Currently, there are 17 academic departments and schools participating in the program.
These units along with their current IGMCS course offerings are listed below.
Please check the latest Graduate Catalog and Academic Timetable to verify course availability. Also, always check with your advisor or your IGMCS department liaison about course availability well ahead of time since some courses may be added or dropped from the Timetable late. In addition, consideration may be given to courses not listed here, after prior approval from the Program Committee.

### Departments

**Biochemistry and Cellular and Molecular Biology****Chemical and Biomolecular Engineering****Chemistry****Civil and Environmental Engineering****Earth and Planetary Sciences****Ecology and Evolutionary Biology****Electrical Engineering and Computer Science****Genome Science & Technology****Geography****Industrial and Systems Engineering****Information Sciences****Materials Science and Engineering****Mathematics****Mechanical, Aerospace and Biomedical Engineering****Microbiology****Nuclear Engineering****Physics****Statistics**

## Biochemistry and Cellular and Molecular Biology

**Departmental Liaison: Dr. Albrecht von Arnim ( )**

### Courses

**BCMB 510 Computational Structural Biochemistry**(1)

Introduction to computational tools, internet resources and databases for biological research to analyze and model protein structures and to study protein-ligand interactions.

(DE) Corequisite(s): 511.

Registration Permission: Consent of instructor.

**BCMB 511 Advanced Protein Chemistry and Cellular Biology**(3)

Cellular structure and function at molecular and supramolecular level in progression: protein structure and function; membrane structure and function; bioenergetics and membrane proteins.

(DE) Corequisite(s): 510.

Recommended Background: Prior knowledge of cell biology and biochemistry.

Registration Permission: Consent of instructor.

**BCMB 515 Experimental Techniques I**(2-4)

Introduction to modern experimental methodology and instrumentation in biochemistry, molecular biology and cell biology, including cell culture; spectrophotometry; microscopy; nucleic acid purification and analysis; protein assays; enzyme purification; electrophysiology; computer analysis of nucleic acid and protein sequences. Team-taught lecture/demonstration format.

Repeatability: May be repeated. Maximum 6 hours.

Comment(s): Primarily for departmental graduate students.

**BCMB 517 Physical Biochemistry**(3)

Physics and chemistry of biological systems and molecules. Thermodynamics; diffusion and transport; physical chemistry of macromolecules; enzyme kinetics; binding reactions; spectroscopy; electrophysiology.

(DE) Prerequisite(s): 511 or consent of instructor.

**BCMB 560 Advanced Concepts in Structural Biology/Biochemistry**(3)

Concepts related to structural biology/biochemistry with information taken from current literature. Predominantly lecture format with student participation. Specific subject area to be announced.

Repeatability: May be repeated. Maximum 12 hours.

Registration Permission: Consent of instructor.

## Chemical and Biomolecular Engineering

**Departmental Liaison: Dr. Steven Abel ( )**

### Courses

**CBE 506 Engineering Analysis**(3)

Formulation and solution of problems in chemical engineering and materials areas, ordinary and partial differential equations; types of ODE, PDE and solution techniques; transform methods; conformal mapping; variational methods; introduction to numerical methods.

Cross-listed: (Formerly CBE 505. Same as MSE 506/510.)

**CBE 547 Advanced Transport Phenomena**(3)

Unified treatment of momentum transport (fluid flow), energy transport (heat conduction, convection, and radiation), and mass transport (diffusion). Fundamental basis of transport phenomena and momentum transport: viscous, viscoelastic, and potential flows. (Formerly CBE 548)

**CBE 633 Multiscale Materials Modeling**(3)

Development of multiscale simulation strategies for engineering of advanced micro-and-nano structured materials via integration of essential information from different scales, i.e., molecular, mesoscopic and continuum.

(Also taught as Special Topics CBE 691 in spring 2012.)

## Chemistry

**Departmental Liaison: Dr. Robert Hinde ( )**

### Courses

**CHEM 570 Quantum Chemistry and Spectroscopy**(3)

Basic principles of quantum mechanics and their applications to molecular orbital theory, molecular structure, and spectroscopy; introduction to group theory.

Recommended Background: 2 semesters of physical chemistry.

**CHEM 572 Thermodynamics and Statistical Mechanics**(3)

Macroscopic and microscopic description of equilibrium systems. Basic principles of thermodynamics and statistical mechanics, and application to selected chemical systems.

Recommended Background: 2 semesters of physical chemistry.

**CHEM 670 Special Topics in Physical Chemistry**(3)

Topics of current significance. At present, Coupled-Channel Methods for Quantum Dynamics is the only 670 topic approved. However, other topics may qualify. See the Chemistry Dept. liaison for more information.

Repeatability: May be repeated. Maximum 12 hours.

(DE) Prerequisite(s): 570, 572, and 573 or consent of instructor.

Section offered in Fall of 2011 is not IGMCS eligible.

## Civil and Environmental Engineering

**Departmental Liaison: Dr. Joshua Fu ( )**

### Courses

**CE 538 / 561 Finite Element Applications for Geotechnical/Structural Engineering**(3)

Application of finite element method to typical problems in geotechnical engineering. Confined and unconfined flow through porous media; two-dimensional stress and strain; two-dimensional elements; representation of nonlinear soil behavior with elastic and elastic-plastic models. Taught concurrently with 561.

Application of finite element method to typical problems in structural engineering. Truss, beam and plate elements; two-dimensional stress and strain; two-dimensional elements; representation of nonlinear material behavior with elastic and elastic-plastic models. Taught concurrently with 538.

Credit Restriction: Students may not receive credit for both 538 and 561.

Recommended Background: Course work in soil behavior and matrix computation.

**CE 551 Traffic and Engineering Characteristics**(3)

Characteristics of human, vehicle, and roadway in transportation system; microscopic and macroscopic traffic models; elements of transportation/highway safety.

**CE 651 Analysis Techniques for Transportation Systems I**(3)

Topics on mathematical, statistical, operations research, or computer science techniques that may be applied to modeling and analysis of transportation systems.

Registration Restriction(s): Minimum student level - graduate.

