# Computation, Simulation & Modeling

Steering Committee Coordinator: Please contact Dr. Weizhong Dai regarding any questions about the Numerical Simulation & Modeling track in CAM.

**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 557, MATH 574, MATH 575 CSC 557 (Special Topics: Computer Science) 0-3-3 (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.

Math 574 (Numerical Solutions for PDE I) 0-3-3. Preq, MATH 407, 414. Finite difference
schemes and their accuracy, stability and convergence. Schemes for parabolic and hyperbolic
PDEs.

Math 575 (Numerical Solutions for PDE II) 0-3-3. Preq, MATH 407, 414, 574. Finite
difference schemes for elliptic PDEs, iterative methods, and introduction to finite
element methods and multigrid methods.

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

(see advisor)

CSC 541, MATH 435, MATH 535, CSC 470, CSC 570, CSC579, CAM 657 CSC 541 (High Performance
Computer Architecture)

0-3-3. Preq, CSC 364. Topics include: principles of scalable performance, multiprocessor
system design, message-passing systems, vector computers, data flow computers, and
multithreaded architecture.

Math 435 (Introduction to Graph Theory)

0-3-3. 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)

0-3-3. 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.

CSC 470 (Computer Graphics).

0-3-3. Preq, CSC 325. Fundamentals of two and three dimensional computer graphics.
Topics include line drawing, polygon rendering, clipping algorithms, two and three
dimensional transformations, and projection techniques. (G)

CSC 570 (Advanced Topics in Computer Graphics)

0-3-3. Preq, CSC 470. Techniques used to produce realistic images of three-dimensional
objects on computer graphics hardware. Topics include: reflection models, shading
techniques, ray tracing, texture and animation.

CSC 579 (Data Mining and Knowledge Discovery)

0-3-3; Prerequisite: CSC325/equivalent OR consent of instructor. Topics include: Introduction
to Data Mining (DM), Knowledge Discovery in large databases, Data preprocessing and
normalization, Dimensionality reduction, DM primitives, Mining frequent itemsets in
large DBMS, Association rule mining, Classification and evaluation measures. **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.