**High Performance Computing, High Availability Computing**

**Steering Committee Coordinator:**

Please contact Dr. Box regarding any questions about the High Performance Computing track in CAM.

**Core Courses****Math Core** (9 SCH): (Common to all Tracks)

MATH 414 & MATH 415 with either MATH 407 or STAT 620/STAT 621

Math 407 (Partial Differential Equations) 3 Credit Hours. Preq, MATH 245, Solution of linear first order equations. Formation and solution of second order problems of parabolic, elliptic, and hyperbolic type. (G)

Math 414 (Numerical Analysis) 3 Credit Hours. Preq, MATH 245, knowledge of a programming language. Roots of polynomial and other nonlinear equations. Interpolating polynomials. Numerical differentiation. Numerical Integration. Direct methods for solving linear systems.(G)

Math 415 (Numerical Analysis) 3 Credit Hours. Preq, MATH 245, knowledge of a programming language. Numerical applications of linear algebra. Curve fitting. Function approximation. Numerical solution of systems of equations, differential equations, systems of differential equations, boundary value problems. (G)

STAT 620 (Theory of Probability) 3 Credit Hours. Preq, any 500 level STAT Course, and MATH 244. Combinatorial analysis, conditional probability, distribution theory, random variables, random vectors, limit theorems and random walks.

STAT 621 (Theory of Statistics) 3 Credit Hours. Preq, STAT 520 or 620. Point estimation, interval estimation, statistical hypothesis, statistical tests, non parametric inference, and normal distribution theory.

**CS Core** (6 SCH): (Common to all Tracks)

CSC 428 & CSC 438

CSC 428 (Object Oriented Programming and Data Structures). 3 Credit Hours. Preq, consent of instructor. Programming paradigms, syntax, semantics, data types, expression, control statements and sub programs; object oriented concepts, abstract data types, recursion, queues and trees. (G)

CSC 438 (Special Topics in Software Development). 3 Credit Hours. Preq, consent of instructor. Selected topics in the area of software design that are of current importance or special interest .(G)**Supporting Core** (CS - 3 SCH, MATH - 6 SCH)

CSC 581 or CSC 541, MATH 435, MATH 585 or MATH 535

CSC 541 (High Performance Computer Architecture) 3 Credit Hours. Preq, CSC 364. Topics include: principles of scalable performance, multiprocessor system design, message-passing systems, vector computers, data flow computers, and multithreaded architecture.

CSC 581 (Parallel Algorithms) 3 Credit Hours. Preq, CSC 240. Models of parallel computers, basic communication operations, algorithms for searching, sorting, graph structures, and systolic systems, dynamic programming, performance and scalability of parallel systems.

Math 435 (Introduction to Graph Theory) 3 Credit Hours. Preq, MATH 307, 311, or 318. Fundamental concepts of undirected and directed graphs, trees, connectivity, planarity, colorability, network flows, Hamiltonian and Eulerian graphs, matching theory and applications. (G)

Math 535 (Graph Theory) 3 Credit Hours. Preq, MATH 435 or consent of instructor. Fundamental concepts of graph theory, connectivity and traversability, algebraic and topological methods, graph minors, extremal graph theory, planarity, colorability, and random graphs.

Math 585 (Topics in Discrete Mathematics) 3 Credit Hours (15). May be repeated for 3 hours credit each time. This course will enable faculty in Discrete Mathematics to teach current topics and items related to their research specialty to graduate students. Topics will depend on faculty’s area of expertise and interest, but can include the matroid theory, fixed point theory in ordered sets, order and graph reconstruction, or splitter theorems for graphs.

**Suggested Elective Courses** (21 SCH total)

(Please, see advisor)

CSC 582 or CSC 585, CSC 557, STAT 620, STAT 506, CAM 657

CSC 557 (Special Topics: Computer Science) 3 Credit Hours (9). The topics or topics will be selected by the instructor from the various sub-area of computer science. May be repeated as topics change.

CSC 582 (Parallel Computational Methods) 3 Credit Hours. Preq, CSC 240, MATH 415. Parallel implementations of FFT, interpolation, integration, Eigensytsems, matrix maximization, ODEs, PDEs.

CSC 585 (High Performance and Availability Computing) 3 Credit Hours. Preq, CSC 345 or equivalent or consent of instructor. Study of and development in High Availability and Performance and Performance Computing (HAPC) and related fields, combing reading, research, and hands-on-oriented education.

STAT 620 (Theory of Probability) 3 Credit Hours. Preq, any 500 level STAT Course, and MATH 244. Combinatorial analysis, conditional probability, distribution theory, random variables, random vectors, limit theorems and random walks.

STAT 506 (Regression Analysis) 3 Credit Hours. Preq, STAT 405 or equivalent. Simple and multiple regressions, inferences in regression, model formulation and diagnostics, analysis of covariance, non linear models, estimation and inference. Use of computers in data analysis.

**Directed Study** (6 SCH)

CAM 650 or equivalent courses with other prefixes.

**Qualifying Exam**

MATH: CAM 685

CS: CAM 686

**Dissertation** (18 SCH)

CAM 651

**Total** (72 SCH)= MATH 15SCH + CS 9SCH + Elective 21 SCH + Directed Study 6 SCH + CAM610 3SCH + Dissertation 18 SCH.