Computational Sciences Certificate Program (CSCP)
The Institute for Scientific Computation developed the Computational Sciences Certificate Program to meet the increased need for computational techniques that help solve complex science and engineering problems. This program targets science and engineering students enrolled in graduate studies, providing them with a broadbased multidisciplinary enhancement to their degree program and preparing them with the intellectual infrastructure necessary as a leader in computational science, engineering, and technology. By completing this certification program, a graduate will receive an official certified transcript that will add value and marketability to their advanced degree.
The Computational Sciences Certificate Program provides formal documentation on a student's transcript that they successfully completed courses focused on computational aspects that supplement their degree in science or engineering. To fulfill the certification requirements, a student must complete four total courses, as described by the program curriculum, and a capstone project within their home department.
Program Requirements
Requirements Effective Fall
Core Courses Select one of the following 
Credit Hours 3 


CSCE 659/ ECEN 659 Credits 3. 3 Lecture Hours. A unified treatment of parallel and distributed numerical algorithms; parallel and distributed computation models, parallel computation of arithmetic expressions; fast algorithms for numerical linear algrebra, partial differential equations and nonlinear optimization. 
Parallel/Distributed Numerical Algorithms and Applications1  3 
MATH 609
Credits 4. 3 Lecture Hours. 3 Lab Hours. Interpolation, numerical evaluation of definite integrals and solution of ordinary differential equations; stability and convergence of methods and error estimates. Knowledge of computer programming (C or FORTRAN). 
Numerical Analysis  4 
STAT 604  Topics in Statistical Computations  3 
Elective Courses Select three of the following, one of which must be exclusive of the student's home department2 
Credit Hours 9 

AERO 615
Credits 3. 3 Lecture Hours. Methods for solving internal flow problems; viscous and inviscid compressible flow, Euler/Navier Stokes solvers, boundary conditions. MATH 601 or approval of instructor. 
Numerical Methods for Internal Flow  3 
ATMO 618/ GEOP 618/ OCNG 618 Credits 3. 3 Lecture Hours. Mathematical theory and numerical techniques for modeling physical systems and processes in the Geosciences; discretization of continuum equations for solids and fluids; finite difference methods, convergence, consistency, and stability; finite element and spectral methods in fluid dynamics and seismology; iterative solvers; implicit and explicit methods for diffusion and advection. Graduate classification or approval of instructor. 
Numerical Methods for the Geosciences  3 
CSCE 603
Credits 3. 3 Lecture Hours. Introduction to the concepts and design methodologies of database systems for noncomputer science majors; emphasis on E. F. Codd's relational model with handson design application. No credit will be given for both CSCE 310 and CSCE 603. CSCE 601 and graduate classification. 
Database Systems and Applications  3 
CSCE 605
Credits 3. 3 Lecture Hours. Advanced topics in compiler writing; parser generators and compilercompilers; dynamic storage and scope resolution; data flow analysis and code optimization. 
Compiler Design  3 
CSCE 620/ VIZA 670 Credits 3. 3 Lecture Hours. Design and analysis of algorithms for solving geometrical problems; includes convex hull problems, Voronoi diagrams, range searching and proximity problems. 
Computational Geometry  3 
CSCE 626
Credits 3. 3 Lecture Hours. Design of algorithms for use on highly parallel machines; areatime complexity of problems and general lower bound theory; application (of these concepts) to artificial intelligence, computer vision and VLSI design automation. 
Parallel Algorithm Design and Analysis  3 
CSCE 654
Credits 3. 3 Lecture Hours. Principles of highperformance scientific computing systems, vectorization, programming on supercomputers, numerical methods for supercomputers, performance measuring of supercomputers, multitasking. 
Supercomputing  3 
CSCE 660/ MATH 660 Credits 3. 3 Lecture Hours. Techniques in matrix computation: elimination methods, matrix decomposition, generalized inverses, orthogonalization and leastsquares, eigenvalue problems and singular value decomposition, iterative methods and error analysis. 
