Summer 2015 | Fall 2015 | Spring 2016 |

## 600- Level Courses

**MTH 609: Data Security and Cryptography, 3 credits.**

Access, information flow, and inference controls. Network security and management. Encryption algorithms. Cryptographic techniques.

(Colisted with CSC 609)

*Prerequisite: MTH 517 (or CSC 517) or MTH 527 (or CSC 527).*

**MTH 612: Complexity Theory, 3 credits.**

Models of computation. Hierarchy theorems. Intractability. NP-completeness.

(Colisted with CSC 612.)

*Prerequisite: MTH 527 (or CSC 527).*

**MTH 621: Mathematical Probability, 3 credits.**

Development of the measure-theoretic approach probability. Random variables, central limit theory, laws of large numbers, martingales.

*Prerequisite: Permission of department chairman.*

**MTH 625: Multivariate Analysis, 3 credits.**

Sampling theory for multivariate normal populations. Component and factor analysis. Stochastic difference equations.

*Prerequisite: MTH 525.*

**MTH 630, 631: Real Variables, 3 credits each.**

Lebesgue measure and the Lebesgue Integral for R^{1}, Banach Spaces. General measure theory, topological groups and Haar Measure.

*Prerequisite: MTH 532.*

**MTH 632, 633: Complex Variables, 3 credits each.**

Complex numbers line or transformation, analytic function, conformality. Cauchy's Theorem, representation theorems, harmonic functions.

*Prerequisite: MTH 531.*

**MTH 638: Stochastic Processes, 3 credits.**

*Prerequisite: MTH 631.*

**MTH 640, 641: Algebraic Topology, 3 credits.**

Homotopy, covering space, Eilenberg-Steenrod axioms for (co) homology theories, Mayer-Vietoris sequences, Universal Coefficient theorem, Kunneth formula, computations and applications.

*Prerequisite: MTH 532.*

**MTH 647: Computational Geometry, 3 credits.**

Algorithms for solving geometric problems arising from application domains including raphics, robotics, and GIS.

*Prerequisite: MTH 517 or permission of instructor.*

**MTH 651, 652: Differential Geometry, 3 credits each.**

**MTH 657: Lie Groups, 3 credits.**

**MTH 661, 662: Abstract Algebra, 3 credits each.**

*Prerequisite: MTH 562.*

**MTH 670: Directed Reading of Research, 2-4 credits.**

**MTH 680, 681: Topics in Analysis, 3 credits each.**

**MTH 682, 683: Topics in Topology, 3 credits each.**

**MTH 685: Topics in Algebra, 3 credits.**

**MTH 686, 687: Topics in Mathematics, 3 credits each.**

**MTH 690: Seminar for Beginning Graduate Students, 1-3 credits.**

The selection of topics will be flexible but will be of interest to beginning graduate students.

**MTH 692: Seminar, 1-2 credits.**