Graduate Course Descriptions

The History of the Calculus (3.00)

MATH 5010

Studies the evolution of the various mathematical ideas leading up to the development of calculus in the 17th century, and how those ideas were perfected and extended by succeeding generations of mathematicians. Emphasizes primary source materials. Prerequisite: MATH 2310 and 3351, or instructor permission.

The History of Mathematics (3.00)

MATH 5030

Studies the development of mathematics from classical antiquity to the end of the 19th century, focusing on critical periods in the evolution of geometry, number theory, algebra, probability, and set theory. Emphasizes primary source materials. Prerequisite: MATH 2310 and 3351, or instructor permission.

Mathematical Probability (3.00)

MATH 5090

Mathematical Probability

Probability (3.00)

MATH 5100

Studies the development and analysis of probability models through the basic concepts of sample spaces, random variables, probability distributions, expectations, and conditional probability. Additional topics include distributions of transformed variables, moment generating functions, and the central limit theorem. Prerequisite: MATH 1320 or equivalent, and graduate standing. Credit cannot be received for both MATH 3100 and 5100.

Advanced Ordinary Differential Equations (3.00)

MATH 5250

Studies the qualitative geometrical theory of ordinary differential equations. Includes basic well posedness; linear systems and periodic systems; stability theory; perturbation of linear systems; center manifold theorem; periodic solutions and Poincaré-Bendixson theory; Hopf bifurcation; introduction to chaotic dynamics; control theoretic questions; differential geometric methods. Prerequisite: MATH 2310, 3250, 3351 or instructor permission.

Proofs in Analysis (3.00)

MATH 5305

This course reviews the proofs of the main theorems in analysis in preparation for the advanced graduate analysis courses. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.

Advanced Multivariate Calculus (3.00)

MATH 5330

Differential and Integral Calculus in Euclidean spaces; implicit and inverse function theorems, differential forms and Stokes' Theorem. Prerequisite: MATH 5310.

Complex Variables with Applications (3.00)

MATH 5340

Analytic functions, Cauchy formulas, power series, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: graduate standing.

New Course in Mathematics (1.00 - 4.00)

MATH 5559

This course provides the opportunity to offer a new topic in the subject of mathematics.

Number Theory (3.00)

MATH 5653

Includes congruences, quadratic reciprocity, Diophantine equations, and number-theoretic functions, among others. Prerequisite: MATH 3354 or instructor permission.