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2017-2018 Academic Catalog [ARCHIVED CATALOG]
Mathematics Courses
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Mathematics and Statistics
Mathematics and Statistics
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MAT 115 - Introduction to Statistics 4 credits (Fall and Spring)
Cross-listed as: SST 115 . Introduces the notions of variability and uncertainty and such common statistical concepts as point and interval estimation and hypothesis testing. Data-oriented, with real-world examples chosen from the social and biological sciences. The computer is used for data analysis and to illustrate probabilistic and statistical concepts. A student who takes MAT-115 cannot receive credit for MAT 209 .
Prerequisite: Two years of high school algebra and second semester of first-year standing.
Instructor: Staff -
MAT 123 - Functions and Differential Calculus 4 credits (Fall)
An introductory course in mathematics and the first in a two-course sequence. This first semester is an introduction to the differential calculus of functions of one variable with an extensive review of precalculus topics such as algebra and functions. This review, together with an emphasis on developing problem-solving skills, is designed to help students learn to do mathematics at the college level. MAT 123-MAT 124 has the same calculus content as MAT 131 .
Prerequisite: Two years of high school algebra.
Instructor: Staff -
MAT 124 - Functions and Integral Calculus 4 credits (Spring)
A continuation of MAT 123 . An introduction to the integral calculus of functions of one variable. Topics include the definite integral, techniques of integration, and applications of the integral. Successful completion of this course prepares students for MAT 133 .
Prerequisite: MAT 123 .
Instructor: Staff -
MAT 131 - Calculus I 4 credits (Fall)
The first in a two-course sequence. An introduction to the differential and integral calculus of functions of one variable. Also introduces a few concepts and methods of differential equations.
Prerequisite: Good preparation, including trigonometry, or departmental placement.
Instructor: Staff -
MAT 133 - Calculus II 4 credits (Fall and Spring)
A continuation of MAT 131 . Topics include functions of more than one variable: partial and total derivatives, multiple integrals, vector-valued functions, and parametrized curves. Additional topics may include applications to differential equations, line integrals, and Green’s Theorem.
Prerequisite: Mathematics MAT 124 or MAT 131 .
Instructor: Staff -
MAT 208 - Discrete Structures 4 credits (Spring)
See CSC 208 .
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MAT 209 - Applied Statistics 4 credits (Fall and Spring)
The course covers the application of basic statistical methods such as univariate graphics and summary statistics, basic statistical inference for one and two samples, linear regression (simple and multiple), one- and two-way ANOVA, and categorical data analysis. Students use statistical software to analyze data and conduct simulations. A student who takes Mathematics 209 cannot receive credit for MAT 115 .
Prerequisite: MAT 124 or MAT 131 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 215 - Linear Algebra 4 credits (Fall and Spring)
A unified study of the concepts underlying linear systems and linear transformations and of the techniques for using them. Topics: matrix algebra, rank, orthogonality, vector spaces and dimension, eigenvectors and eigenvalues. Typical applications: fitting lines and curves to data, Markov processes, linear differential equations.
Prerequisite: MAT 133 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 218 - Discrete Bridges to Advanced Mathematics 4 credits (Fall and Spring)
Discrete Bridges to Advanced Mathematics courses prepare students for the 300-level foundations courses through careful attention to mathematical proof writing and creative problem solving. Skill building is a fundamental component: skills include working with fundamental tools of logic to write convincing arguments, grappling deeply with difficult mathematical problems, and reading upper-level undergraduate mathematical texts. Math 218 addresses counting techniques and other discrete topics needed for computer science. May be repeated once for credit when content changes with permission of instructor. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 215 .
Instructor: Staff -
MAT 220 - Differential Equations 4 credits (Spring)
First and second order differential equations; series solutions and Fourier series; linear and nonlinear systems of differential equations; applications.
Prerequisite: MAT 215 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 222 - Bridges to Advanced Mathematics 4 credits (Fall or Spring)
Bridges to Advanced Mathematics courses prepare students for 300-level foundations courses through careful attention to mathematical proof writing and creative problem solving. Skill building is a fundamental component: skills include working with fundamental tools of logic to write convincing arguments, grappling deeply with difficult mathematical problems, and reading upper-level undergraduate mathematics texts. May be repeated once for credit when content changes with permission of instructor. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 215 .
Instructor: Staff -
MAT 271 - Problem-Solving Seminar 1 credits (Fall)
Students solve challenging mathematics problems and present solutions. Prepares students to take the Putnam Examination, if they wish. May be repeated for credit.
Prerequisite or co-requisite: Completion of, or concurrent registration in
S/D/F only.
Instructor: Staff -
MAT 306 - Mathematical Modeling 4 credits (Spring)
An introduction to the process and techniques of modeling “real-world” situations, using topics from linear algebra and differential equations. Appropriate mathematics, including numerical methods, developed when needed. Models drawn from both the social and natural sciences.
Prerequisite: MAT 220 .