Registration Permission: Consent of instructor.

**CE 652 Analysis Techniques for Transportation Systems II**(3)

Advanced topics of application of mathematical, statistical and computer science techniques in modeling and analysis of transportation systems.

(DE) Prerequisite(s): 651.

Registration Restriction(s): Minimum student level - graduate.

**ENVE 521 Climate Impacts on Water Resources**(3)

Theoretical and analytical approaches to the impact of climate variability and change on water resources. Oceanic-atmospheric variability and its impact on precipitation, snowpack, soil moisture and streamflow; analysis of spatial / temporal climatic and hydrologic datasets; paleo hydrology; parametric and non-parametric forecasting of streamflow; watershed models incorporating down-scaling of Global Circulation Model (GCM) forecasts of precipitation, temperature and the resulting land use changes.

**ENVE 561 Climate and Environmental Informatics**(3)

Introduction to applied time series, spatial statistics, and geographical data sciences for climate and the environmental applications with an emphasis on extreme events, regional analysis, uncertainty characterization and risk management. Case studies and class projects focused on integration of disparate data and analysis techniques to solve problems in climate change impacts.

**ENVE 562 Three Dimensional Climate Modeling**(3)

Theory and applied algorithms for three-dimensional climate modeling including conservation laws, prognostic and diagnostic relationships and climate model formulations. emphasis on numerical methods, coordinate systems, spatial and temporal discretizations, parameterization and model validation.

**ENVE 577 Air Pollution Climatology**(3)

Linkages between climate change and pollutant emissions, transport, transformation, and deposition. Both the impact of air quality on climate and the impact of climate on air quality will be examined using general circulation and meteorological models. Regional-scale effects of land utilization, incident radiation, climate perturbations and air quality parameters such as ozone, particulate matter, and greenhouse gases will be investigated.

**ENVE 595 / 691 Special Topic: Impact Analysis of the Climate Extreme Events**(3)

Research outcomes. Theory and practice of extreme events in climate change issues. The course will emphasize new development of climate studies. Students will learn critique extreme events articles and publications. The earth system models, GCMs, will be introduced and how to use its outputs to assess climate extreme effects. Global and regional climate modeling for impacts of extreme events based on IPCC CMIPS data availability and analysis of impacts of the climate extreme in large scale statistical and mathematical data analysis. The tools will be used such as empirical code, Data Mining, NCL, IDL, and Matlab. The Kraken and Newton machines are available for the data simulations and analyses. Hopefully students will have some accomplishment through this course, such as a draft for a conference and/or journal paper and useful findings.

**ENVE 595 Water Resources and Atmospheric Impacts of Climate Change**(3)

Problems and topics related to current developments in field.

**ENVE 672 Air Pollution Dispersion Modeling**(3)

Diffusion of air pollution in the atmosphere; application of USEPA computer models for atmospheric dispersion from industrial, area, mobile sources, and spills; evaluation and production of meteorological data and comparison of model predictions to ambient measurements; new source review and permitting requirements. Models have been in parallel computation.

(DE) Prerequisite(s): 574.

**ENVE 691 Advanced Climate and Air Pollution Modeling**(3)

Selected advanced problems of current interest.

## Earth and Planetary Sciences

**Departmental Liaison: Dr. Edmund Perfect ( )**

### Courses

**GEOL 401 Quantitative Methods in Geology**(3)

Applications of calculus and differential equations to problems in the earth sciences. Examples of the diffusion equation in hydrogeology; the wave equation in geophysics; mechanical modeling and boundary conditions in structural geology and tectonics.

Contact Hour Distribution: 3 hours lecture.

Recommended Background: Introductory geology and calculus or consent of instructor.

**GEOL 425 Data Analysis for Geoscientists**(3)

Overview of sampling schemes, data analysis, and statistical methods as applicable to Earth sciences.

Recommended Background: Introductory geology and introductory calculus, or consent of instructor.

**GEOL 473 Principles of Near-Surface Geophysics**(3)

Basics of several standard near-surface geophysics techniques (for example, seismic reflection, seismic refraction, surface wave and GPR, electrical resistivity, magnetics, and EM), using state-of-the-art field equipment to develop the skills necessary to process and interpret data. Includes a significant field component.

Recommended Background: Introductory calculus.

**GEOL 501 Fractal Models in Earth Sciences**(3)

An introduction to the theory and methods of fractal analysis as applicable to earth sciences. Topics include deterministic and statistical fractals, self-affine fractals, multifractals, percolation, renormalization group theory, cellular automata, and methods of estimating fractal parameters (e.g., dimension and lacunarity). Applications to be discussed include: characterization of coastlines, drainage basins, and fracture networks; terrain simulation; modeling porous media and hydraulic properties; rock fragmentation; spatial variability of mineral deposits; and temporal variability of earthquakes and floods.

Recommended Background: 6-8 hours of course work in earth sciences, calculus, or consent of instructor.

**GEOL 525 Data Analysis for Geoscientists**(3)

Overview of sampling schemes, data analysis, and statistical methods as applicable to earth sciences.

Recommended Background: Introductory geology and introductory calculus.

**GEOL 539 Geologic Applications of Remote Sensing**(3)

An introduction to the use of visible, infrared, microwave/radio, and nuclear remote sensing techniques in the geologic study of the Earth. Topics covered include mineral spectroscopy, light scattering models, instrumentation for remote sensing, calibration and atmospheric removal, multi- and hyperspectral image cube analysis, and ground-truthing techniques. Emphasis on working directly with remote sensing data to solve geologic problems.

Contact Hour Distribution: 2 hours lecture and one 2-hour lab.

Recommended Background: Mineralogy, calculus and physics or consent of instructor.

**GEOL 590 Special Problems in Geology**(1-3)

Student- or instructor-initiated course offered at the convenience of the department, with focus on specialized topics in the geological sciences.

Repeatability: May be repeated. Maximum 12 hours.

Registration Permission: Consent of instructor.

**GEOL 675 Seminar in Geophysics**(3)

Advanced treatment of selected topics in geophysics.

Repeatability: May be repeated. Maximum 9 hours.