Computational Linear Algebra  3 
CVEN 680
Credits 3. 3 Lecture Hours. Unsteady threedimensional NavierStokes equations in general nonorthogonal curvilinear coordinates; algebraic and elliptic grid generation; turbulence modeling for complex flows; advanced numerical methods for unsteady incompressible turbulent flows; largeeddy simulations; Reynoldsaveraged NavierStokes simulation; chimera domain decomposition and interactive zonal approach. CVEN 688 or approval of instructor. 
Advanced Computation Methods for Fluid Flow  3 
CVEN 688
Credits 3. 3 Lecture Hours. Finitedifference and finiteelement methods and basic numerical concepts for the solution of dispersion, propagation and equilibrium problems commonly encountered in real fluid flows; theoretical accuracy analysis techniques. Undergraduate course in fluid mechanics, MATH 601 and/or basic course in linear algebra, and knowledge of one programming language. 
Computational Fluid Dynamics  3 
GEOP 620
Credits 3. 3 Lecture Hours. Inferences about Earth structure from geophysical data; explicit treatment of sparse and noisy observations; construction of smooth Earth models; linear inversion of marine magnetic anomalies from seafloor magnetization; smooth inversion of DC sounding data from electrical structure; seismic tomography and geodetic faultplane reconstructions; advanced methods for nonlinear deterministic inversion. Graduate classification. 
Geophysical Inverse Theory  3 
MATH 610  Numerical Methods in Partial Differential Equations  4 
MATH 648
Credits 3. 3 Lecture Hours. Broad introduction to algorithmic algebraic geometry, including numerical and complexity theoretic aspects; theory behind the most efficient modern algorithms for polynomial system solving and the best current quantitative/geometric estimates on algebraic sets over various rings is derived. MATH 653 or or approval of instructor. 
Computational Algebraic Geometry  3 
MATH 661
Credits 3. 3 Lecture Hours. Will develop basic mathematical theory of finite element method; construction of finite element spaces and piecewise polynomial approximation; RitzGalerkin methods and variational crimes; energy and maximum norm estimates; mixed finite element method; applications to diffusionreaction problems. 
Mathematical Theory of Finite Element Methods  3 
MATH 676
Credits 3. 3 Lecture Hours. Basic finite element methods; structure of finite element codes; assembling linear systems of equations and algorithmic aspects; linear iterative solvers; adaptive mesh refinement; vectorvalued and mixed problems; nonlinear problems; visualization; parallelization aspects. Additional topics may be chosen by instructor. MATH 610, ENGR finite element class on MATH 419 or MATH 609, approval of instructor, and knowledge of C++. 
Finite Element Methods in Scientific Computing  3 
MEEN 672
Credits 3. 3 Lecture Hours. Weak or variational formulation of differential equations governing one and two dimensional problems of engineering; finite element model development and analysis of standard problems of solid mechanics (bars, beams, and plane elasticity), heat transfer and fluid mechanics; timedependent problems; computer implementation and use of simple finite element codes in solving engineering problems. Senior or graduate classification. 
Introduction to Finite Element Method  3 
NUEN 618  Multiphysics Computations in Nuclear Science and Engineering  3 
PETE 656
Credits 3. 3 Lecture Hours. Numerical simulation of flow in porous media based on numerical methods for partial differential equations; supplemented by published papers and research topics; development of a reservoir simulator. Graduate classification, basic reservoir simulation (or equivalent course), linear algebra and matrix computations (or equivalent course), advanced calculus (or equivalent course), and programming experience. 
Advanced Numerical Methods for Reservoir Simulation  3 
STAT 605
Credits 3. 3 Lecture Hours. Programming languages, statistical software and computing environments; development of programming skills using modern methodologies; data extraction and code management; interfacing lowerlevel languages with data analysis software; simulation; MC integration; MCMC procedures; permutation tests; bootstrapping. 
Advanced Statistical Computations  3 
STAT 608  Regression Analysis  3 
STAT 626  Methods in Time Series Analysis  3 
STAT 636
Credits 3. 3 Lecture Hours. Multivariate extension of the chisquare and ttests, discrimination and classification procedures; applications to diagnostic problems in biological, medical, anthropological and social research; multivariate analysis of variance, principal component and factor analysis, canonical correlations. 
