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# CSEM Course Information

### UT Course Information

### List of Courses by Area

Download a list of approved courses to satisfy Area A, B, & C requirements. Note: All course selections must be approved by the Graduate Adviser. See Graduate Catalog for full course descriptions.

__Area C Policy__

- The course must explore the underlying scientific principles of the natural, social, or other system that constitutes the target application area. [Engage the science.]
- The course may include some computational or mathematical modeling components, but it must explore the purpose and physical interpretation of the computation and models. [CSE is done to foster some scientific or societal goal, and the course must discuss this aspect in much more than a passing way.]

### CSEM Course Inventory

CSE 380 | Tools and Techniques of Computational Science |
Graduate level introduction to the practical use of high performance computing hardware and software engineering principles for scientific technical computing. Topics include computer architectures, operating systems, programming languages, data structures, interoperability, and software development, management and performance. Three lecture hours a week for one semester. Prerequisite: Graduate standing or consent of instructor. |

CSE 382G | Computer Graphics |
(Same as Computer Science 384G) Advanced material in computer graphics, including in-depth treatments of techniques for realistic image synthesis, advanced geometric modeling methods, animation and dynamic simulation, scientific visualization, and high-performance graphics architectures. Three lecture hours a week for one semester. Prerequisite: Graduate standing; and Computer Science 354 or another introductory course in computer graphics, or equivalent background and consent of instructor. Computational and Applied Mathematics 384G and Computational Science, Engineering, and Mathematics 382G may not both be counted. |

CSE 383C | Numerical Analysis: Linear Algebra |
(Same as Computer Science 383C, Mathematics 383E and Statistics and Scientific Computation 393C) Survey of numerical methods in linear algebra: floating-point computation, solution of linear equations, least squares problems, algebraic eigenvalue problems. Three lecture hours a week for one semester. Prerequisite: Graduate standing, either consent of instructor or Mathematics 341 or 340L, and either Mathematics 368K or Computer Science 367. Computational and Applied Mathematics 383C and Computational Science, Engineering, and Mathematics 383C may not both be counted. |

CSE 383D | Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations |
(Same as Computer Science 383D, Mathematics 383F and Statistics and Scientific Computation 383D) Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations. Three lecture hours a week for one semester. Prerequisite: Graduate standing; either consent of instructor or Mathematics 427K and 365C; and Computational Science, Engineering, and Mathematics 383C or the equivalent. Computational and Applied Mathematics 383D and Computational Science, Engineering, and Mathematics 383D may not both be counted. |

CSE 383K | Numerical Analysis: Algebra and Approximation |
(Same as Mathematics 387C) Graduate level introduction to scientific computing, theory and application of numerical linear algebra, solution of nonlinear equations, and numerical approximation of functions. Three lecture hours per week for one semester. Prerequisite: Graduate standing, or consent of instructor. Computational and Applied Mathematics 386K and Computational Science, Engineering, and Mathematics 383K may not both be counted. |

CSE 383L | Numerical Analysis: Differential Equations |
(Same as Mathematics 387D) Graduate level introduction to the theory and practice of commonly used numerical algorithms for the solution of ordinary differential equations, and elliptic, parabolic, and hyperbolic partial differential equations. Three lecture hours per week for one semester. Prerequisite: Graduate standing, and Computer Science 383C or Mathematics 387C, or consent of instructor. |

CSE 383M | Statistical and Discrete Methods for Scientific Computing |
Studies probabilistic and statistical inference, statistical model fitting, computational geometry, image processing, computational graph theory, and information theory. Prerequisite: Graduate standing. Computational and Applied Mathematics 383M, 395T (Topic: Computational Statistics with Application to Bioinformatics), and Computational Science, Engineering, and Mathematics 383M may not each be counted. |

CSE 384K | Theory of Probability |
(Same as Mathematics 385C) Three lecture hours a week for one semester. Prerequisite: Graduate standing and consent of instructor. Computational and Applied Mathematics 384K and Computational Science, Engineering, and Mathematics 384K may not both be counted. |

CSE 384L | Theory of Probability |
(Same as Mathematics 385D) Three lecture hours a week for one semester. Prerequisite: Graduate standing, consent of instructor, and Computational Science, Engineering, and Mathematics 384K or the equivalent. Computational and Applied Mathematics 384L and Computational Science, Engineering, and Mathematics 384L may not both be counted. |

CSE 384R | Mathematical Statistics I |
(Same as Mathematics 384C and Statistics and Scientific Computation 384 (Topic 2)) General theory of mathematical statistics. Hypothesis testing, estimation, decision theory. Three lecture hours a week for one semester. Prerequisite: Graduate standing, and Mathematics 378K or consent of instructor or the graduate adviser in mathematical statistics. Computational and Applied Mathematics 384R and Computational Science, Engineering, and Mathematics 384R may not both be counted. |