Registration Permission: Consent of instructor.

**GEOL 685 Seminar in Hydrogeology**(3)

Repeatability: May be repeated. Maximum 9 hours.

Registration Permission: Consent of instructor.

## Ecology and Evolutionary Biology

**Departmental Liaison: Dr. Paul Armsworth ( )**

### Courses

**EEB 406 Models in Biology (Sec. 8)**(3)

Difference and differential equation models of biological systems.

Cross-listed: (Same as Mathematics 405.) (Formerly EEB 461.)

(DE) Prerequisite(s): Math 142, 148, 152, or permission from instructor.

**EEB 460 Evolution**(3)

Principles, facts, and theories regarding biological evolution. Concepts, processes, and product in development of organic diversity. Historical development of ideas concerning biological evolution.

Recommended: Biology 240.

**EEB 511 Core Evolution**(4)

Readings, lectures, and discussion about key concepts in evolution.

**EEB 560 Biometry**(3)

Statistical applications in biological research.

Recommended: Statistics course.

**EEB 575 Ecological Genetics**(3)

Genetics of natural populations, using both single-locus and quantitative genetical approaches.

Recommended: Statistics course.

**EEB 581 Mathematical Ecology I**(3)

Deterministic and stochastic models of populations, communities, and ecosystems.

Cross-listed: (Same as Mathematics 581.)

(DE) Prerequisite(s): MATH 431, 453, or permission from instructor.

**EEB 582 Mathematical Ecology II**(3)

Continuation of 581.

Cross-listed: (Same as Mathematics 582.)

(DE) Prerequisite(s): 581 or permission from instructor.

**EEB 585 Mathematical Evolutionary Theory**(3)

Population genetics and evolutionary ecology.

(Same as Mathematics 583.)

(DE) Prerequisite(s): MATH 431, 453, or permission from instructor.

**EEB 610 Advanced Topics in Mathematical, Theoretical and Computational Ecology**(1-3)

Exposure and in-depth training in contemporary topics and approaches important to advanced research in mathematical, theoretical, and computational ecology. Consult departmental listing for offerings.

Repeatability: May be repeated with consent of department. Maximum 9 hours.

**EEB 681 Advanced Mathematical Ecology I**(3)

Selected topics in theoretical and applied mathematical ecology: population, community, ecosystem ecology and applied topics such as demography, ecotoxicology, epidemiology, environmental change, and resource management.

Cross-listed: (Same as Mathematics 681.)

Repeatability: May be repeated. Maximum 6 hours.

(DE) Prerequisite(s): 581, 582, or permission from instructor.

**EEB 682 Advanced Mathematical Ecology II**(3)

Continuation of 681

(Same as Mathematics 682.)

Repeatability: May be repeated. Maximum 6 hours.

(DE) Prerequisite(s): 681 or permission from instructor.

## Electrical Engineering and Computer Science

**Departmental Liaison: Dr. Jack Dongarra ( )**

### Courses

**COSC 505 Programming for Scientists and Engineers**(3)

This course will provide an introduction to high-performance scientific computing tools, methods, and environments for the solution of problems in science and engineering. This course is NOT for EECS students.

Formerly COSC 594 Programming for Scientists and Engineers.

**COSC 526 Data Mining**(3)

A comprehensive introduction to the field of data mining. Topics covered include data preprocessing, predictive modeling, association analysis, clustering, classification, and anomaly detection. Prereq: Discrete mathematics or statistics and programming.

**COSC 527 Biologically Inspired Computation**(3)

A course that explores information processing and self-organization in biological systems. Topics include dynamical systems concepts (attractors, basins of attraction, Wolfram classes, stability, Lyapunov functions, information theory, thermodynamic limits of computation), cellular automata (Langton's lambda, phase transitions, computation and life at the "edge of chaos"), and excitable media (cardiac tissue, slime mold, reaction-diffusion systems, activator-inhibitor systems, Turing patterns and animal hair-coats), just to name a few. Students' understanding of complex systems and dynamical processes is enhanced by videos of biological systems and in-class demonstrations and experiments using multi-agent simulations.

Prerequisites: basic programming ability, linear algebra (e.g., Math 251), differential equations (e.g., Math 231, 241, but primarily just the concepts of differential equations and partial derivatives), probability and statistics (e.g., Math 323). Basic biology and physics are helpful as well.

**COSC 530 Computer Systems Organization**(3)

Architectures and systems organization for serial and parallel machines.

Recommended Background: Course work in architecture or machine organization.

**COSC 557 Visualization**(3)

Graphical techniques to reveal intrinsic properties in data, acquired or computationally simulated, from various scientific, medical and engineering applications. Topics may include visual perception, structure and storage of high-dimensional data (structured and unstructured), visualization of scalar fields, vector fields, tensor fields, or other complex quantities, time-varying data, advanced light transport (single-scattering and multiple scattering), transfer functions, graphs and manifolds, level sets, interpolation, hierarchical and paralle acceleration methods. The design and use of leading production visualization packages will also be covered. Recommended background: COSC 556 Computer Graphics.

**COSC 565 Survey of Programming Languages**(3)

Survey of different programming paradigms and their application to real-world applications. Topics may include scripting languages, event-based languages, functional languages, logic-based languages, and other cutting-edge language paradigms.

Recommended Background: COSC 302.

**COSC 571 Numerical Mathematics I**(3)

See Math 571.

**COSC 594 Computer Systems Organization**(3)

Architectures and systems organization for serial and parallel machines.

Recommended Background: Course work in architecture or machine organization.

(also listed as CS 530)

**COSC 594 Introduction to Computer Science for Computational Scientists**(3)

An introduction to high performance computing, data structures, parallel processing techniques, building a cluster, performance issues, design of algorithms, use of sw packages. Emphasis on program design, data structures, computational complexity, and scientific computing environments.

Prerequisites: programming and numerical methods.

**COSC 594 Programming for Scientists and Engineers**(3)

See COSC 505.

**COSC 594 Scientific Computing for Engineers**(3)

Spring 2012.