Applied Multivariate Analysis  3 
Other  
Capstone Project3  
Total Semester Credit Hours  12 
 MATH 609 will also satisfy the CSCE 653 prerequisite.
 With the approval by the director of the Institute for Scientific Computation (ISC), student may substitute a course outside those listed as elective options. In such situations, the student must justify the substitution to and seek approval from the ISC's director prior to enrolling in the course. The director will include their support for the substitution in a memorandum to the Office of Graduate Studies (OGS) after the student files their degree plan with OGS and copies of these documents with the ISC.
 The capstone project's goal is to provide students with experience in the computational sciences. The capstone project may be fulfilled by:
 an independent study graduate course within the student's home department, or
 an independent study graduate course outside the student's home department, or
 as part of a MS thesis or project required by the student's home department, or
 as part of a PhD dissertation.
Requirements Prior to Fall
Core Courses Select two of the following exclusive of one's home department1 
Credit Hours 6 


CSCE 659/ ECEN 659 Credits 3. 3 Lecture Hours. A unified treatment of parallel and distributed numerical algorithms; parallel and distributed computation models, parallel computation of arithmetic expressions; fast algorithms for numerical linear algrebra, partial differential equations and nonlinear optimization. 
Parallel/Distributed Numerical Algorithms and Applications2  3 
MATH 609
Credits 4. 3 Lecture Hours. 3 Lab Hours. Interpolation, numerical evaluation of definite integrals and solution of ordinary differential equations; stability and convergence of methods and error estimates. Knowledge of computer programming (C or FORTRAN). 
Numerical Analysis  4 
STAT 604  Topics in Statistical Computations  3 
Elective Courses Select two of the following exclusive of the student's home department1 
Credit Hours 6 

CSCE 603
Credits 3. 3 Lecture Hours. Introduction to the concepts and design methodologies of database systems for noncomputer science majors; emphasis on E. F. Codd's relational model with handson design application. No credit will be given for both CSCE 310 and CSCE 603. CSCE 601 and graduate classification. 
Database Systems and Applications  3 
CSCE 654
Credits 3. 3 Lecture Hours. Principles of highperformance scientific computing systems, vectorization, programming on supercomputers, numerical methods for supercomputers, performance measuring of supercomputers, multitasking. 
Supercomputing  3 
CSCE 660/ MATH 660 Credits 3. 3 Lecture Hours. Techniques in matrix computation: elimination methods, matrix decomposition, generalized inverses, orthogonalization and leastsquares, eigenvalue problems and singular value decomposition, iterative methods and error analysis. 
Computational Linear Algebra  3 
MATH 610  Numerical Methods in Partial Differential Equations  4 
STAT 605
Credits 3. 3 Lecture Hours. Programming languages, statistical software and computing environments; development of programming skills using modern methodologies; data extraction and code management; interfacing lowerlevel languages with data analysis software; simulation; MC integration; MCMC procedures; permutation tests; bootstrapping. 
Advanced Statistical Computations  3 
STAT 608  Regression Analysis  3 
STAT 626  Methods in Time Series Analysis  3 
STAT 636
Credits 3. 3 Lecture Hours. Multivariate extension of the chisquare and ttests, discrimination and classification procedures; applications to diagnostic problems in biological, medical, anthropological and social research; multivariate analysis of variance, principal component and factor analysis, canonical correlations. 
Applied Multivariate Analysis  3 
Other  
Capstone Project3  
Total Semester Credit Hours  12 
 Outside courses listed on the student's degree plan can be used to satisfy the four course requirements.
 MATH 609 will satisfy the CSCE 653 prerequisite.
 The goal of the capstone project is to provide students with experience in the area of computational science. The intended length of the project is one semester. This project may be fulfilled by:
 an independent study graduate course in the home department, or
 an independent study graduate course outside the home department, or
 as part of a MS thesis or project required by the home department, or
 as part of a PhD dissertation.
Program Completion
Upon fulfilling the CSCP requirements, the student must officially notify the ISC (via memorandum delivered to the ISC office) and supply a copy of their degree plan filed with OGS. The student must also ensure the ISC has documentation of an approved, certified, and completed capstone project. The ISC's director will then notify OGS that the student successfully completed the CSCP requirements.