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
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 212 or a score or 5 on the BC calculus AP exam. 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 212 and MATH 213. Offered every fall.
The senior seminar in mathematics provides a structure to aid students in successfully completing the Mathematics and Statistics Capstone requirement. Students who participate in a 3-2 program ordinarily take this course in their junior year. Students with December anticipated graduation dates take the seminar in their sixth semester (in the third semester before graduation). This schedule makes it possible for students who do not succeed in their first try at the capstone to take full advantage of the “second chance” option without delaying their graduation timeline. \n Students who do not successfully complete their capstone in the fall semester will be assigned NG (no grade) at the end of the senior seminar. This designation will change to a CR when the student successfully completes the capstone, usually at the end of the following semester. This course is a core requirement for the mathematics major. Prerequisite: MATH 222 and at least one 300+-level course in Mathematics or Statistics. The course is offered every fall semester. The course is credit/no credit.
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.
This course provides a mathematical introduction to probability and statistics using R statistical software. The primary goal of the course is to learn and apply Monte-Carlo simulation techniques to a wide variety of problems. We focus on solving problems from a numerical point of view, with methods to complete numerical integration, root finding, curve fitting, variance reduction and optimization. Core knowledge of R and basic programming concepts are introduced. Case studies and projects are independently completed throughout the semester. This counts toward the statistical/data science (column E) elective for the major. Prerequisite: STAT 106 or STAT 116. Offered every other year.
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. Prerequisite: any STAT course at the 200 level or higher. 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.