Part I will start with current trends in high-end computing systems and environments, and continue with a practical short description on parallel programming with MPI, OpenMP, and Pthreads. Part II will illustrate the modeling of problems from physics and engineering in terms of partial differential equations (PDEs), and their numerical discretization using finite difference, finite element, and spectral approximation. Part III will be on solvers: both iterative for the solution of sparse problems of part II, and direct for dense matrix problems. Algorithmic and practical implementation aspects will be covered. Finally in Part IV, various software tools will be surveyed and used. This will include PETSc, Sca/LAPACK, MATLAB, and some tools and techniques for scientific debugging and performance analysis.

**ECE 529 Application of Linear Algebra in Engineering Systems**(3)

Fundamental concepts of linear algebra to problems in engineering systems: steady state and dynamic systems. Geometric and physical interpretations of relevant concepts: least square problems, LU, QR, and SVD decompositions of system matrix, eigenvalue problems, and similarity transformations in solving difference and differential equations; numerical stability aspects of various algorithms; application of linear algebra concepts in control and optimization studies; introduction to linear programming. Computer projects.

Cross-listed: (Same as Biomedical Engineering 529; Chemical and Biomolecular Engineering 529; Industrial Engineering 529; Materials Science and Engineering 529; Mechanical Engineering 529; Nuclear Engineering 529.)

**ECE 557 Computer Architecture and Design**(3)

An exploration of the central issues in computer architecture: instruction set design, addressing and register set design, control unit design, microprogramming, memory hierarchies (cache and main memories, mass storage, virtual memory), pipelining, bus organization, RISC (Reduced Instruction Set Computers), and CISC (Complex Instruction Set Computers), implementation issues, technology trends, architecture modeling and simulation.

**ECE 575 HPC Modeling and Visualization**(3)

Application of high performance computer modeling to assess and visualize the impact of smoke and heat transfer to buildings, electronic equipment, and on human survivability. In-depth fire hazard analysis case studies. Advanced topics include software performance analysis and parallel processing.

Registration Permission: Consent of Instructor

**ECE 657 Advanced Computer Architecture and Design**(3)

Advanced computer architecture issues including topics such as superscalar architectures, parallel algorithms, principles of parallelism detection and vectorizing compilers, interconnection networks, SIMD/MIMD machines, processor synchronization, shared and distributed memory, data coherence, multiprocessors, multicomputers, dataflow machines, special purpose processors.

(DE) Prerequisite(s): 557.

## Genome Science & Technology

**Departmental Liaison: Dr. Albrecht von Arnim ( )**

### Courses

**LFSC 507 Bioinformatics and Computational Biology**(1-3)

Topics to be covered include the application of computing, modeling, data analysis, and information technology to fundamental problems in the life sciences.

Repeatability: May be repeated. Maximum 12 hours.

**LFSC 517 Genomics and Bioinformatics**(3)

This course covers molecular evolution and comparative genomics. Computational approaches are a cornerstone of this field. It is taught by computational biologist Dr. Igor Zhulin.

**LFSC 520 Genome Science and Technology I**(4)

Overview of genomics, advanced genetics principles. Either LFSC 520 or LFSC 521, but not both, may be counted toward the IGMCS.

**LFSC 521 Genome Science and Technology II**(4)

Analytical technologies and special techniques. Either LFSC 520 or LFSC 521, but not both, may be counted toward the IGMCS.

**LFSC 595 Special Topics in Genome Science and Technology**(1-3)

Tutorials or lectures in variety of special topics to be chosen by instructor.

Eligible sections include: A Survey of Biology for Computational Researchers.

Repeatability: May be repeated. Maximum 12 hours.

**LFSC 596 Special Topics in Genome Science and Technology**(1-3)

Tutorials or lectures in variety of special topics to be chosen by instructor.

Repeatability: May be repeated. Maximum 12 hours.

**LFSC 695 Advanced Topics in Genome Science and Technology**(1-3)

Tutorials or lectures on variety of advanced topics to be chosen by instructor.

Repeatability: May be repeated. Maximum 12 hours.

**LFSC 696 Advanced Topics in Genome Science and Technology**(1-3)

Tutorials or lectures on variety of advanced topics to be chosen by instructor.

Repeatability: May be repeated. Maximum 12 hours.

## Geography

**Departmental Liaison: Dr. Nicholas Nagle ( )**

### Courses

**GEOG 411 Introduction to Geographic Information Science**(3)

Concepts and methods of spatial analysis and their application using geographic information systems software and techniques. Emphasizes both theoretical and applied aspects of GIS.

Contact Hour Distribution: 2 hours lecture and 2 hours lab.

(DE) Prerequisite(s): 310 or consent of instructor.

**GEOG 414 Spatial Databases and Data Management**(3)

Types, sources, acquisition, and documentation of spatial data. Spatial database management methods and strategies for data sharing.

Contact Hour Distribution: 2 hours lecture and 2 hours lab.

(DE) Prerequisite(s): 411 or consent of instructor.

**GEOG 510 Geographic Software Design**(3)

Algorithms for spatial analysis, software design, and program implementation in stand alone and distributed computing environments.

Repeatability: May be repeated. Maximum 6 hours.

Registration Permission: Consent of instructor.

**GEOG 515 Topics in Quantitative Geography**(4)

Multivariate analysis applied to spatial and temporal problems in geography; research problems utilizing appropriate computer programs; usefulness to geographic research of techniques developed by other disciplines.

Contact Hour Distribution: 3 hours lecture and 2 hours lab per week.

Repeatability: May be repeated with consent of instructor. Maximum 8 hours.

Recommended Background: 415 or consent of instructor.

**GEOG 517 Geographic Information Management and Processing**(3)

Concepts and methods in management of geographic information. Database design, manipulation, sampling and analysis.

Registration Permission: Consent of instructor.

**GEOG 611 Seminar in Geographic Information Science**(3)

Repeatability: May be repeated. Maximum 6 hours.

(DE) Prerequisite(s): 517 and 518 or consent of instructor.

