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 broad-based 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.

Requirements Effective Fall 2016

Core Courses Select one of the following		Credit Hours 3
CSCE 659/ ECEN 659 CSCE 659/ECEN 659 — Parallel/Distributed Numerical Algorithms and Applications 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. CSCE 653 and MATH 304.	Parallel/Distributed Numerical Algorithms and Applications1	3
MATH 609 MATH 609 — Numerical Analysis 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 STAT 604 — Topics in Statistical Computations Credits 3. 3 Lecture Hours. Efficient uses of existing statistical computer programs (SAS, R, etc.); generation of random numbers; using and creating functions and subroutines; statistical graphics; programming of simulation studies; and data management issues. MATH 221, MATH 251, or MATH 253.	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 AERO 615 — Numerical Methods for Internal Flow 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 ATMO 618/GEOP 618/OCNG 618 — Numerical Methods for the Geosciences 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 CSCE 603 — Database Systems and Applications Credits 3. 3 Lecture Hours. Introduction to the concepts and design methodologies of database systems for non-computer science majors; emphasis on E. F. Codd's relational model with hands-on 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 CSCE 605 — Compiler Design Credits 3. 3 Lecture Hours. Advanced topics in compiler writing; parser generators and compiler-compilers; dynamic storage and scope resolution; data flow analysis and code optimization. CSCE 434.	Compiler Design	3
CSCE 620/ VIZA 670 CSCE 620/VIZA 670 — Computational Geometry 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. CSCE 311.	Computational Geometry	3
CSCE 626 CSCE 626 — Parallel Algorithm Design and Analysis Credits 3. 3 Lecture Hours. Design of algorithms for use on highly parallel machines; area-time complexity of problems and general lower bound theory; application (of these concepts) to artificial intelligence, computer vision and VLSI design automation. CSCE 221.	Parallel Algorithm Design and Analysis	3
CSCE 654 CSCE 654 — Supercomputing Credits 3. 3 Lecture Hours. Principles of high-performance scientific computing systems, vectorization, programming on supercomputers, numerical methods for supercomputers, performance measuring of supercomputers, multitasking. CSCE 614.	Supercomputing	3
CSCE 660/ MATH 660 CSCE 660/MATH 660 — Computational Linear Algebra Credits 3. 3 Lecture Hours. Techniques in matrix computation: elimination methods, matrix decomposition, generalized inverses, orthogonalization and least-squares, eigenvalue problems and singular value decomposition, iterative methods and error analysis. CSCE 442 (or equivalent) or MATH 417 (or equivalent).	Computational Linear Algebra	3
CVEN 680 CVEN 680 — Advanced Computation Methods for Fluid Flow Credits 3. 3 Lecture Hours. Unsteady three-dimensional Navier-Stokes equations in general nonorthogonal curvilinear coordinates; algebraic and elliptic grid generation; turbulence modeling for complex flows; advanced numerical methods for unsteady incompressible turbulent flows; large-eddy simulations; Reynolds-averaged Navier-Stokes simulation; chimera domain decomposition and interactive zonal approach. CVEN 688 or approval of instructor.	Advanced Computation Methods for Fluid Flow	3
CVEN 688 CVEN 688 — Computational Fluid Dynamics Credits 3. 3 Lecture Hours. Finite-difference and finite-element 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 GEOP 620 — Geophysical Inverse Theory 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 fault-plane reconstructions; advanced methods for nonlinear deterministic inversion. Graduate classification.	Geophysical Inverse Theory	3
MATH 610 MATH 610 — Numerical Methods in Partial Differential Equations Credits 4. 3 Lecture Hours. 3 Lab Hours. Introduction to finite difference and finite element methods for solving partial differential equations; stability and convergence of methods and error bounds. MATH 417 or MATH 609 (or equivalent) and knowledge of computer programming.	Numerical Methods in Partial Differential Equations	4
MATH 648 MATH 648 — Computational Algebraic Geometry 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 MATH 661 — Mathematical Theory of Finite Element Methods Credits 3. 3 Lecture Hours. Will develop basic mathematical theory of finite element method; construction of finite element spaces and piece-wise polynomial approximation; Ritz-Galerkin methods and variational crimes; energy and maximum norm estimates; mixed finite element method; applications to diffusion-reaction problems.	Mathematical Theory of Finite Element Methods	3
MATH 676 MATH 676 — Finite Element Methods in Scientific Computing 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; vector-valued 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 MEEN 672 — Introduction to Finite Element Method 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; time-dependent 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 NUEN 618 — Multiphysics Computations in Nuclear Science and Engineering Credits 3. 3 Lecture Hours. Tightly coupled multiphysics simulation techniques and application to typical problems arising in nuclear science and engineering (reactor dynamics and safety transients, conjugate heat transfer, radiative transfer, fluid structure interaction). MATH 609 and NUEN 606.	Multiphysics Computations in Nuclear Science and Engineering	3
PETE 656 PETE 656 — Advanced Numerical Methods for Reservoir Simulation 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 STAT 605 — Advanced Statistical Computations 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 lower-level languages with data analysis software; simulation; MC integration; MC-MC procedures; permutation tests; bootstrapping. STAT 612 and STAT 648.	Advanced Statistical Computations	3
STAT 608 STAT 608 — Regression Analysis Credits 3. 3 Lecture Hours. Multiple, curvilinear, nonlinear, robust, logistic and principal components regression analysis; regression diagnostics, transformations, analysis of covariance. STAT 601 or STAT 641.	Regression Analysis	3
STAT 626 STAT 626 — Methods in Time Series Analysis Credits 3. 3 Lecture Hours. Introduction to statistical time series analysis; autocorrelation and spectral characteristics of univariate, autoregressive, moving average models; identification, estimation and forecasting. STAT 601 or STAT 642 or approval of instructor.	Methods in Time Series Analysis	3
STAT 636 STAT 636 — Applied Multivariate Analysis Credits 3. 3 Lecture Hours. Multivariate extension of the chi-square and t-tests, 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. MATH 304 and STAT 608.	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:
1. an independent study graduate course within the student's home department, or
2. an independent study graduate course outside the student's home department, or
3. as part of a MS thesis or project required by the student's home department, or
4. as part of a PhD dissertation.
To fulfill this requirement, the ISC's associate director or director must approve the capstone project, certify its computational component, and document its completion.