CSE 384S | Mathematical Statistics II |
(Same as Mathematics 384D and Statistics and Scientific Computation 384 (Topic 3)) Continuation of Computational and Applied Mathematics 384R. Three lecture hours a week for one semester. Prerequisite: Graduate standing, consent of instructor, and Computational Science, Engineering, and Mathematics 384R or the equivalent. Computational and Applied Mathematics 384S and Computational Science, Engineering, and Mathematics 384S may not both be counted. |

CSE 384T | Regression Analysis |
(Same as Mathematics 384G and Statistics and Scientific Computation 384 (Topic 4)) Simple and multiple linear regression, inference in regression, prediction of new observations, diagnosis and remedial measures, transformations, and model building. Emphasis on both understanding the theory and applying theory to analyze data. Three lecture hours a week for one semester. Prerequisite: Graduate standing; and Mathematics 362K and 378K, Statistics and Scientific Computation 382, or consent of instructor. Computational and Applied Mathematics 384T and Computational Science, Engineering, and Mathematics 384T may not both be counted. |

CSE 384U | Design and Analysis of Experiments |
(Same as Mathematics 384E and Statistics and Scientific Computation 384 (Topic 6)) Design and analysis of experiments, including one-way and two-way layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; and split plot designs. Three lecture hours a week for one semester. Prerequisite: Graduate standing; and Mathematics 362K and 378K, Statistics and Scientific Computation 382, or consent of instructor. Computational and Applied Mathematics 384U and Computational Science, Engineering, and Mathematics 384U may not both be counted. |

CSE 385M | Methods of Mathematical Physics I |
(Same as Physics 381M) Theory of analytic functions; linear algebra and vector spaces; orthogonal functions; ordinary differential equations; partial differential equations; Green's functions; complex variables. Three lecture hours a week for one semester. Prerequisite: Graduate standing. Computational and Applied Mathematics 381M and Computational Science, Engineering, and Mathematics 385M may not both be counted. |

CSE 385N | Methods of Mathematical Physics II |
(Same as Physics 381N) Continuation of Computational Science, Engineering, and Mathematics 385M. Topology, functional analysis, approximation methods, group theory, differential manifolds. Three lecture hours a week for one semester. Prerequisite: Graduate standing, and Computational Science, Engineering, and Mathematics 385M or the equivalent. Computational and Applied Mathematics 381N and Computational Science, Engineering, and Mathematics 385N may not both be counted. |

CSE 385R | Real Analysis |
(Same as Mathematics 381C) Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Three lecture hours a week for one semester. Prerequisite: Graduate standing and consent of instructor or the graduate adviser. Computational and Applied Mathematics 381R and Computational Science, Engineering, and Mathematics 385R may not both be counted. |

CSE 385S | Complex Analysis |
(Same as Mathematics 381D) Introduction to complex analysis. Three lecture hours a week for one semester. Prerequisite: Graduate standing and consent of instructor or the graduate adviser. Computational and Applied Mathematics 381D and Computational Science, Engineering, and Mathematics 385S may not both be counted. |

CSE 386C | Methods of Applied Mathematics |
(Same as Mathematics 383C) Topics include basic normed linear space theory; fixed-point theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to Sturm-Liouville problems; approximation and computational methods such as the Galerkin, Rayleigh-Ritz, and Newton procedures. Three lecture hours a week for one semester. Prerequisite: Graduate standing. Computational and Applied Mathematics 385C and Computational Science, Engineering, and Mathematics 386C may not both be counted. |

CSE 386D | Methods of Applied Mathematics |
(Same as Mathematics 383D) Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems. Three lecture hours a week for one semester. Prerequisite: Graduate standing and Computational Science, Engineering, and Mathematics 386C or equivalent. Computational and Applied Mathematics 385D and Computational Science, Engineering, and Mathematics 386D may not both be counted. |

CSE 386L | Mathematical Methods in Science and Engineering |
Basic concepts in real and complex analysis, ordinary and partial differential equations, and other areas of applied mathematics with application to engineering and science. Three lecture hours a week for one semester. Prerequisite: Graduate standing. Computational and Applied Mathematics 386L and Computational Science, Engineering, and Mathematics 386L may not both be counted. |

CSE 386M | Functional Analysis in Theoretical Mechanics |
(Same as Engineering Mechanics 386M) An introduction to modern concepts in functional analysis and linear operator theory, with emphasis on their application to problems in theoretical mechanics; topological and metric spaces, norm linear spaces, theory of linear operators on Hilbert spaces, applications to boundary value problems in elasticity and dynamical systems. Three lecture hours a week for one semester. Prerequisite: Graduate standing and Computational Science, Engineering, and Mathematics 386L or equivalent. Computational and Applied Mathematics 386M and Computational Science, Engineering, and Mathematics 386M may not both be counted. |