## Industrial and Systems Engineering

**Departmental Liaison: Dr. Jim Ostrowski ( )**

### Courses

**IE 552 Advanced Linear Programming and Extensions**(3)

Linear programming solution procedures, duality, sensitivity, and parametric analysis; and quadratic, separable, integer, and goal programming.

**IE 602 Nonlinear Optimization**(3)

Kuhn-Tucker theory in nonlinear programming, solution procedures for constrained and unconstrained nonlinear programs, search techniques, quadratic programming, duality and sensitivity analysis.

Cross-listed: Management Science 651

**IE 604 Network Flow Optimization**(3)

Fundamental theory, algorithms, and applications of deterministic network-flow models, and analytical procedures for a special class of stochastic networks (GERT networks). Linear programming and its relationship to network analysis. Algorithms for various kinds of shortest and k-shortest path models. Labeling procedures for maximal flows in capacitated networks. The Out-Of-Kilter algorithm for cost minimization flow models. Primal Simplex network optimization procedures for pure and generalized networks. Traveling-Salesman problem algorithms with extensions to multiple salesmen. CPM, PERT and network-flow models in project management. Introduction to multi-commodity networks. Extensive use of network optimization software.

(DE) Prerequisite(s): 522.

Registration Restriction(s): Minimum student level – graduate.

**IE 609 Stochastic Programming**(3)

Topics include modeling of uncertainty, two-stage stochastic programs, the value of information, Benders decomposition, L-shaped method, stochastic integer programs and multistage stochastic programs.

**IE 610 Heuristics in Optimization**(3)

Heuristic methods and their applications to optimization problems, including neighborhood search and major meta-heuristics methods.

**IE 611 Integer Programming**(3)

Theoretical foundations of Integer Programming and its application to optimization problems, including branch-and-bound, cutting planes, polyhedral analysis, and complexity.

## Information Sciences

**Departmental Liaison: Dr. Peiling Wang ( )**

### Courses

**INSC 565 Digital Libraries**(3)

Technological and social aspects of electronic publishing and digital libraries. Technologies and standards that enable electronic publishing and digital libraries. History of electronic publishing and digital libraries and their impact on user needs and information provision.

**INSC 581 Information Network Applications**(3)

Scholarly and community-based electronic communications. National and international standards, tools, resources; identification, analysis, evaluation, and management of tools and resources; construction of local technologies as developed and applicable.

Formerly INSC 567.

**INSC 584 Database Management Systems**(3)

Defining data needs, data structures, role of operating systems in data management, file organization, database management systems, logical data models, internal data models, database administration and evaluation. Design and implementation of application using database management system.

**INSC 587 Mining the Web**(3)

Covers strategies for mining the web, web engines and directories, cognitive accessibility, web design and development, and usability engineering.

**INSC 588 Human-Computer Interaction**(3)

Survey of human-computer interaction and introduction to human and technological factors of importance to design of usable information systems. Basic phenomena of human perception, cognition, memory, and problem solving, and relationship to user-centered design. Methods and techniques for interaction design and evaluation.

**INSC 594 Graduate Research Participation**(3)

Advanced research techniques under supervision of staff research director whose area coincides with interests of student.

Grading Restriction: Satisfactory/No Credit grading only.

Repeatability: May be repeated. Maximum 6 hours.

Registration Permission: Consent of advisor and research director.

Note: Need prior approval for the minor.

## Materials Science and Engineering

**Departmental Liaison: Dr. David Keffer ( )**

### Courses

**MSE 510 Engineering Analysis**(3)

Formulation and solution of problems in chemical engineering and materials areas, ordinary and partial differential equations; types of ODE, PDE and solution techniques; transform methods; conformal mapping; variational methods; introduction to numerical methods.

Cross-listed: (Same as CBE 506. Formerly MSE 506)

**MSE 611 Fundamentals of Thermodynamics, Phase Transformations, and Material Simulations at Small Length Scales**(3)

Covers fundamentals of thermodynamics of materials at small length scales, particularly as related to the dynamics of phase transformations. Topics will include fundamentals of statistical mechanics, mean-field Landau theory of phase transformations, and dynamics of phase transformations. Basics will be illustrated using various simulation methods, including molecular dynamics, Monte Carlo simulations, and phase-field modeling. Topics will be chosen according to time and student's interests.

(DE) Prerequisite(s): 511.

Comment(s): Prior knowledge may satisfy prerequisites, with consent of instructor.

**MSE 612 Computational Plasticity and Micromechanics**(3)

Computational modeling and simulation methods will be introduced with applications in plasticity, fracture and fatigue, microstructural evolution, and material instability in engineering structural materials. Topics include the classic finite element method based on constitutive modeling, cohesive interface model, discrete dislocation dynamics, atomistic/continuum coupling techniques, and current research areas that are pertinent to the research efforts at UT and ORNL.

**MSE 613 Modeling and Simulation in Materials Science and Engineering I. Quantum Mechanics**(3)

Introduction to and applications of quantum mechanical modeling and simulation of advanced materials at electronic and atomic levels of description. Development of structure/property relationships for functional, structural, and energy materials. Registration Restriction(s): Minimum student level – graduate.

**MSE 614 Modeling and Simulation in Materials Science and Engineering II. Classical Mechanics**(3)

Introduction to and applications of classical modeling and simulation of advanced materials at atomic and mesoscale levels of description. Development of structure/property relationships for functional, structural, and energy materials.

Registration Restriction(s): Minimum student level – graduate.

Registration Permission: Consent of instructor.

## Mathematics

**Departmental Liaison: Dr. Vasilios Alexiades ( )**

### Courses

**MATH 405 Models in Biology**(3)

Difference and differential equation models of biological systems. Credit

Restriction: May not be applied toward graduate degree in Mathematics.

(DE) Prerequisite(s): 142 or 148 or 152.

**MATH 411 Mathematical Modeling**(3)

Construction and analysis of mathematical models used in science and industry. Projects emphasized.

Recommended Background: Courses in differential equations and linear algebra.

**MATH 424 Stochastic Processes**(3)

Markov chains, Poisson processes and Brownian motion. Other topics as selected by instructor.

(DE) Prerequisite(s): 423.