Requirements Prior to Fall 2016

Core Courses Select two of the following exclusive of one's home department1		Credit Hours 6
CSCE 659/ ECEN 659 CSCE 659/ECEN 659 — Parallel/Distributed Numerical Algorithms and Applications 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. CSCE 653 and MATH 304.	Parallel/Distributed Numerical Algorithms and Applications2	3
MATH 609 MATH 609 — Numerical Analysis 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 STAT 604 — Topics in Statistical Computations Credits 3. 3 Lecture Hours. Efficient uses of existing statistical computer programs (SAS, R, etc.); generation of random numbers; using and creating functions and subroutines; statistical graphics; programming of simulation studies; and data management issues. MATH 221, MATH 251, or MATH 253.	Topics in Statistical Computations	3
Elective Courses Select two of the following exclusive of the student's home department1		Credit Hours 6
CSCE 603 CSCE 603 — Database Systems and Applications Credits 3. 3 Lecture Hours. Introduction to the concepts and design methodologies of database systems for non-computer science majors; emphasis on E. F. Codd's relational model with hands-on 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 CSCE 654 — Supercomputing Credits 3. 3 Lecture Hours. Principles of high-performance scientific computing systems, vectorization, programming on supercomputers, numerical methods for supercomputers, performance measuring of supercomputers, multitasking. CSCE 614.	Supercomputing	3
CSCE 660/ MATH 660 CSCE 660/MATH 660 — Computational Linear Algebra Credits 3. 3 Lecture Hours. Techniques in matrix computation: elimination methods, matrix decomposition, generalized inverses, orthogonalization and least-squares, eigenvalue problems and singular value decomposition, iterative methods and error analysis. CSCE 442 (or equivalent) or MATH 417 (or equivalent).	Computational Linear Algebra	3
MATH 610 MATH 610 — Numerical Methods in Partial Differential Equations Credits 4. 3 Lecture Hours. 3 Lab Hours. Introduction to finite difference and finite element methods for solving partial differential equations; stability and convergence of methods and error bounds. MATH 417 or MATH 609 (or equivalent) and knowledge of computer programming.	Numerical Methods in Partial Differential Equations	4
STAT 605 STAT 605 — Advanced Statistical Computations 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 lower-level languages with data analysis software; simulation; MC integration; MC-MC procedures; permutation tests; bootstrapping. STAT 612 and STAT 648.	Advanced Statistical Computations	3
STAT 608 STAT 608 — Regression Analysis Credits 3. 3 Lecture Hours. Multiple, curvilinear, nonlinear, robust, logistic and principal components regression analysis; regression diagnostics, transformations, analysis of covariance. STAT 601 or STAT 641.	Regression Analysis	3
STAT 626 STAT 626 — Methods in Time Series Analysis Credits 3. 3 Lecture Hours. Introduction to statistical time series analysis; autocorrelation and spectral characteristics of univariate, autoregressive, moving average models; identification, estimation and forecasting. STAT 601 or STAT 642 or approval of instructor.	Methods in Time Series Analysis	3
STAT 636 STAT 636 — Applied Multivariate Analysis Credits 3. 3 Lecture Hours. Multivariate extension of the chi-square and t-tests, 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. MATH 304 and STAT 608.	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:
1. an independent study graduate course in the home department, or
2. an independent study graduate course outside the home department, or
3. as part of a MS thesis or project required by the home department, or
4. as part of a PhD dissertation.
To fulfill this requirement, the faculty member supervising the capstone project must write a memo describing the project and certifying the project's computational component; this memo must be placed in the student's file in the home department.

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.