Brian D. Jones began teaching at Kenyon in 1995. His research interests are applied probability, random graphs, mathematical modeling, combinatorial probability and generating functions. In 2007, he designed the course Random Structures, a class focused on problem solving that draws from all of these topics. His current research includes using probability to characterize the coefficients of special large degree polynomials and applying probabilistic methods to bracket distances on the continuum using discrete metrics. He often contributes statistical analyses to the research of Kenyon colleagues in biology, with recent works including acidic effects on cell division of E. coli, transcriptomic response and recovery of E. coli after acid shock and transcriptomic response in Bacillus subtilis under pH stress.

Brian has a particular passion for writing creative, challenging and fun problems in mathematics and statistics. He has worked in industry as a process development engineer, mathematical…

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Brian D. Jones began teaching at Kenyon in 1995. His research interests are applied probability, random graphs, mathematical modeling, combinatorial probability and generating functions. In 2007, he designed the course Random Structures, a class focused on problem solving that draws from all of these topics. His current research includes using probability to characterize the coefficients of special large degree polynomials and applying probabilistic methods to bracket distances on the continuum using discrete metrics. He often contributes statistical analyses to the research of Kenyon colleagues in biology, with recent works including acidic effects on cell division of E. coli, transcriptomic response and recovery of E. coli after acid shock and transcriptomic response in Bacillus subtilis under pH stress.

Brian has a particular passion for writing creative, challenging and fun problems in mathematics and statistics. He has worked in industry as a process development engineer, mathematical modeler and statistical analyst and these experiences often find their way into his exercises and projects.

Outside the classroom, Jones enjoys music of all genres, baseball, running, hiking, canoeing and juggling. He has served as advisor to the Kenyon College chess and juggling clubs.

### Education

1995 — Doctor of Philosophy from The Ohio State University

1989 — Master of Science from The Ohio State University

1985 — Bachelor of Science from The Ohio State University

### Courses Recently Taught

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 111

## Calculus I

#### MATH 111

The first in a three-semester calculus sequence, this course covers the basic ideas of differential calculus. Differential calculus is concerned primarily with the fundamental problem of determining instantaneous rates of change. In this course we will study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We will cover in detail the underlying theory, techniques and applications of the derivative. The problem of anti-differentiation, identifying quantities given their rates of change, also will be introduced. The course will conclude by relating the process of anti-differentiation to the problem of finding the area beneath curves, thus providing an intuitive link between differential calculus and integral calculus. Those who have had a year of high school calculus but do not have advanced placement credit for MATH 111 should take the calculus placement exam to determine whether they are ready for MATH 112. Students who have 0.5 units of credit for calculus may not receive credit for MATH 111. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

MATH 206

MATH 227

## Combinatorics

#### MATH 227

Combinatorics is, broadly speaking, the study of finite sets and finite mathematical structures. A great many mathematical topics are included in this description, including graph theory, combinatorial designs, partially ordered sets, networks, lattices and Boolean algebras and combinatorial methods of counting, including combinations and permutations, partitions, generating functions, recurring relations, the principle of inclusion and exclusion, and the Stirling and Catalan numbers. This course will cover a selection of these topics. Combinatorial mathematics has applications in a wide variety of nonmathematical areas, including computer science (both in algorithms and in hardware design), chemistry, sociology, government and urban planning; this course may be especially appropriate for students interested in the mathematics related to one of these fields. Prerequisite: MATH 112 or a score or 4 or 5 on the BC Calculus AP exam or permission of instructor. Offered every other year.

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 236

## Random Structures

#### MATH 236

This course will explore the theory, structure, applications and interesting consequences when probability is introduced to mathematical objects. Some of the core topics will be random graphs, random walks and Markov processes, as well as randomness applied to sets, permutations, polynomials, functions, integer partitions and codes. Previous study of all of these mathematical objects is not a prerequisite, as essential background will be covered during the course. In addition to studying the random structures themselves, a concurrent focus of the course will be the development of mathematical tools to analyze them, such as combinatorial concepts, indicator variables, generating functions, discrete distributions, laws of large numbers, asymptotic theory and computer simulation. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus AP exam or permission of instructor. Generally offered every other year.