**MATH 453 Matrix Algebra II**(3)

Advanced topics in matrix theory including Jordan canonical form.

(DE) Prerequisite(s): 251 or 257.

**MATH 471 Numerical Analysis**(3)

Introduction to computation, instabilities, and rounding. Interpolation and approximation by polynomials and piecewise polynomials. Quadrature and numerical solution of initial and boundary value problems of ordinary differential equations, stiff systems.

Cross-listed: (Same as Computer Science 471.)

Recommended Background: Course in basic numerical methods.

**MATH 472 Numerical Algebra**(3)

Direct and iterative methods for systems of linear equations. Solution of single nonlinear equation and nonlinear systems. Orthogonal decomposition, least squares and algebraic eigenvalue problem.

Cross-listed: (Same as Computer Science 472.)

Recommended Background: Course in basic numerical methods and linear algebra.

**MATH 475 Industrial Mathematics**(3)

Modeling, analysis, and computation applied to scientific/technical/industrial problems.

Recommended Background: Course in differential equations and familiarity with an operating system and a programming language.

**MATH 511 Methods in Applied Mathematics I**(3)

Fundamentals and techniques associated with discrete models of physical, engineering and biological systems: difference equations, networks and graphs, optimization, and other topics.

Recommended Background: Courses in advanced calculus and linear algebra.

**MATH 512 Methods in Applied Mathematics II**(3)

Fundamentals and techniques associated with continuous models of physical, engineering, and biological systems: development, solution and qualitative analysis of ordinary and partial differential equations, and calculus of variations.

(DE) Prerequisite(s): 511.

**MATH 513 Mathematical Principles of Fluid Mechanics I**(3)

Equations of motion, incompressible and compressible potential flow, shock waves, viscous flows. Navier-Stokes equations.

Recommended Background: Advanced courses in ordinary and partial differential equations and advanced calculus.

**MATH 514 Mathematical Principles of Fluid Mechanics II**(3)

Continuation of 513.

(DE) Prerequisite(s): 513.

**MATH 515 Analytical Applied Mathematics I**(3)

Analysis of advanced techniques in modern context for applied problems: dimensional analysis and scaling, perturbation theory, variational approaches, transform theory, wave phenomena and conservation laws, stability and bifurcation, distributions, integral equations.

Recommended Background: Courses in advanced calculus, linear algebra, and either advanced differential equations or 512.

**MATH 516 Analytical Applied Mathematics II**(3)

Continuation of 515.

(DE) Prerequisite(s): 515.

**MATH 517 Mathematical Methods in Physics I**(3)

Cross-listed: (See Physics 571.)

**MATH 527 Stochastic Modeling**(3)

Variable topics in probability applied to real world situations. Topics may include queuing theory, branching processes, Monte Carlo simulation, stochastic finance and other topics as selected by instructor.

Recommended Background: One year of advanced calculus and one year of undergraduate probability or mathematical statistics.

**MATH 537 Mathematical Principles of Continuum Mechanics I**(3)

Conservation principles, equations of equilibrium and motion for fluids and elastic solids, constitutive relations and stress, convexity properties, bifurcation phenomena, existence theory.

Recommended Background: Courses in advanced calculus and advanced differential equations.

**MATH 538 Mathematical Principles of Continuum Mechanics II**(3)

Continuation of 537.

(DE) Prerequisite(s): 537.

**MATH 571 Numerical Mathematics I**(3)

Direct and iterative methods for linear systems. The algebraic eigenvalue problem and the singular decomposition theorem. Newton and quasi-Newton methods for systems of nonlinear equations.

Cross-listed: (Same as Computer Science 571.)

Recommended Background: Courses in advanced calculus and basic numerical analysis.

**MATH 572 Numerical Mathematics II**(3)

Numerical techniques for initial value problems of ordinary differential equations. Two-point boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers.

Cross-listed: (Same as Computer Science 572.)

(DE) Prerequisite(s): 571.

**MATH 576 Linear and Nonlinear Programming**(3)

Linear programming, the simplex and interior methods. Integer, convex, stochastic and other topics in nonlinear programming. Applications to real world problems.

Recommended Background: Courses in numerical algorithms, linear algebra and advanced calculus.

**MATH 577 Optimization**(3)

Mathematical foundations of constrained and unconstrained optimization. Lagrange multipliers, the Farkas lemma, the Kuhn-Tucker-Karush theorem. Analysis of major algorithms and applications to real world problems.

Recommended Background: Courses in numerical algorithms, linear algebra and advanced calculus.

**MATH 578 Numerical Methods for Partial Differential Equations**(3)

Numerical approximation of solutions of partial differential equations including conservation laws and hyperbolic, parabolic, and elliptic problems. Derivation, physical meaning, and implementation of schemes.

Recommended Background: A course in partial differential equations or 512 or 515, and familiarity with an operating system and a programming language.

**MATH 585 Optimal Control Theory**(3)

Deterministic optimal control. Examples involving calculus of variations, optimal trajectories, and engineering control problems. Introduction to stochastic control.

Recommended Background: One year of advanced calculus and undergraduate differential equations.

**MATH 679 Seminar in Numerical Mathematics - Wavelets, Fast Algorithms, and PDEs**(3)

This course introduces and applies fast multiscale and multiresolution methods (e.g., fast multipole methods, wavelets, local Fourier basis, etc) to solve problems which are common in science and engineering. These techniques are a part of real analysis based algorithms. Requires Some familiarity with (lower) graduate level Fourier analysis, partial differential equations, numerical analysis or signal analysis is required; or with instructor's consent. Working knowledge of one of the programming languages (C, C++, FORTRAN, and Python) is also required. Offered in the Spring ('08).

## Mechanical, Aerospace and Biomedical Engineering

**Departmental Liaison: Dr. Kivanc Ekici ( )**

### Courses

**ES 551 Finite Elements for Engineering Applications**(3)

Modern computational theory applied to conservation principles across the engineering sciences. Weak forms, extremization, boundary conditions, discrete implementation via finite element, finite difference, finite volume methods. Asymptotic error estimates, accuracy, convergence, stability. Linear problem applications in 1, 2 and 3 dimensions, extensions to non-linearity, non-smooth data, unsteady, spectral analysis techniques, coupled equation systems. Computer projects in heat transfer, structural mechanics, mechanical vibrations, fluid mechanics, heat/mass transport. (Same as Aerospace Engineering 571; Biomedical Engineering 561; Mechanical Engineering 561.) Comment(s): Bachelor degree in engineering or natural science required.