CSE 389C | Introduction to Mathematical Modeling in Science and Engineering I |
Part I of an introduction to the elements of classical mechanics, physics, chemistry, and biology needed to begin work in computational engineering and sciences. Develops from first principles the classical mathematical theories underlying many of the models of physical phenomena important in modern applications. Three lecture hours a week for one semester. Prerequisite: Graduate standing. Computational and Applied Mathematics 389C and Computational Science, Engineering, and Mathematics 389C may not both be counted. |

CSE 389D | Introduction to Mathematical Modeling in Science and Engineering II |
Part II of an introduction to elements of classical mechanics, physcis, chemistry, and biology needed to work in computational engineering and sciences. Develops from first principles the classical mathematical theories underlying many of the models of physical phenomena important in modern applications. Three lecture hours a week for one semester. Prerequisite: Graduate standing and Computational Science, Engineering, and Mathematics 389C or equivalent. Computational and Applied Mathematics 389D and Computational Science, Engineering, and Mathematics 389D may not both be counted. |

CSE 190, 390 | Individual Research |
Must be arranged by mutual agreement between student and faculty member. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. May be repeated for credit. Prerequisite: Graduate standing and consent of instructor. |

CSE 392 | Topics in Computer Science |
Advanced topics in the theory and application of Computer Science. Recent topics include geometric modeling and visualization, and high-performance and parallel computing. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Prerequisite: Graduate standing. |

CSE 393 | Topics in Numerical Analysis |
Advanced topics in the theory and application of Numerical Analysis. Recent topics include numerical methods for partial differential equations, computational problems in linear algebra, iterative methods and fast algorithms, numerical methods in functional approximation, and computational and variational methods for inverse problems. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor. |

CSE 393F | Finite Element Methods |
(Same as Aerospace Engineering 384P (Topic 4: Finite Element Methods) and Engineering Mechanics 394F) Derivation and implementation of the finite element method; basic coding techniques; application to problems of stress and diffusion. Three lecture hours a week for one semester. Prerequisite: Graduate standing and consent of instructor. Computational and Applied Mathematics 394F and Computational Science, Engineering, and Mathematics 393F may not both be counted. |

CSE 393H | Advanced Theory of Finite Element Methods |
Contemporary topics in the theory and application of finite element methods. Three lecture hours a week for one semester. Prerequisite: Graduate standing, Computational Science, Engineering, and Mathematics 393F or the equivalent, and Engineering Mechanics 386L or the equivalent. Computational and Applied Mathematics 394H and Computational Science, Engineering, and Mathematics 393H may not both be counted. |

CSE 393N | Numerical Methods for Flow and Transport Problems |
Approximate solution methods for flow and transport problems in engineering and applied science. Finite element, finite difference, and residual methods for linear and nonlinear problems. Three lecture hours a week for one semester. Prerequisite: Graduate standing. Computational and Applied Mathematics 393N and Computational Science, Engineering, and Mathematics 393N may not both be counted. |

CSE 394 | Topics in Probability and Statistics |
Advanced topics in the theory and application of probability and statistics. Recent topics include nonparametric statistics and advanced probability. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor. |

CSE 396 | Topics in Applied Mathematics |
Advanced topics in the theory and application of Applied Mathematics. Recent topics have included partial differential equations, dynamical systems, kinetic theory, quantum mechanics, ergodic theory, statistical mechanics, Hamiltonian dynamics, nonlinear functional analysis, Euler and Navier-Stokes equations, microlocal calculus and spectral asymptotics, calculus of variations, and nonlinear partial differential equations. Three lecture hours a week for one semester. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor. |

CSE 397 | Topics in Computational Science and Engineering |
Advanced topics in the theory and application of computational science and engineering. May be repeated for credit when the topics vary. Some sections may be offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing. |

CSE 698 | Thesis |
The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in Computational Science, Engineering, and Mathematics and consent of the graduate adviser; for 698B, Computational Science, Engineering, and Mathematics 698A. |

CSE 398R | Master's Report |
Preparation of a report to fulfill the requirement for the master's degree under the report option. Independent study. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in Computational Science, Engineering, and Mathematics and consent of the graduate adviser. |

CSE 399, 699R, 999R | Dissertation |
Independent study. Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree. |

CSE 399W, 699W, 999W | Dissertation |
Independent study. Offered on the credit/no credit basis only. Prerequisite: Computational Science, Engineering, and Mathematics 399R, 699R, or 999R. |