MATH 336

## Probability

#### MATH 336

This course provides a calculus-based introduction to probability. Topics include basic probability theory, random variables, discrete and continuous distributions, mathematical expectation, functions of random variables and asymptotic theory. Prerequisite: MATH 213. Offered every fall.

MATH 347

## Mathematical Models

#### MATH 347

This course introduces students to the concepts, techniques and power of mathematical modeling. Both deterministic and probabilistic models will be explored, with examples taken from the social, physical and life sciences. Students engage cooperatively and individually in the formulation of mathematical models and in learning mathematical techniques used to investigate those models. Prerequisite: STAT 106 and MATH 224 or 258 or permission of instructor. Offered every other year.

MATH 416

## Linear Regression Models

#### MATH 416

This course will focus on linear regression models. Simple linear regression with one predictor variable will serve as the starting point. Models, inferences, diagnostics and remedial measures for dealing with invalid assumptions will be examined. The matrix approach to simple linear regression will be presented and used to develop more general multiple regression models. Building and evaluating models for real data will be the ultimate goal of the course. Time series models, nonlinear regression models, and logistic regression models also may be studied if time permits. Prerequisite: MATH 106, 213 and 224 or permission of instructor. Offered every other spring.

MATH 436

## Mathematical Statistics

#### MATH 436

This course follows MATH 336 and introduces the mathematical theory of statistics. Topics include sampling distributions, order statistics, point estimation, maximum likelihood estimation, methods for comparing estimators, interval estimation, moment generating functions, bivariate transformations, likelihood ratio tests and hypothesis testing. Computer simulations will accompany and corroborate many of the theoretical results. Course methods often will be applied to real data sets. Prerequisite: MATH 336. Offered every other spring.

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 be used to fulfill requirements for the major. Individual studies will earn 0.25–0.50 units of credit. To 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). The department expects the student to meet regularly with his or her instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the registrar's deadline. Permission of instructor and department chair required. No prerequisite.\n\n

MATH 498

## Senior Honors

#### MATH 498

This course will consist largely of an independent project in which students read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study will culminate in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Permission of department chair required. Prerequisite: Senior standing and at least one "depth sequence" completed.

STAT 106

## Elements of Statistics

#### STAT 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.

STAT 206

## Data Analysis

#### STAT 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: STAT 106 or 116 or a score of 4 or 5 on the Statistics AP exam. Offered every semester.

STAT 436

## Mathematical Statistics

#### STAT 436

This course follows MATH 336 and introduces the mathematical theory of statistics. Topics include sampling distributions, order statistics, point estimation, maximum likelihood estimation, methods for comparing estimators, interval estimation, moment generating functions, bivariate transformations, likelihood ratio tests and hypothesis testing. Computer simulations will accompany and corroborate many of the theoretical results. Course methods often will be applied to real data sets. Prerequisite: MATH 336. Offered every other spring.

### Academic & Scholarly Achievements

2008

Wilks, J. C., Cleeton, S. H., Lee, G. E., Kitko, R. D., Jones, B. D., BonDurant, S. S., Slonczewski, J. L. Acid and Base Stress and Transcriptomic Response in Bacillus subtilis. Submitted to *Journal of Applied and Environmental Microbiology*, August 2008.

2008

Kannan, G., Wilks, J. C., Fitzgerald, D. M., Jones, B. D., BonDurant, S. S., Slonczewski, J. L. Rapid Acid Treatment of *Escherichia coli*: Transcriptomic Response and Recovery. *BMC Microbiology* **8:37**, 2008.

http://www.biomedcentral.com/1471-2180/8/37

2006

Hayes, E. T., Wilks, J. C., Sanfilippo, P., Yohannes, E., Tate, D. P., Jones, B. D., Radmacher, M. D., BonDurant, S. S., Slonczewski, J. L. Oxygen Limitation Modulates pH Regulation of Catabolism and Hydrogenases, Multidrug Transporters, and Envelope Composition in *Escherichia coli*K-12. *BMC Microbiology* **6:89**, 2006.

http://www.biomedcentral.com/1471-2180/6/89

2001

1999