Note: Plus-2 option available. Not offered every year. Offered in alternate years.
Instructor: Staff -
MAT 309 - Design and Analysis of Experiments 4 credits (Spring)
In addition to a short review of hypothesis testing, confidence intervals, and 1-way ANOVA, this course incorporates experiments from several disciplines to explore design and analysis techniques. Topics include factorial designs, block designs (including latin square and split plot designs), random, fixed, and mixed effects models, crossed and nested factors, contrasts, checking assumptions, and proper analysis when assumptions are not met.
Prerequisite: MAT 209 or MAT 336 .
Note: Plus-2 option available. Not offered every year. Offered in alternate years.
Instructor: Staff -
MAT 310 - Statistical Modeling 4 credits (Fall)
This course will focus on investigative statistics labs emphasizing the process of data collection and data analysis relevant for science, social science, and mathematics students. This course incorporates case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include nonparametric tests, designing an experiment, and generalized linear models.
Prerequisite: MAT 209 or MAT 336 .
Instructor: Staff -
MAT 314 - Topics in Applied Mathematics 4 credits (Spring)
Topics include, but are not limited to, one of the following: Chaos and Fractals (one- and two-dimensional discrete dynamics, iterated function systems, fractal dimension), Fourier Analysis (fast Fourier transform, Fourier series, wavelets), or Partial Differential Equations (heat and wave equation, eigenfunction expansions). May be repeated for credit when content changes. For current course content see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: Varies depending on topic.
Note: Plus-2 option available. Offered in alternate years.
Instructor: Staff -
MAT 316 - Foundations of Analysis 4 credits (Fall and Spring)
A thorough study of the topology of the real line and of limits of functions of one real variable. This theory is then used to develop the theory of the derivative and integral of functions of one real variable and also sequences and series of real numbers and functions.
Prerequisite: MAT 218 or MAT 222 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 317 - Advanced Topics in Analysis 4 credits (Fall)
Analysts seek to understand mathematical entities, such as numbers, vectors, and functions, through approximation, convergence, and representation. This approach has yielded important insights in pure mathematics, in areas like differential equations, geometry, and number theory, as well asapplications in areas like signal processing, data analysis, and quantum theory. This course will build on the foundations of analysis, exploring an advanced topic in this area. The course will regularly provide an opportunity to pursue research. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 316 .
Instructor: Staff -
MAT 321 - Foundations of Abstract Algebra 4 credits (Fall and Spring)
The study of algebraic structures, with emphasis on formal systems such as groups, rings, and fields.
Prerequisite: MAT 218 or MAT 222 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 322 - Advanced Topics in Algebra 4 credits (Spring)
Algebraists study sets with operations, such as matrices under addition and multiplication. Algebraic structures are central in modern mathematics, arising in areas like number theory and combinatorics, topology and geometry, and also finding applications in fields like cryptography and coding theory - even data analysis and music theory. This course will build on the foundations of abstract algebra, exploring an advanced topic in this area. The course will regularly provide an opportunity to pursue research. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: MAT 321 .
Instructor: Staff -
MAT 335 - Probability and Statistics I 4 credits (Fall)
An introduction to the mathematical theory of probability and statistical inference. Discrete and continuous distributions, as well as sampling distributions and the limit theorems of probability, will be introduced. The importance of randomization and simulation for computing statistical probabilities will be explored.
Prerequisite: MAT 215 ; and MAT 209 , or MAT 218 , or MAT 220 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 336 - Probability and Statistics II 4 credits (Spring)
A systematic treatment of mathematical statistics based on probability theory. Topics will include: principles of estimation and hypothesis testing, chi-square tests, linear models including regression and analysis of variance, and nonparametric inference. A variety of applications will be considered.
Prerequisite: MAT 335 .
Note: Plus-2 option available.
Instructor: Staff -
MAT 444 - Senior Seminar 4 credits (Spring)
Advanced course with varying content. Strongly recommended for students considering further work in mathematics and statistics. May be repeated for credit when content changes. For current course content please see the variable topic course listing below or search the online live schedule of courses.
Prerequisite: Will vary depending on topic.
Note: Plus-2 option available.
Instructor: Staff
Special Topics-Fall
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MAT 295-01 - Special Topic: Introduction to Data Science 4 credits (Fall)
This course introduces core topics in data science using R programming. This includes introductions to getting and cleaning data, data management, exploratory data analysis, reproducible research, and data visualization. This course incorporates case studies from multiple disciplines and emphasizes the importance of properly communicating statistical ideas.
Prerequisite: MAT 209 . Suggested: CSC 151 or computer programming experience.
Instructor: Jonkman, Kuiper
Special Topics-Spring
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MAT 295-01 & 02 - Special Topic: Introduction to Data Science 4 credits (Spring)
This course introduces core topics in data science using R programming. This includes introductions to getting and cleaning data, data management, exploratory data analysis, reproducible research, and data visualization. This course incorporates case studies from multiple disciplines and emphasizes the importance of properly communicating statistical ideas.