**ES 552 Computational Fluid-Thermal Systems**(3)

Modern approximation theory applied to incompressible-thermal flows. Navier-Stokes equations, well-posedness, boundary conditions, non-dimensional groups, conjugate heat transfer, algebraic/differential closure models for turbulence. Weak forms, extremization, finite element/finite volume discrete implementations, a priori error estimates, accuracy, convergence, stability. Numerical linear algebra, sparse matrix methods. Applications in boundary layers, stream function-vorticity, pressure projection, free-surface, pseudo- compressibility completion theories. Solution-adaptive h- and r-meshing, optimal solution estimates. Augmentation theories for stability, numerical diffusion, Fourier spectral analyses, optimal forms. Computer projects. (Same as Aerospace Engineering 572; Biomedical Engineering 562; Mechanical Engineering 562.)

(DE) Prerequisite(s): 551.

**ES 651 Advanced Topics in Computational Fluid**(3)

Dynamics (3) Modern approximation theory for Euler and Navier-Stokes conservation systems, compressible flow, hyperbolic forms, boundary conditions. Weak forms, extremization, finite element/finite volume/flux vector discrete implementations, a priori error estimates, accuracy, convergence, stability. Numerical linear algebra, approximate factorization, sparse matrix methods. Dissipation, Fourier spectral analysis, smooth and non-smooth solutions. (Same as Aerospace Engineering 661; Mechanical Engineering 651.)

(DE) Prerequisite(s): 552.

**ES 652 Advanced Computational Fluid Dynamics Practice**(3)

Applications of modern CFD theory and code practice for Euler and Navier-Stokes conservation systems. Computer projects in incompressible/compressible flow, viscous, turbulent, reacting and/or inviscid/potential subsonic to hypersonic flows. (Same as Aerospace Engineering 662; Mechanical Engineering 652.)

(DE) Prerequisite(s): 645 and 651.

**ME 518 Computational Fluid Dynamics**(3)

Finite difference and finite volume techniques for solving compressible and incompressible fluid flow problems. Classification of partial differential equations and their discrete approximations. Explicit and Implicit techniques for solving unsteady Euler and Navier-Stokes equations including finite volume and finite difference formulations. Formulation of boundary conditions, artificial viscosity and multigrid acceleration. Stability analysis and convergence. Grid generation.

Cross-listed: (Same as Aerospace Engineering 518; Biomedical Engineering 518.) Recommended Background: Fluid mechanics, differential equations, and compressible flows. Registration Permission: Consent of instructor.

**ME 525 Combustion and Chemically Reacting Flows I**(3)

Fundamentals: thermochemistry, chemical kinetics and conservation equations; phenomenological approach to laminar flames; diffusion and premixed flame theory; single droplet combustion; deflagration and detonation theory; stabilization of combustion waves in laminar streams; flammability limits of premixed laminar flames; introduction to turbulent flames.

(DE) Prerequisite(s): 522 and 541 or consent of instructor.

**ME 526 Combustion and Chemically Reacting Flows II**(3)

Advanced topics: phenomenological approaches to turbulent flames; fundamentals of turbulent flow; application of probability density functions to turbulent flames; turbulent reacting flows with premixed and/or non-premixed reactants; spray combustion models; fluidized bed combustion; chemically reacting boundary layer flow; gas turbine and/or rocket motor combustors; furnaces; introduction to supersonic combustion and hypersonic flows.

(DE) Prerequisite(s): 525.

**ME 570 Numerical Methods for Engineers**(3)

Review and implementation of basic numerical techniques. Explicit and implicit solution techniques of ordinary differential equations and partial differential equations. Applications include heat transfer and fluid mechanics. (Formerly AE 599).

Recommended Background: Numerical analysis, fluid mechanics, heat transfer and differential equations. Registration Permission: Consent of Instructor.

**ME 645 Hydrodynamic Instability**(3)

Theory of hydrodynamic instability. Stability of shear flows, rotating flows, boundary layer, two fluid flows, capillary instability, convective/absolute stability. Normal mode analysis, energy theory of stability, linear stability analysis. Raleigh-Benard, Taylor, Raleigh-Taylor, Kevin-Helmholtz, Gortler instability. Orr-Sommerfeld equation, bifurcation theory, and transition to turbulence.

(DE) Prerequisite(s): 540 and 542.

## Microbiology

**Departmental Liaison: Dr. Igor Jouline ( )**

### Courses

**MICR 540 Genomics and Bioinformatics**(3)

Fundamentals of a new scientific discipline based on sequencing genomes (entire DNA) of individual organisms. Goals, principles and types of genome analysis are covered in a traditional lecture course. Computational tools for genome analysis (bioinformatics) are presented in both lecture and hands-on (computer-laboratory) settings.

**MICR 670 Advanced Topics in Environmental Microbiology**(1-3)

IGMCS eligibility is subject to course topic. Section numbers of eligible courses will be listed as they become available.

Repeatability: May be repeated. Maximum 12 hours.

Registration Permission: Consent of instructor.

## Nuclear Engineering

**Departmental Liaison: Dr. Ivan Maldonado ( )**

### Courses

**NE 470 Nuclear Reactor Theory I**(3)

Fundamentals of reactor physics relative to cross sections kinematics of elastic scattering, reactor kinetics, reactor systems, and nuclear data. Analytical and numerical methods applicable to general criticality problems, eigenvalue searches, perturbation theory, and the multigroup diffusion equations.

**NE 571 Reactor Theory and Design**(3)

Analytical and numerical techniques for neutronics modeling of nuclear systems. Forward and adjoint Boltzmann transport equation. Multigroup diffusion theory. Core analysis methods and codes.

