Mathematics Courses
Semester
specific course descriptions
110. Concepts of Mathematics.
An introduction to significant ideas of mathematics, intended for students who will not specialize in mathematics or science. Topics are chosen to display historical perspective, mathematics as a universal language and as an art, and the logical structure of mathematics. This course is intended for non-majors; it does not count toward either the major or minor in mathematics; students who have passed a calculus course (Mathematics 135, 136 or 205) may not receive course credit for Mathematics 110.
113. Applied Statistics.
An introduction to statistics with emphasis on applications. Topics include the description of data with numerical summaries and graphs, the production of data through sampling and experimental design, techniques of making inferences from data such as confidence intervals, and hypothesis tests for both categorical and quantitative data. The course includes an introduction to computer analysis of data with a statistical computing package. Also offered through Statistics.
123. Mathematics of Art.
This course explores the connections between mathematics and art: how mathematics can provide a vocabulary for describing and explaining art; how artists have used mathematics to achieve artistic goals; and how art has been used to explain mathematical ideas. This course is intended for non-majors; it does not count toward either the major or minor in mathematics.
134. Precalculus.
A development of skills and concepts necessary for the study of calculus. Topics include the algebraic, logarithmic, exponential and trigonometric functions; Cartesian coordinates; and the interplay between algebraic and geometric problems. This course is intended for students whose background in high school was not strong enough to prepare them for calculus; it does not count for distribution credit or for the major or minor in mathematics. Students who have passed a calculus course (Mathematics 135, 136 or 205) may not receive course credit for Mathematics 134. Offered in fall semester only.
135. Calculus I.
The study of differential calculus. The focus is on understanding derivatives as a rate of change. Students also develop a deeper understanding of functions and how they are used in modeling natural phenomena. Topics include limits; continuity and differentiability; derivatives; graphing and optimization problems; and a wide variety of applications.
136. Calculus II.
The study of integral calculus. Topics include understanding -Riemann sums and the definition of the definite integral; techniques of integration; approximation techniques; improper integrals; a wide variety of applications; and related topics. Prerequisite: Mathematics 135 or the equivalent.
205. Multivariable Calculus.
This course extends the fundamental concepts and applications of calculus, such as differentiation, integration, graphical analysis and optimization, to functions of several variables. Additional topics include the gradient vector, parametric equations, and series. Prerequisite: Mathematics 136 or the equivalent.
206. Vector Calculus.
A direct continuation of Mathematics 205, the main focus of this course is the study of smooth vector fields on Euclidean spaces and their associated line and flux integrals over parameterized paths and surfaces. The main objective is to develop and prove the three fundamental integral theorems of vector calculus: the Fundamental Theorem of Calculus for Line Integrals, Stokes’ Theorem and the Divergence Theorem. Prerequisite: Mathematics 205.
213.
Applied Regression Analysis.
A continuation of Mathematics 113 intended for students in the physical, social or behavioral sciences. Topics include simple and multiple linear regression, model diagnostics and testing, residual analysis, transformations, indicator variables, variable selection techniques, logistic regression and analysis of variance. Most methods assume use of a statistical computing package. Prerequisite: Mathematics 113 or Economics 200 or permission of instructor. Also offered through Statistics.
217. Linear Algebra.
A study of finite dimensional linear spaces, systems of linear equations, matrices, determinants, bases, linear transformations, change of bases and eigenvalues.
226. Design and Analysis of Experiments.
An introduction to the statistical design and analysis of experiments, this course covers the basic elements of experimental design, including randomization, blocking and replication. Topics include completely randomized design, randomized complete block design, Latin square and factorial designs. Analysis of variance techniques for analyzing data collected using these methods is extensively discussed. Additional topics in survey sampling are covered as time allows. Thorough use of a statistical software package is incorporated. Prerequisite: Mathematics 113 or Economics 200 or permission of instructor. Also offered through Statistics.
230. Differential Equations.
An introduction to the various methods of solving differential equations. Types of equations considered include first order ordinary equations and second order linear ordinary equations. Topics may include the Laplace transform, numerical methods, power series methods, systems of equations and an introduction to partial differential equations. Applications are presented. Prerequisite: Mathematics 136. Offered in spring semester.
250. Mathematical Problem-Solving.
Students meet once a week to tackle a wide variety of appealing math problems, learn effective techniques for making progress on any problem, and spend time writing and presenting their solutions. Participation in the Putnam mathematics competition in early December is encouraged but not required. This course is worth 0.25 credit, meets once per week, and is graded pass/fail. Since topics vary from semester to semester, students may repeat this course for credit.
280. A Bridge to Higher Mathematics.
This course is designed to introduce students to the concepts and methods of higher mathematics. Techniques of mathematical proof are emphasized. Topics include logic, set theory, relations, functions, induction, cardinality, and others selected by the instructor.
305. Real Analysis.
A rigorous introduction to fundamental concepts of real analysis. Topics may include sequences and series, power series, Taylor series and the calculus of power series; metric spaces, continuous functions on metric spaces, completeness, compactness, connectedness; sequences of functions, pointwise and uniform convergence of functions. Prerequisites: Mathematics 205 and 280. Offered in fall semester.
