

The second in a three-semester calculus sequence, this course has two primary foci. The first is integration, including techniques of integration, numerical methods and applications of integration. This study leads into the analysis of differential equations by separation of variables, Euler's method and slope fields. The second focus is the notion of convergence, as manifested in improper integrals, sequences and series, particularly Taylor series. Prerequisite: MATH 111 or AP score of 4 or 5 on Calculus AB exam or an AB subscore of 4 or 5 on the Calculus BC exam or permission of instructor. Offered every semester.

MATH 206

## Data Analysis

#### MATH 206

This course focuses on choosing, fitting, assessing and using statistical models. Simple linear regression, multiple regression, analysis of variance, general linear models, logistic regression and discrete data analysis will provide the foundation for the course. Classical interference methods that rely on the normality of the error terms will be thoroughly discussed, and general approaches for dealing with data where such conditions are not met will be provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, will be presented. Students will use statistical software throughout the course to write and present statistical reports. The culminating project will be a complete data analysis report for a real problem chosen by the student. The MATH 106-206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science and many other fields. Prerequisite: MATH 106 or 116 or a score of 4 or 5 on the Statistics AP exam. Offered every spring.

MATH 224

## Linear Algebra

#### MATH 224

This course will focus on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are highly useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising often in fields such as computer science, physics, chemistry, biology and economics. In this course, we will use a computer algebra system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality and diagonalization. Applications will be included throughout the course. Prerequisite: MATH 213. Typically offered three out of four semesters.

MATH 231

## Mathematical Problem Solving

#### MATH 231

Looking at a problem in a creative way and seeking out different methods toward solving it are essential skills in mathematics and elsewhere. In this course, students will build their problem-solving intuition and skills by working on challenging and fun mathematical problems. Common problem-solving techniques in mathematics will be covered in each class meeting, followed by collaboration and group discussions, which will be the central part of the course. The course will culminate with the Putnam exam on the first Saturday in December. Interested students who have a conflict with that date should contact the instructor. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus exam or permission of instructor.

MATH 291

## Special Topic

#### MATH 291

Special Topic

MATH 333

## Differential Equations

#### MATH 333

Differential equations arise naturally to model dynamical systems such as often occur in physics, biology, chemistry and economics, and have given major impetus to other fields in mathematics, such as topology and the theory of chaos. This course covers basic analytic, numerical and qualitative methods for the solution and understanding of ordinary differential equations. Computer-based technology will be used. Prerequisite: MATH 224 or PHYS 245 or permission of instructor. Offered every other year.

MATH 341

## Real Analysis I

#### MATH 341

This course is a first introduction to real analysis. "Real" refers to the real numbers. Much of our work will revolve around the real number system. We will start by carefully considering the axioms that describe it. "Analysis" is the branch of mathematics that deals with limiting processes. Thus the concept of distance also will be a major theme of the course. In the context of a general metric space (a space in which we can measure distances), we will consider open and closed sets, limits of sequences, limits of functions, continuity, completeness compactness, and connectedness. Other topics may be included, if time permits. Junior standing is recommended. Prerequisite: MATH 213 and 222. Offered every other fall.

MATH 352

## Complex Functions

#### MATH 352

The course starts with an introduction to the complex numbers and the complex plane. Next students are asked to consider what it might mean to say that a complex function is differentiable (or analytic, as it is called in this context). For a complex function that takes a complex number z to f(z), it is easy to write down (and make sense of) the statement that f is analytic at z if \n\n<img src="http://www.kenyon.edu/files/resources/math_catalog.jpg" alt="" width="100" />\n\nexists. Subsequently, we will study the amazing results that come from making such a seemingly innocent assumption. Differentiability for functions of one complex variable turns out to be a very different thing from differentiability in functions of one real variable. Topics covered will include analyticity and the Cauchy-Riemann equations, complex integration, Cauchy's theorem and its consequences, connections to power series, and the residue theorem and its applications. Prerequisite: MATH 224. Offered every other year.

