Affiliated Departments & Programs

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

The first-year seminar in mathematics provides an introduction to the rich and diverse nature of mathematics. Topics covered vary from one semester to the next (depending on faculty expertise) but typically span algebra and number theory, dynamical systems, probability and statistics, discrete mathematics, topology, geometry, logic, analysis and applied math. The course includes guest lectures from professors at Kenyon, a panel discussion with upper-class math majors and opportunities to learn about summer experiences and careers in mathematics. The course goals are threefold: to provide an overview of modern mathematics, which, while not exhaustive, exposes students to some exciting open questions and research problems in mathematics; to introduce students to some of the mathematical research being done at Kenyon; and to answer whatever questions students might have during their first semester here, while exposing them to useful resources and opportunities that are helpful in launching a meaningful college experience. Open only to first-year students. This course does not count toward any requirement for the major. Prerequisite or corequisite: MATH 112 (or equivalent) and concurrent enrollment in another MATH, STAT or SCMP course or permission of instructor. Offered every fall semester.

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 study instantaneous rates of change from both a qualitative geometric and a quantitative analytic perspective. We 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 is introduced. The course concludes 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. This counts toward the core course requirement for the major. Prerequisite: solid grounding in algebra, trigonometry and elementary functions. Offered every semester.

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 covers 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. This counts toward the discrete/combinatorial (column C) elective requirement for the major. Prerequisite: MATH 112 or a score or 4 or 5 on the BC calculus AP exam or permission of instructor. Offered every other year.

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. This counts toward either a discrete/combinatorial (column C) or continuous/analytic (column B) elective requirement for the major. Prerequisite: MATH 213. Offered every fall.

This course introduces students to the concepts, techniques and power of mathematical modeling. Both deterministic and probabilistic models are 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. This counts toward the computational/modeling/applied (column D) elective requirement for the major. Prerequisite: STAT 106 and MATH 224 or 258, or permission of instructor. Offered every other year.

This course consists 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 culminates 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 the completion of at least one two-semester sequence at the junior-senior level.

This is a basic course in statistics. The topics 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 are 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 is used throughout the course, and students engage in a wide variety of hands-on projects. This counts toward the core course requirement for the major. Students with credit for STAT 116 cannot take STAT 106 for credit. No prerequisite. Offered every semester.

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 provide the foundation for the course. Classical interference methods that rely on the normality of the error terms are thoroughly discussed, and general approaches for dealing with data where such conditions are not met are provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, are presented. Students use statistical software throughout the course to write and present statistical reports. The culminating project is 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. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or 116, or a score of 4 or 5 on the AP statistics exam. Offered every semester.

Each offering of this course approaches the study of variability using a particular set of statistical tools (such as Bayesian Analysis, biostatistics, sports analytics, experimental design or statistical machine learning). Specific statistical methodology within a subfield of the discipline is examined. A large component of each offering involves intensive projects in which students are expected to determine which statistical methods are appropriate for a given setting before analyzing data. As part of these projects and daily activities, students use R to analyze data to make inferences about the population characteristics of interest. Additionally, written and oral communication are a regular part of the course. The course may be repeated for credit as long as the subfield is different. That is, students may receive credit for each specific subfield only once. This counts toward the statistical/data science (column E) elective for the major and toward an elective for the math and statistics minor. Prerequisite: any STAT course at the 200 level or higher or permission of the instructor. Offered every spring.\nAdditional information for different subfields: https://www.kenyon.edu/academics/departments-and-majors/mathematics-statistics/academic-program-requirements/courses-in-statistics/stat-306-topics/

This course focuses on linear regression models. Simple linear regression with one predictor variable serves as the starting point. Models, inferences, diagnostics and remedial measures for dealing with invalid assumptions are examined. The matrix approach to simple linear regression is presented and used to develop more general multiple regression models. Building and evaluating models for real data are the ultimate goals of the course. Time series models, nonlinear regression models and logistic regression models also may be studied if time permits. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or 116, and MATH 224. Offered every other spring.

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 accompany and corroborate many of the theoretical results. Course methods often are applied to real data sets. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: MATH 336. Offered every other spring.