Course Catalog

Course Catalog

Our coursework highlights the role of mathematics as a mode of formal reasoning in the tradition of the quadrivium, as a practical art in application to the quantitative sciences, and as a discipline in its own right.

Select a course level: 100-level | 200-level | 300-level | 400-level

MATH 100 Number, Magnitude, Form – The development of the concepts of number, magnitude, and form in mathematics. Topics include the natural numbers, the real numbers, and transfinite numbers, length, area, volume, dimension, and fractals, and knots. Emphasis is on the understanding of ideas and the ability to express them through mathematical arguments.
Prerequisite: Math Placement Exam.

MATH 110 College Algebra – A survey of equations involving linear, quadratic, polynomial, rational, exponential, and logarithmic functions. Systems of equations and applications.
Prerequisite: Math Placement Exam.

MATH 120 Finite Mathematics – Application of quantitative tools as an aid to problem solving in a variety of areas. Topics include solution techniques for systems of linear equations and inequalities, basic principles of probability and statistics, elementary finance, Markov chains, matrices, and more.
Prerequisite: Math Placement Exam.

MATH 150 Functions – A survey of the fundamental mathematical functions and their applications including the linear, absolute value, polynomial, rational, exponential, logarithmic, and trigonometric functions.
Prerequisite: MATH 110 or Math Placement Exam.

MATH 151 Calculus I – Differential and elementary integral calculus of functions of one variable. Topics include limits, continuity, derivatives, linear approximation, the Fundamental Theorem of Calculus, and elementary techniques of integration.
MATH 150 or Math Placement Exam.

MATH 201 History of Mathematics – The history of mathematics from its origins to the present with an emphasis on significant problems and their solutions.
Prerequisite: MATH 151 or permission of instructor.

MATH 230 Statistics – Self-contained introduction to statistics with economic applications. Elements of probability theory, sampling theory, statistical estimation, regression analysis, and hypothesis testing. Elementary econometrics and other applications of statistical tools to economic data.
Prerequisite: MATH 150. Crosslisted with ECON 230.

MATH 250 Calculus II – Continuation and extension of Calculus I. Topics include more advanced integration techniques, limits and improper integrals, vector-valued functions of a single variable, scalar-valued functions of N variables, partial derivatives, geometric volumes, sequences and series.
MATH 151.

MATH 251 Vector Calculus – Calculus of functions in several variables. Topics include the geometry of Euclidean space, vector algebra, forms, matrices, vector-valued functions, the inverse and implicit function theorems, line and surface integrals, differential forms, and the theorems of Green, Gauss, and Stokes. Applications to physics.
Prerequisite: MATH 250.

MATH 252 Ordinary Differential Equations – An introduction to the theory of ordinary differential equations with an emphasis on methods of solution. Topics include first-order equations, existence and uniqueness, linear equations, equations with constant coefficients, variation of parameters, Laplace transforms, series solutions, systems of equations, numerical methods.
Prerequisite: MATH 250 .

MATH 270 Scientific Programming – An introduction to programming via the solution of various problems in mathematics and the sciences. Problem description, development of a model, creation and implementation of a computational method of solution, and assessment of results.
Prerequisite: MATH 151.

MATH 310 Algebraic Structures – An introduction to abstract algebra. Topics include groups, subgroups, quotient groups, homomorphisms, rings, ideals, and fields. Emphasis on constructing, writing, and presenting proofs.
MATH 251.

MATH 311 Linear Structures – A study of abstract linear algebra. Topics include vector spaces, linear transformations, matrices, eigenvalues, inner product spaces, and the Spectral Theorem.
Prerequisite: MATH 251.

MATH 312 Number Theory – A study of the basic properties of the integers including divisibility, primes and their distribution, unique factorization, the Euclidean algorithm, congruences, primitive roots, arithmetic functions, quadratic reciprocity, Diophantine equations, and other topics.
Prerequisite: MATH 251.

MATH 330 Probability – An introduction to probability theory. Topics include sample spaces, discrete and continuous random variables, density functions, conditional probability, probability distributions, and the Central Limit Theorem.
Prerequisite: MATH 250.

MATH 350 Real Analysis – A rigorous study of the theoretical structure of calculus including the real numbers, metric spaces, limits, continuity, differentiation, integration, the Fundamental Theorem of Calculus, infinite series, and power series.
Prerequisite: MATH 310 or MATH 311.

MATH 351 Complex Analysis – An introduction to the study of functions of a complex variable. Topics include the complex numbers, analytic functions, the elementary functions, complex integration, Taylor and Laurent series, residues, conformal mapping, and applications.
Prerequisite: MATH 251.

MATH 352 Partial Differential Equations – An introduction to second-order partial differential equations in two variables. Topics include wave motion and Fourier series, heat flow and the Fourier integral, Laplace's equation and complex variables, second-order equations in more than two variables, spherical harmonics, and associated special functions of mathematical physics.
Prerequisite: MATH 252.

MATH 360 Differential Geometry – A classical treatment of the differential geometry of curves and surfaces in three-dimensional space. Topics include: Frenet frames, the local theory of parameterized curves, regular surfaces, tangent planes, first and second fundamental forms, the Gauss map, parallel transport and the Gauss-Bonnet Theorem.
Prerequisite: MATH 251.

MATH 361 Knot Theory – The geometry and topology of knots, links, surfaces, and three-dimensional manifolds. Topics include: Continuity, topological equivalence, isotopy, Reidemeister moves, colorings, Alexander and Jones polynomials, Euler characteristic, the classification of surfaces, polyhedral solids and Heegard splittings.
MATH 310 or MATH 311.

MATH 490 Senior Seminar – Student presentations of selected mathematical problems and directed readings.
Prerequisite: Senior status.

MATH 491 Undergraduate Research – Student-Faculty collaboration on research projects of mutual interest.
Prerequisite: Permission of the department.