Graduate Courses in Mathematics (MTH prefix)

415. Number Theory - Properties of natural numbers, unipue factorization, residue solution of congruences, arithmetic functions, quadratic reciprocity law, distribution of primes, Diophantine equations, continued fractions, algebraic numbers. Prerequisite: MTH 311.

419. Probability - An introduction to elementary probability laws, random variables, distribution theory, multivariate and conditional distributions, transformations of random variables and elementary convergence concepts. Prerequisite: MTH 311 and MTH 333, or may be taken concurrently with 333 with consent of the instructor.

439. Advanced Calculus I - Elements of point set theory and an in-depth study of the basic ideas of sequences, limits, continuity and differentiability. Prerequisites: MTH 311 and 333.

440. Advanced Calculus II - A continuation of MTH 439 with topics in Taylor, Fourier and other special series and an in-depth study of Riemann-Darboux Integration. Prerequisite: MTH 439.

451. College Geometry - A survey of topics from classical Euclidean geometry, modern Euclidean geometry, projective geometry, transformational geometry and non-Euclidean geometries. Prerequisites: MTH 234 and 311.

502. Mathematical Statistics I - Random variables, discrete and continuous distributions, multiple random variables, distributions of functions of random variables, convergence concepts. Prerequisites: MTH 439 or equivalent.

503. Mathematical Statistics II - Sufficient and complete statistics, likelihood and moment estimation, properties of estimators, interval estimation and hypothesis tests. Prerequisite: MTH 502.

505. Numerical Methods In Differential Equations - Numerical integration, numerical solutions of initial value problems, numerical solutions of boundary value problems. Prerequisites: MTH 305 and 337.

508. General Topology - Metric spaces, topological spaces, and Cartesian product spaces are studied together with certain topological properties such as compactness, connectivity, and separability. Prerequisite: MTH 439.

511. Abstract Algebra I - Groups, subgroups, homomorphisms, isomorphisms, cosets, factor groups, the Fundamental Theorem of Group Homomorphisms, the Fundamental Theorem of Finite Abelian Groups. Prerequisite: MTH 312.

512. Abstract Algebra II - Rings and ideals, vector spaces, fields, integral domains, introduction to Galois Theory. Prerequisite: MTH 511.

513. Complex Variables I - Differential calculus of functions of complex variables. Prerequisite: MTH 439.

514. Complex Variables II - Integral calculus of functions of complex variables. Prerequisite: MTH 513.

517. Linear Algebra - Finite dimensional vector spaces, linear transformations and matrices, with emphasis on numerical aspects. Prerequisite: Undergraduate major in mathematics, including MTH 317.

538. Structure of the Real Number System - Brief review of infinite sets, Peano's postulates, relations, equivalence classes, and isomorphisms. Rigorous development of the integers as equivalence classes of ordered pairs. Development of the real number system using Dedekind cuts. Comparison with Cauchy sequence development, complex numbers and quaternions. Prerequisite: 12 semester hours of advanced mathematics.

539. Real Variables I - Study of functions and metric spaces. Prerequisite: MTH 440.

540. Real Variables II - Study of measure theory and the Lebesque integral. Prerequisite: MTH 539.

545. History of Mathematics - A survey with emphasis on both practical and philosophical developments, and on anecdotal material. Prerequisites: 12 semester hours of mathematics including MTH 233, 234.

564. Advanced Topics In Mathematics - Topics in advanced mathematics. May be repeated for credit on a different topic with departmental approval. Prerequisite: Graduate standing in mathematics and consent of instructor.

575.* Advanced Graduate Studies - 1 to 3 conference hours per week. Individual studies in advanced mathematics. May be repeated for credit on a different topic with departmental approval. Prerequisite: Graduate standing in mathematics and approval by department chairman.

576.* Advanced Graduate Studies - 1 to 3 conference hours per week. Same as 575 for credit in a different topic.

589.** Thesis Research - 1 to 3 semester hours. Research and preparation for writing the thesis. Prerequisite: Approval of graduate adviser.

590.** Thesis Writing - 3 to 9 semester hours. Writing of thesis. Prerequisite: MTH 589.

* No more than 6 semester hours of Advanced Graduate Studies credit may be counted toward a degree without special permission from the Dean of the College.

** Once a student begins work on a thesis he or she must register for 589 and/or 590 each semester or summer session until the thesis is completed. A student may not register for 590 until the thesis proposal is approved. A maximum of three semester hours each of 589 and 590 will be counted toward the M.S. in mathematics or statistics or mathematics teaching.