Course Information: 600 level
621. Computational Matrix Theory.Credit Hours: 3 Course Level: 600 Catalog Description: Matrix norms singular value decomposition, QR factorization, least-square problems, conditioning and satiability, eigenvalue problems, and iterative methods for solving large systems. |
641. Modern Algebra 2.Credit Hours: 3 Course Level: 600 Prerequisites: MATH 545. Catalog Description: Concepts from set theory and the equivalence of the Axiom of Choice. Zorn's Lemma and the Well-Ordering Theorem; a study of the structure of groups, rings, fields, and vector spaces; elementary factorization theory; extensions of ring and fields; modules and ideals; and lattices. Semester Offered: Instructor E-mail: Comments From Graduate Director: Continuation of Math 541. This is the basic graduate sequence in algebra. Note that algebra is one of the areas of the M.S. Advanced Exams/Ph.D. entrance exams. Math 541 follows in the spring with a second semester, Math 641, and both courses are needed if you are taking the exam. Math 541-641 is a basic prerequisite for advanced courses in combinatorics, graph theory, and number theory. It is a popular course for first year M.S. students and for first year Ph.D. students who expect to take the Entrance Exam in that area. |
645. Number Theory 2.Credit Hours: 3 Course Level: 600 Prerequisites: MATH 305. Catalog Description: Introduction to classical number theory covering such topics as divisibility, the Euclidean algorithm, Diophantine equations, congruences, primitive roots, quadratic residues, number-theoretic functions distribution of primes, irrationals, and combinatorial methods. Special numbers such as those of Bernoulli, Euler, and Stirling. Semester Offered: Instructor E-mail: Comments From Graduate Director: A continuation of Math 545. The sequence Math 545-645 is course is offered about every other year and provides a graduate-level introduction to Number Theory. |
651. Real Variables 2.Credit Hours: 3 Course Level: 600 Prerequisites: MATH 551. Catalog Description: A development of the Lebesgue integral, function spaces and differentiation, complex measures, the Lebesgue-Radon-Nikodym theorem. Semester Offered: Instructor E-mail: Comments From Graduate Director: Continuation of Math 551. This is a basic graduate two-semester course (551/651) in real analysis. Real analysis is one of the areas of the M.S. Advanced Exams/Ph.D. entrance exams and the full-year sequence should be taken if preparing for the exam. Math 651 is recommended particularly for students intending to take the doctoral sequence in functional analysis and other doctoral-level courses in analysis and applied mathematics. However, the material is basic for anyone planning to teach upper level mathematics at the college level. |
655. Complex Variables 2.Credit Hours: 3 Course Level: 600 Prerequisites: MATH 555. Catalog Description: Number systems, the complex plane and its geometry. Holomorphic functions, power series, elementary functions, complex integration, representation theorems, the calculus of residues, analytic continuation and analytic function, elliptic functions, Holomorphic functions of several complex variables. |