306. Complex Analysis.
Topics include algebra, geometry and topology of the complex number field, differential and integral calculus of functions of a complex variable. Taylor and Laurent series, integral theorems and applications. Prerequisites: Mathematics 205 and 280. Offered in spring semester.
315. Group Theory.
An introduction to the abstract theory of groups. Topics include the structure of groups, permutation groups, subgroups and quotient groups. Prerequisite: Mathematics 280. Offered in spring semester.
316. Ring Theory.
An introduction to the abstract theory of algebraic structures including rings and fields. Topics may include ideals, quotients, the structure of fields, Galois theory. Prerequisite: Mathematics 280. Offered in fall semester.
317. Mathematical Logic.
An introduction to modern mathematical logic, including the most important results in the subject. Topics include propositional and predicate logic; models, formal deductions and the Gödel Completeness Theorem; applications to algebra, analysis and number theory; decidability and the Gödel Incompleteness Theorem. Treatment of the subject matter is rigorous, but historical and philosophical aspects are discussed. Prerequisite: Mathematics 280. Also offered as Computer Science 317 and Philosophy 317.
318. Graph Theory.
Graph theory deals with the study of a finite set of points connected by lines. Problems in such diverse areas as transportation networks, social networks and chemical bonds can be formulated and solved by the use of graph theory. The course includes theory, algorithms, applications and history. Prerequisite: Mathematics 217 or 280. Also offered as Computer Science 318.
323. History of Mathematics.
This seminar is primarily for juniors and seniors.
324. Numerical Analysis.
Topics covered include finite differences, interpolation, numerical integration and differentiation, numerical solution of differential equations and related subjects. Prerequisite: Mathematics 217. Also offered as Computer Science 324.
325. Probability.
This course covers the theory of probability and random variables, counting methods, discrete and continuous distributions, mathematical expectation, multivariate random variables, functions of random variables and limit theorems. Prerequisite: Mathematics 205. Also offered through Statistics.
326. Mathematical Statistics.
Following Mathematics 325, this course deals with the theory of parameter estimation, properties of estimators and topics of statistical inference, including confidence intervals, tests of hypotheses, simple and multiple linear regression, and analysis of variance. Prerequisite: Mathematics 325. Also offered through Statistics.
330. Differential Equations II.
This course continues the study of differential equations from Mathematics 230. The study considers higher order equations, systems of equations, Sturm-Liouville problems, Bessel’s equation and partial differential equations. Existence and uniqueness theorems and ordinary and singular points are discussed and applications are given. Prerequisites: Mathematics 217 and 230.
333. Mathematical Methods of Physics.
Important problems in the physical sciences and engineering often require powerful mathematical methods for their solution. This course provides an introduction to the formalism of these methods and emphasizes their application to problems drawn from diverse areas of classical and modern physics. Representative topics include the integral theorems of Gauss and Stokes, Fourier series, matrix methods, selected techniques from the theory of partial differential equations and the calculus of variations with applications to Lagrangian mechanics. The course also introduces students to the computer algebra system Mathematica as an aid in visualization and problem-solving. Prerequisites: Mathematics 205 and Physics 152. Also offered as Physics 333.
341. Number Theory.
The theory of numbers addresses questions concerning the integers, such as “Is there a formula for prime numbers?” This course covers the Euclidean algorithm, congruences, Diophantine equations and continued fractions. Further topics may include magic squares, quadratic fields or quadratic reciprocity. Prerequisite: Mathematics 217 or Mathematics 280 or permission of the instructor.
343. Time Series Analysis.
Statistical methods for analyzing data that vary over time are investigated. Topics include forecasting systems, regression methods, moving averages, exponential smoothing, seasonal data, analysis of residuals, prediction intervals and Box-Jenkins models. Application to real data, particularly economic data, is emphasized along with the mathematical theory underlying the various models and techniques. Prerequisite: Mathematics 136 or permission of the instructor. Also offered as Economics 343 and through Statistics.
370. Topology.
An introduction to topology. Topics may include the general notion of a topological space, subspaces, metrics, continuous maps, connectedness, compactness, deformation of curves (homotopy) and the fundamental group of a space. Prerequisite: Mathematics 280.
380. Theory of Computation.
The basic theoretical underpinnings of computer organization and programming. Topics include the Chomsky hierarchy of languages and how to design various classes of automata to recognize computer languages. Application of mathematical proof techniques to the study of automata and grammars enhances understanding of both proof and language. Prerequisites: Computer Science 319 and Mathematics 280. Also offered as Computer Science 380.
389,390. Independent Projects.
Permission required.
395. College Geometry.
This course presents a selection of nice results from Euclidean geometry, such as the Euler line, the nine-point circle, and inversion. Students will explore these topics dynamically using geometric construction software. A portion of the course is also devoted to non-Euclidean geometry, such as spherical, projective, or hyperbolic geometry. This course is especially recommended for prospective secondary school teachers. Prerequisite: Mathematics 217 or Mathematics 280.
489. SYE: Senior Project
for Majors.
Permission required.
498.
SYE: Senior Honors Project for Majors.
Permission required.