Prerequisite: MAT 209 . Suggested CSC 151 or computer programming experience.
Instructor: Kuiper, Jonkman -
MAT 395-01 - Advanced Special Topic: Applied Data Science 4 credits (Spring)
Students will work in small teams on an applied data science project completing the full spectrum of the data science process including developing the problem statement, collecting and processing data, implementing the quantitative methods in an appropriate programming environment, and generating conclusions supported by data.
Prerequisite: CSC 207 and MAT 306 , MAT 310 or MAT 295 Intro to Data Science
Instructor: Blanchard
Variable Topics - Fall
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MAT 218-01 - Discrete Bridges to Advanced Mathematics: Graph Theory 4 credits (Fall)
Graph Theory. A graph consists of a set of vertices and a set of edges - you can draw a graph simply by placing some dots on a page to represent vertices, and then connecting certain pairs of dots with lines to represent the edges. Graphs are useful for understanding any kind of networks - the internet itself could be viewed as a graph, with links between pages representing edges; in fact Google’s PageRank algorithm makes heavy use of ideas from graph theory. In this course, we will use graphs as a means to develop problem solving skills and to improve our ability to construct logical mathematical arguments. After beginning with basic topics including the chromatic number, planarity, trees, Euler circuits, and Hamiltonian paths, we will move on to more advanced topics in which we apply techniques from Linear Algebra, such as eigenvalues and inner products, to obtain deeper and less intuitive results about graphs.
Prerequisite: MAT 215 .
Instructor: C. French -
MAT 218-02 - Discrete Bridges to Advanced Mathematics: Number Theory 4 credits (Fall)
Number Theory. This course will provide an introduction to fundamental concepts in number theory. Time permitting, we will study: natural numbers and divisibility, linear equations, basic properties of prime numbers, modular arithmetic and congruences, Fermat’s Little Theorem, Euler’s Theorem, public key cryptography, primitive roots, and quadratic reciprocity. Among core goals of this course is to practice, and improve, the communication of rigorous mathematical arguments.
Prerequisite: MAT 215 .
Instructor: M. Ortz -
MAT 317-01 - Advanced Topics in Analysis: Complex Analysis 4 credits (Fall)
Theory of analytic functions of a complex variable. Students will pursue an independent project in analytic number theory or iterated function systems.
Prerequisite: MAT 316 .
Instructor: Shuman
Variable Topics- Spring
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MAT 218-01 - Discrete Bridges to Adv Mathematics: Graph Theory 4 credits (Spring)
A graph consists of a set of vertices and a set of edges - you can draw a graph simply by placing some dots on a page to represent vertices, and then connecting certain pairs of dots with lines to represent the edges. Graphs are useful for understanding any kind of networks - the internet itself could be viewed as a graph, with links between pages representing edges; in fact Google’s PageRank algorithm makes heavy use of ideas from graph theory. In this course, we will use graphs as a means to develop problem solving skills and to improve our ability to construct logical mathematical arguments. After beginning with basic topics including the chromatic number, planarity, trees, Euler circuits, and Hamiltonian cycles.
Prerequisite: MAT 215 .
Instructor: Uzzell -
MAT 222-01 - Bridges to Advanced Mathematics: Differential Geometry 4 credits (Spring)
Einstein showed that gravity may be viewed as curvature of space-time. Curvature makes sense when we view a surface from outside, but how can we understand or study curvature from within a space? This course will introduce the tools mathematicians use for such study, and will thus serve as the mathematical background needed for understanding General Relativity. Topics will include tangent spaces and vector fields, differential forms, tensors, Lie Derivatives, geodesics, and the Riemannian connection.
Prerequisite: MAT 215 .
Instructor: French -
MAT 322-01 - Advanced Topics in Algebra: Field Theory 4 credits (Spring)
The study of fields, algebraic extensions, finite and cyclotomic fields, geometric constructions and Galois Theory.
Prerequisite: MAT 321 .
Instructor: Wolf -
MAT 444-01 - Senior Seminar: Bayesian Statistical Analysis 4 credits (Spring)
The debate between classical (or “frequentist”) statisticians and “Bayesian” statisticians has produced controversy, and sometimes surprising levels of animosity, for decades. Recent advances in computing have revolutionized statistical practice by making it easier to obtain Bayesian solutions to complicated problems, which in turn has helped unify the statistical community. This course will introduce the differences and underlying similarities between classical and Bayesian methods. Students will learn the basics of Bayesian analysis using R and JAGS software, and see how Bayesian methods have revolutionized the use of statistics in fields such as medicine, environmental studies, political science, and genetics. We will also explore advanced topics, such as hierarchical models and meta-analysis, which are particularly well suited to a Bayesian approach.
Prerequisite: MAT 335 . MAT 309 or MAT 310 with permission of instructor.
Instructor: Jonkman
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