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 will vary from one semester to the next (depending on faculty expertise) but will 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: 1) to provide an overview of modern mathematics, which, while not exhaustive, will expose students to some exciting open questions and research problems in mathematics; 2) to introduce students to some of the mathematical research being done at Kenyon and; 3) 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 towards any requirement for the major. Prerequisite or corequisite: MATH 112 (or equivalent) and concurrently enrolled in another MATH, STAT or SCMP course or permission of instructor. Offered every fall 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 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. 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.

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. This does not count toward any requirement for the major. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus exam or permission of instructor.

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 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. 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.

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. Individual study course may be counted as electives in the mathematics major, subject to consultation with and approval by the department of Mathematics and Statistics. Permission of instructor and department chair required. No prerequisite.\n\n

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 the completion of at least one two-semester sequence at the junior-senor level.

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. 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 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. This counts toward the Statistical/Data Science (Column E) elective for the major and will also count toward an elective for the math and statistics minor. Prerequisite: STAT 106 or 116 or a score of 4 or 5 on the Statistics AP exam. Offered every semester.

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. This counts toward the Statistical/Data Science (Column E) elective for the major. Prerequisite: STAT 106 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 will accompany and corroborate many of the theoretical results. Course methods often will be 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.