(RE) Prerequisite(s): 470 or consent of instructor.

## Physics

**Departmental Liaison: Dr. Thomas Papenbrock ( )**

### Courses

**PHYS 513 Problems in Theoretical Physics I**(3)

Fundamentals of physics: classical mechanics (Newtonian mechanics, Lagrangian and Hamiltonian dynamics) and electrostatics and magnetostatics.

**PHYS 514 Problems in Theoretical Physics II**(3)

Fundamentals of physics: electrodynamics, relativity, and quantum mechanics.

**PHYS 571 Mathematical Methods in Physics I**(3)

Linear vector spaces, matrices, tensors, curvilinear coordinates, functions of a complex variable, partial differential equations and boundary value problems, Green's functions, integral transforms, integral equations, spherical harmonics, Bessel functions, calculus of variations.

Cross-listed: (Same as Mathematics 517.)

Recommended Background: Advanced calculus and differential equations.

**PHYS 572 Mathematical Methods in Physics II**(3)

Advanced Problems. Topics may vary according to interests of students and instructor.

Cross-listed: (Same as Mathematics 518.)

(DE) Prerequisite(s): 571.

**PHYS 573 Numerical Methods in Physics**(3)

Numerical methods for solution of physical problems, use of digital computers, analysis of errors.

(DE) Prerequisite(s): 571 or consent of instructor.

**PHYS 642 Advanced Topics in Modern Physics**(3)

IGMCS Eligible Topics: "Modern Biological Physics: Network and Systems Biology"

**PHYS 643 Computational Physics**(3)

Developing computer algorithms for solving representative problems in various fields of physics, celestial dynamics in astrophysics, boundary value problems in electromagnetism, atomic and nuclear structures, band structure in solid state physics, transport problems in statistical mechanics, Monte Carlo simulation of liquids, fitting and interpolation of data, correlation analysis, or optimization strategy.

(DE) Prerequisite(s): 521, 531, and 571.

Registration Restriction(s): Minimum student level – graduate.

## Statistics

**Departmental Liaison: Dr. Hamparsum Bozdogan ( )**

### Courses

**STAT 537 Statistics for Research I**(3)

Principles and application of statistical methodology, integrated with considerable use of major statistical computing system. Probability and probability distributions, forming and testing hypotheses using parametric and nonparametric inference methods. Matrix-based simple linear regression and correlation.

**STAT 538 Statistics for Research II**(3)

General linear model as applied to multiple regression and analysis of variance. Diagnostic and influence techniques. One-way, factorial, blocking, and nested designs, preplanned versus post-hoc contrasts. Random factors and repeated measures.

(RE) Prerequisite(s): 537 or 532.

**STAT 563 Probability**(3)

Basic probability and probability models; random variables and distributional models; kernel density estimation; cubic splines; likelihood inference and maximum likelihood estimation and model fitting with information criteria; moment and moment generating functions; functions of random variables; goodness of fit tests and quantile modeling of distributions.

(DE) Prerequisite(s): Mathematics 241.

Registration Permission: Prerequisite (s) or consent of instructor required.

**STAT 564 Statistical Inference II**(3)

Sampling distributions; point and interval estimation; fixed width entropy confidence intervals; likelihood theory; Fisher information and its inverse; large sample, deviance, and bootstrap confidence intervals; Bayesian estimation and hypothesis testing; information approach to hypothesis testing; uniformly most powerful and likelihood ratio tests, theory of linear models, estimation, model building and inference.

(DE) Prerequisite(s): 563.

**STAT 572 Applied Regression Analysis**(3)

Simple linear regression. Matrix approach to multiple linear regression. Partial and sequential sums of squares, interaction and confounding, use of dummy variables, model selection. Leverage, influence and collinearity. Autocorrelated errors. Generalized linear models, maximum likelihood estimation, logistic regression, analysis of deviance. Nonlinear models, inference, ill-conditioning. Robust regression, M-estimators, iteratively reweighted least squares. Nonparametric regression, kernel, splines, testing lack of fit.

(DE) Prerequisite(s): 571 and matrix algebra.

**STAT 579 Applied Multivariate Methods**(3)

Multivariate techniques: Hotellings T-sq. MANOVA, discriminant analysis, canonical correlation, principal component analysis, and factor analysis. Computer oriented approach: analysis and interpretation. Knowledge of basic matrices and SAS essential.

(DE) Prerequisite(s): 538 or knowledge of regression and analysis of variance.

**STAT 662 Computational Methods in Statistics**(3)

Up-to-date computational methods in statistics: open architecture interactive computational languages supplemented by other statistical packages with graphical capabilities. Statistical computing, numerical methods for linear models and generalized linear models, nonlinear statistical methods, matrix computations and special matrices, essentials of Monte Carlo simulation, and resampling techniques.

Recommended Background: Knowledge of programming language and 572 or consent of instructor.

**STAT 674 Advanced Data Mining**(3)

Interacting roles of statistical learning and data mining. Statistical data structures, measurement, visualization and exploration. Multidimensional scaling, classification methods, decision trees, neural networks, association rules and market basket analysis. Cluster analysis. Bayesian clustering, evaluation and selection of models and information criterion. Boosting and bagging. Support vector machines, optimization, search methods, and algorithms.

(DE) Prerequisite(s): 564, 579 and knowledge of programming language or consent of instructor.

**STAT 677 Statistical Modeling**(3)

Modern techniques of statistical modeling: predictive, likelihood, Bayesian, and information-based model selection and evaluation paradigms. Application of techniques in various types of models for both continuous and discrete data modeling problems. Interactive computational tools.

(DE) Prerequisite(s): 564 and 572 or 538 or consent of instructor.

**STAT 679 Multivariate Statistical Modeling**(3)

Modern information based techniques and model selection in multivariate analysis, informational tests of significance with multivariate data, multivariate analysis of variance, multivariate regression and variable selection, multisample cluster analysis, common principal component model, factor analysis model, covariance structural models with latent variables, mixture-model cluster analysis.

Recommended Background: Matrix algebra and 564 or matrix-based linear models with experience in interactive computing or consent of instructor.