Sewanee: The University of the South

Mathematics Courses

MATH 100 Topics in Mathematics

Intended for prospective majors outside of mathematics, computer science, and the physical sciences, this course focuses on one or more important areas of mathematics with emphasis on the creativity and power of abstract representation, mathematical inquiry, and logical reasoning. Specific past topics have included calculus, probability, number theory, group theory, and encryption. Current topics vary by instructor. (Credit, full course.) Staff

MATH 101 Calculus I

An elementary course introducing the student to the basic concepts of calculus: functions, transcendental functions, limits, derivatives, and integrals. Emphasis on problem solving. (Credit, full course.) Staff

MATH 102 Calculus II

A continuation of Calculus I. Topics include further theory and applications of integration, techniques of integration, and introduction to series. Prerequisite: Math 101 or placement. (Credit, full course.) Staff

MATH 207 Multidimensional Calculus

Calculus of several variables. Vectors, partial and directional derivatives, space curves, gradients, maxima and minima, linear and differentiable transformations, vector fields, line integrals, multidimensional Riemann integrals, and applications in physics and geometry are considered. Prerequisite: Math 102 or placement. (Credit, full course.) Staff

MATH 210 Linear Algebra

A course designed to provide some important mathematical tools useful in a variety of fields. Systems of linear equations, vectors and matrices, determinants, vector spaces, linear transformations, inner and cross products, and eigenvalues and canonical forms are considered. Prerequisite: Math 102 or placement. (Credit, full course.) Staff

MATH 212 Differential Equations

Ordinary differential equations, with applications. Methods of numerical approximation, power series, and Laplace transforms. Existence and uniqueness of solution. Prerequisite: Mathematics 102 or placement. (Credit, full course.) Parrish

MATH 215 Discrete Mathematical Structures

This course is required for most courses in mathematics or computer science numbered 300 or above. Topics normally include the following: logic, sets, functions, relations, proof techniques, mathematical induction, combinatorics, recursion, and algebraic structures. The subject matter is of current interest to both mathematics and computer science students. Prerequisite: Math 101 or higher or placement. (Credit, full course.) Staff

MATH 301 Numerical Analysis

Includes interpolation and curve-fitting, quadrature, iterative methods in linear and non-linear algebra, difference equations, and applications of the above to the approximate solution of ordinary and partial differential equations. Prerequisites: Math 207 and 215. (Credit, full course.) Staff

MATH 303 Analysis I (writing-intensive)

A rigorous treatment of continuity, differentiation, and integration for functions of a real variable. The course also includes convergence of series and sequences of functions as well as topology of the real line. Prerequisites: Math 207 and 215. (Credit, full course.) Rudd

MATH 305 Abstract Algebra I (writing-intensive)

An introduction to the theory of groups, rings, and fields, including such tools and topics as homomorphisms, quotient structures, and field extensions. Prerequisite: Math 215. (Credit, full course.) Cavagnaro

MATH 306 Abstract Algebra II

Further development of structures and methods introduced in Abstract Algebra I, with emphasis on field extensions and Galois theory. Prequisite: Math 305. (Credit, full course.) Cavagnaro

MATH 311 Functions of a Complex Variable

An introduction to analytic functions. Rational, exponential, logarithmic, and trigonometric functions in the complex plane, Cauchy's integral formula, Taylor series, Laurent series, residues, poles, and conformal mapping are considered along with applications to physical problems and other areas of mathematics. Prerequisites: Math 207 and 215. (Credit, full course.)

MATH 313 Algebraic Number Theory

Largely an algebraic study of the standard number-theoretic functions, congruences, primes, quadratic residues, and other topics selected according to the interests of the students and instructor. Prerequisite: Math 215. (Credit, full course.) Staff

MATH 314 Topology (writing-intensive)

An introduction to point-set topology with emphasis on Euclidean spaces and applications to analysis. Topics include connectedness, compactness, countability conditions, separation properties, metric spaces, continuity, homeomorphisms, and product spaces. Prerequisite: Math 215. (Credit, full course.) Cavagnaro

MATH 321 Probability

An introduction to probability covering continuous and discrete random variables, distribution functions, and the Central Limit Theorem. Prerequisite: Math 207 and 215. (Credit, full course.) Staff

MATH 322 Mathematical Statistics

An introduction to the theoretical development of statistics covering topics such as sampling, statistical inference, distributions, and data analysis. Prerequisite: Math 321. (Credit, full course.) Staff

MATH 330 History of Mathematics

A survey of classical mathematics from ancient times to the development of calculus, together with selected topics from the history of modern mathematics. Prerequisites: Math 102. (Credit, full course.) Cunningham

MATH 332 Mathematical Modeling

An introduction to the creation of mathematical models, both deterministic and probabilistic, for the description of problems drawn from physical, biological, social, and environmental sources. Prerequisites: Math 215 and either CSci 157 or permission of instructor. (Credit, full course.) Cavagnaro

MATH 334 Partial Differential Equations and Modeling

This course addresses the techniques and theory of partial differential equations. Many physical and biological applications and models are explored, including the heat equation, the wave equation, and LaPlace’s equation. Significant attention is given to both theory and applications. Prerequisite: Math 207 and Math 212. (Credit, full course.) Staff

MATH 401 Analysis II

A concentrated study of the theory of functions. Topics may inlcude metric spaces, normed spaces, Banach spaces, inner product spaces, and Hilbert spaces. Prerequisite: Math 303. (Credit, full course.)

MATH 403 Honors Seminar

Study of a selected topic. Participants in the seminar include the mathematics faculty and invited students. (Credit, full course.) Staff

MATH 410 Mathematical Methods in Physics

Vector spaces and linear operators, with applications. Fourier series, boundary value problems, orthogonal functions. Prerequisites: Math 212. (Credit, full course.) Staff

MATH 416 Algebraic Topology

An introduction to algebraic and combinational topology with emphasis on applications to analysis and Euclidean geometry. Topics covered include simplicial homology, the fundamental group, covering spaces, the higher homotopy groups, and the homology sequence. Prerequisite: Math 314. (Credit, full course.) Croom

MATH 430 Calculus on Manifolds

Multivariable calculus including the inverse and implicit function theorems, manifolds (spaces that locally resemble Euclidean space), differential forms, and Stokes’ Theorem for compact, oriented k-manifolds. Prerequisite: Math 210 and 215, or consent of instructor. (Credit, full course.) Staff

MATH 444 Independent Study

No description. (Credit, full course.) Staff

Sewanee: The University of the South