MATH 360

## Topology

#### MATH 360

Topology is an area of mathematics concerned with properties of geometric objects that remain the same when the objects are "continuously deformed." Three of these key properties in topology are compactness, connectedness and continuity, and the mathematics associated with these concepts is the focus of the course. Compactness is a general idea helping us to more fully understand the concept of limit, whether of numbers, functions, or even geometric objects. For example, the fact that a closed interval (or square, or cube, or n-dimensional ball) is compact is required for basic theorems of calculus. Connectedness is a concept generalizing the intuitive idea that an object is in one piece: the most famous of all the fractals, the Mandelbrot Set, is connected, even though its best computer-graphics representation might make this seem doubtful. Continuous functions are studied in calculus, and the general concept can be thought of as a way by which functions permit us to compare properties of different spaces or as a way of modifying one space so that it has the shape or properties of another. Engineering, chemistry and physics are among the subjects that find topology useful. The course will touch on selected topics that are used in applications. Prerequisite: MATH 222 or permission of instructor. Typically offered every two to three years.

MATH 441

## Real Analysis II

#### MATH 441

This course follows Real Analysis I. Topics will include a study differentiation and (Riemann) integration of functions of one variable, sequences and series of functions, power series and their properties, iteration and fixed points. Other topics may be included as time permits. For example: a discussion of Newton's method or other numerical techniques; differentiation and integration of functions of several variables; spaces of continuous functions; the implicit function theorem; and everywhere continuous, nowhere differentiable functions. Prerequisite: MATH 341. Offered every other spring.

MATH 460

## Topology

#### MATH 460

Topology is a relatively new branch of geometry that studies very general properties of geometric objects, how these objects can be modified, and the relations between them. Three key concepts in topology are compactness, connectedness, and continuity, and the mathematics associated with these concepts is the focus of the course. Compactness is a general idea helping us to more fully understand the concept of limit, whether of numbers, functions, or even geometric objects. For example, the fact that a closed interval (or square, or cube, or n-dimensional ball) is compact is required for basic theorems of calculus. Connectedness is a concept generalizing the intuitive idea that an object is in one piece: the most famous of all the fractals, the Mandelbrot Set, is connected, even though its best computer-graphics representation might make this seem doubtful. Continuous functions are studied in calculus, and the general concept can be thought of as a way by which functions permit us to compare properties of different spaces or as a way of modifying one space so that it has the shape or properties of another. Economics, chemistry, and physics are among the subjects that find topology useful. The course will touch on selected topics that are used in applications. Prerequisite: MATH 222 or permission of instructor. Offered every three to five years, depending on student interest.

MATH 493

## Individual Study

#### MATH 493

Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot normally be used to fulfill requirements for the major. Typically, individual study will earn .5 unit or .25 unit of credit.\nTo qualify, a student must identify a member of the Mathematics Department willing to direct the project. The professor, in consultation with the student, will create a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describe in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals, and so on). Individual studies also require the approval of the department chair. The department expects the student to meet regularly with his or her instructor for at least one hour per week.\nStudents must begin discussion of their proposed individual study well in advance, preferably the semester before the course is to take place. Prerequisite: permission of instructor and department chair.

### Academic & Scholarly Achievements

2013

David, G., and Snipes, M. A. A Non-probabilistic proof of the Assouad embedding theorem with bounds on the dimension. Analysis and Geometry in Metric Spaces, Vol. 1 (2013), 36--41.

2013

Snipes, M. A. Flat forms in Banach Spaces. J. Geom. Anal., Vol. 23 (2013), 490-538.

2012

Lutgendorf, M. A., Snipes, M. A., Rau, T., Busch, J. M., Zelig, C. M., and Magann, E. F. Reports to the Navy's Family Advocacy Program: Impact of removal of mandatory reporting for domestic violence. Mil. Med., Vol. 177 (2012), 702--708.

2008

Snipes, M. A., and Ward, L. A. Convergence properties of harmonic measure distributions for planar domains. Complex Var. Elliptic Equ., Vol. 53 (2008), 897--913.

2005

Snipes, M. A., and Ward L. A. Realising step functions as harmonic measure distributions of planar domains. Ann. Acad. Sci. Fenn. Math., Vol. 30 (2005), 353--360.