Contact Jeffrey
Mail Code NS
Jeffrey Barton
Cole Science Center 308B
413.559.5577
Mail Code NS
Jeffrey Barton
Cole Science Center 308B
413.559.5577
Jeffrey Barton's current research lies in the intersection of mathematics and political science where he studies measures of fairness in relation to partisan gerrymandering.
He has published a new mathematical standard for determining fair seat allocations in single-member plurality electoral systems, and he is currently collaborating with economist and political scientist Jon Eguia at Michigan State University on a method for resolving the partisan advantage displayed by a redistricting map into its component parts: state geography, state map-drawing rules, and gerrymandering.
His teaching interests include mathematical modeling, probability, statistics, the mathematics of fairness, and facilitating student collaborations with business and industry partners.
Barton received his B.S. in mathematics and English (creative writing) from Louisiana State University. His Ph.D. was completed in analytic number theory under the direction of Jeff Vaaler at The University of Texas at Austin. He subsequently served on the faculty at Birmingham-Southern College.
This course introduces students to important mathematical ideas in a variety of contexts where issues of fairness naturally arise. A primary focus of the course will be on voting methods, voting rights, voting power, and gerrymandering, including an examination of recent court cases involving the Voting Rights Act. Students will explore different notions of fairness and will use hands-on activities to apply the ideas to scenarios such as the sharing of a cake or the splitting of shared resources in a divorce settlement. We will ask questions such as "Is the division envy free? Is it spite free?", and we will examine whether it is possible for a single solution to satisfy all possible facets of fairness. There are no mathematical prerequisites for this course.
This course introduces students to fundamental statistical methods and tools used in data science to produce, analyze, and communicate about data. Topics will include measures of center and spread, data visualizations, hypothesis testing, confidence intervals, linear regression, and others as time allows. The course emphasizes conceptual understanding and written, oral, and visual communication while de-emphasizing memorization, algebraic manipulation, and by-hand calculation. The course will employ Python code to implement methods and analyze data. There are no formal prerequisites for the course, but comfort with college algebra and some coding experience will be a plus.
This course introduces students to fundamental calculus concepts via rich applied contexts. The course prioritizes mathematical thinking, experimentation, and clear communication while de-emphasizing symbolic manipulation and rote exercises. We will apply the mathematical ideas such as integration, Taylor series, dynamical systems, functions of several variables, and periodic functions in a variety of contexts including epidemiology, ecology, and numerical approximation. Students will use Python programs routinely to carry out calculations, experiment with parameter choices, and create informative graphs. Coding experience is not assumed, but some comfort with coding will be a plus. While there are no formal mathematical prerequisites, students should be comfortable with the material from Calculus I and college level algebra. Keywords:mathematics, calculus, modeling
This course introduces students to fundamental calculus concepts via rich applied contexts. The course prioritizes mathematical thinking, experimentation, and clear communication while de-emphasizing symbolic manipulation and rote exercises. We will apply the ideas of calculus such as derivatives, differential equations, and integrals in a variety of contexts including epidemiology, ecology, and environmental sustainability. Students will use computers routinely to carry out calculations, experiment with parameter choices, and create informative graphs. Coding experience is not assumed, but some comfort with coding will be a plus. While there are no formal mathematical prerequisites, students should be comfortable with college level algebra. Keywords:Calculus, mathematics, modeling, differential equations
This course introduces students to fundamental topics in linear algebra. We will use Python to visualize concepts, implement algorithms, and perform calculations that would be intractable by hand. No prior Python experience is required. The focus of the course will be on applications in a variety of contexts, though there will be some theory as well. Topics will include systems of equations, vectors, matrix algebra, linear independence, eigenvalues and eigenvectors, and matrix factorization. While the course has no formal prerequisites in terms of mathematics or coding, it will require some mathematical maturity and/or comfort with programming. Keywords:Linear algebra, eigenvalues, matrices, vectors
In this course, students will engage with mathematical modeling in two important ways: by learning to use existing models as powerful problem-solving tools and by developing their skills in creating their own models. The kind of models we examine are known as discrete dynamical systems, which are just models that specify mathematically how a quantity changes from one time step to the next. We develop such models in a variety of important contexts including populations and sustainability, infectious diseases, blood alcohol concentration, and ranking systems for sports teams or web searches. We only introduce the mathematics necessary for answering important questions in each context, and we will use Microsoft Office Excel as our modeling software throughout the course. Some mathematical concepts we will cover include exponential growth, equilibrium values, and stability. No prior college-level mathematics or experience with Excel is assumed. Keywords:Modeling, equilibrium values, Excel, math
This course introduces students to foundational topics in probability through applications to games, puzzles, paradoxes, and problems. Included will be discussions of independence, discrete and continuous random variables, conditional probability, Bayes' Theorem, random walks, and the Law of Large Numbers. Along the way we will discover the important role that calculus plays in probability (though no knowledge of calculus is assumed), and we will see glimpses of more advanced topics such as the existence of different sizes of infinity and measure theory. Keywords:Probability, randomness, chance, games, math