Courses
MATH 504
A graduate level introduction to matrix-based computing. Stable and efficient algorithms for linear equations, least squares and eigenvalue problems. Both direct and iterative methods are considered and MATLAB is used as a computing environment.
MATH 491
Available to students with a GPA equal to or greater than 3.00 and with consent of the instructor.
MATH 450
Detailed examination of current topics in Mathematics.
MATH 412
Modeling of stochastic systems. Introduction to Markov chains, renewal processes, queuing theory, reliability and time series models; Ito Calculus, Fokker-Planck and Kolmogorov differential equations; applications to the problems of environmental as well as physical systems such as allocation of resources, inventory control, transportation and finance.
MATH 409
Convergence of sequences in Rn, multivariate Taylor's theorem. Optimality conditions for unconstrained optimization. Newton's and quasi-Newton methods for unconstrained optimization. Equality-constrained optimization, Karush-Kuhn-Tucker theorem for constrained optimization. Inequality-constrained optimization. Interior point methods for constrained optimization. Linear and quadratic programs, their numerical solution.
MATH 495
MATH 451
Detailed examination of current topics in Mathematics.
MATH 413
Review of elementary probability; multivariate random variables and their functions; conditional distribution and expectation; generating functions and transforms; order statistics; multivariate normal distribution; types of convergence; laws of large numbers; central limit theorem.
MATH 410
Quadratic Reciprocity, Quadratic Forms, Gauss' Composition Law and Genus Theory, Cubic and Biquadratic Reciprocity, Number Fields, Hilbert Class Field, Orders in Imaginary Quadratic Fields, The Class Number, Class Field Theory and Cebatorev Density Theorem, Norms and Ideles, Elliptic Functions and Theory of Complex Multiplication. Divisibility, Primes, Congruences, Prime Modules and Primitive Roots, Groups, a review of Rings and Fields, Arithmetic Functions, Diophantine Problems, Farey Fractions ad Geometry of Numbers, Continued Fractions, Multiplicative Number Theory and Dirichlet Series.
MATH 407
Problems of enumeration, structure, and optimization in such finite or discrete systems as graphs, matroids, partially ordered sets, lattices, partitions, codes and block designs.
MATH 503
Linear algebra: Vector and inner product spaces, linear operators, eigenvalue problems; Vector calculus: Review of differential and integral calculus, divergence and Stokes' theorems. Ordinary differential equations: Linear equations, Sturm-Liouville theory and orthogonal functions, system of linear equations; Methods of mathematics for science and engineering students.
MATH 490
Work on the research proposal resulting from MATH 390 with the guidance of an instructor, culminating in a research paper suitable for presentation or publication.
MATH 414
Basic notions of commutative algebra and homological algebra: category of modules over a ring, flatness, Ext and Tor. General properties of schemes: affine schemes. projective schemes, dimension, projective and proper morphisms. Normal and regular schemes. Flat and smooth morphisms. Zariski's main theorem and applications. Coherent sheaves and Cech Cohomology.
MATH 411
Modeling of stochastic systems. Introduction to Markov chains, renewal processes, queuing theory, reliability and time series models; Ito Calculus, Fokker-Planck and Kolmogorov differential equations; applications to the problems of environmental as well as physical systems such as allocation of resources, inventory control, transportation and finance.
MATH 408
Games in extensive form; pure and behavioral strategies; normal form, mixed strategies, equilibrium points; coalitions, characteristic-function form, imputations and solution concepts; related topics and applications.
