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The University of Tennessee

IGMCS: Interdisciplinary Graduate Minor in Computational Science

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Departments/Courses


IGMCS: Participating Departments and Course Offerings

Currently, there are 14 academic departments and schools participating in the program. These units along with their current IGMCS course offerings are listed below. Please check with the latest Graduate Catalog and Academic Calendar to verify course availability.

Departments

Biochemistry & Cellular and Molecular Biology


Departmental Liaison: Dr. Cynthia Peterson (cbpeters@utk.edu)

Courses

401 Biochemistry-Molecular Biology I (4)
First semester of a two course sequence providing in-depth coverage of biochemistry and molecular biology. Covers amino acid structure and chemistry, protein structure and chemistry, protein folding, enzyme behavior and function, reaction mechanisms, catabolism and energy transfer, synthetic metabolism including photosynthesis, and protein transport.
(DE) Prerequisite(s): Biology 240 and Chemistry 350, 360, and 369.

402 Biochemistry-Molecular Biology II (4)
Second semester of a twocourse sequence providing in-depth coverage of biochemistry and molecular biology. Covers structure of DNA and RNA, experimental methods of analyzing nucleic acids, mechanisms of RNA and protein synthesis, mechanisms of DNA replication, repair and recombination, chromosome structure and function, regulation of gene expression, genome structure and genomics, and mechanisms of biological regulation.
(DE) Prerequisite(s): Biology 240 and Chemistry 350, 360, and 369.

471 Biophysical Chemistry (3)
Physicochemical principles with applications to biological systems. Thermodynamics; chemical equilibrium; solution chemistry; transport; electrochemistry; kinetics; enzyme catalyzed reactions. (Same as Chemistry 471.)
(DE) Prerequisite(s): Chemistry 350 and 360, Mathematics 125, and general biology or consent of instructor.

481 Biophysical Chemistry (3)
Physicochemical principles with applications to biological systems. Elementary quantum chemistry; interactions of light with biological molecules; optical and magnetic spectroscopy; light scattering; case studies of selected macromolecules. (Same as Chemistry 481.)
(DE) Prerequisite(s): Chemistry 350 and 360, Mathematics 125, and general biologyor consent of instructor.

510 Computational Structural Biochemistry (1)
Computational approaches to biomolecular structure, including homology modeling, threading, and molecular dynamics. (DE) Prerequisite(s): Prior knowledge of cell biology and biochemistry.
Registration Permission: Consent of instructor.

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) Prerequisite(s): Prior knowledge of cell biology and biochemistry. Registration Permission: Consent of instructor.

512 Advanced Molecular Biology (3)
Regulation of nucleic acid expression and protein activity. Nucleic acid structure and function; replication and repair of nucleic acids; gene expression; protein synthesis; posttranslational protein modification; mitosis and meiosis; cell cycle and cell growth.
(DE) Prerequisite(s): 511 or consent of instructor.

513 Advanced Protein Biochemistry and Cell Biology II (3)
Advanced topics of cellular function and regulation of cell division and growth, and structure and function of supramolecular structures: cytoskeleton and cell junctions and adhesions.
(DE) Prerequisite(s): 511.

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.

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.

559 Biophysical Crystallography (3)
Theories and practices of X-ray diffraction, neutron diffraction and neutron scattering to elucidate the structure of nucleic acids, proteins, nucleosomes, ribosomes and viruses. Application of 3-D structures in designing drugs against AIDS, cancer, cardiac disease and neurodegenerative disorders. Recommended Background: 401 or two 300-level chemistry courses or Physics 240.
Registration Permission: Consent of instructor.

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.

570 Advanced Concepts in Cellular/Molecular Biology (3)
Concepts related to cellular/ molecular biology 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.

580 Advanced Concepts in Genetics/Developmental Biology (3)
Concepts related to genetics/ developmental biology with information taken from current literature. Predominately lecture format with student participation. Specific subject area to be announced. Repeatability: May be repeated. Maximum 12 hours.
Registration Permission: Consent of instructor.

615 Special Topics in Biochemistry, Cellular, and Molecular Biology (3)
Biochemical and biophysical methods, mechanisms of enzyme catalysis, gene expression, membrane structure and function, metabolic regulation, physical biochemistry, molecular genetics, cell ultrastructure and physiology, neurobiology, and related topics. Repeatability: May be repeated. Maximum 9 hours.
(DE) Prerequisite(s): 511 and 512 or consent of instructor.
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Chemistry


Departmental Liaison: Dr. Robert Hinde (rhinde@utk.edu)

Courses

Chemistry 570: Quantum and Computational Chemistry.
This course focuses on the time-independent Schroedinger equation and its applications in molecular quantum mechanics. Particular emphasis is given to ab initio electronic structure computations including Hartree-Fock molecular orbital theory and post-Hartree-Fock treatment of electron correlation in atoms and molecules. As part of this course, students typically perform several ab initio electronic structure computations for small molecules using the GAMESS or NW-Chem suite of electronic structure computer programs. This course has been taught by Prof. Robert Harrison and by Prof. Robert Hinde (individually) in recent years, and is typically offered every fall semester. Students with a full year of undergraduate physics, undergraduate chemistry, and undergraduate calculus, and some exposure to differential equations, are likely to succeed in this course.

Chemistry 572: Statistical Mechanics and Thermodynamics.
This course covers both (1) those aspects of equilibrium thermodynamics of particular interest to chemists, with special emphasis on chemical and phase equilibrium, and (2) the microscopic foundations of equilibrium thermodynamics provided by statistical mechanics. Statistical mechanics forms the underpinning of Monte Carlo computer simulation techniques used to study a wide variety of physical phenomena (such as the microscopic structure of liquids and nonideal gases, ferromagnetism, and polymer structure and dynamics) and students learn the theory behind these simulation techniqes by performing a simple Monte Carlo simulation. This course has been taught by Prof. Robert Hinde in recent years. It is typically offered in the fall semester two out of every three years, and will probably not be offered in 2009 or 2012. Students with a full year of undergraduate physics and undergraduate calculus, and with some undergraduate-level exposure to thermodynamics, are likely to succeed in this course.

Chemistry 670: Special Topics in Physical Chemistry - Coupled-Channel Methods for Quantum Dynamics (3)
The atomic-level dynamics of chemical reactions and of vibrating molecules are governed by the Schroedinger equation, a many-variable partial differential equation. In this course, students will learn about coupled-channel methods for solving this equation numerically and will complete a project that involves the implementation of these methods on a computer. Students with (1) a good command of calculus at the undergraduate level, (2) one year of college physics,(3) some elementary familiarity with ordinary differential equations, and (4) a willingness to write a computer program of moderate size are likely to succeed in this course. No previous familiarity with quantum physics is assumed; we will learn (or review) the underlying quantum mechanics at the beginning of the course. This course will be taught by Prof. Robert Hinde and is tentatively scheduled for 9:40-11:00 am on Tuesday and Thursday (Spring '08).
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Chemical Engineering


Departmental Liaison: Dr. David Keffer (dkeffer@utk.edu)

Courses

ChE/MSE 505: Advanced Mathematics for Engineers (3)
This is a practical problem-solving course designed to prepare an individual with a repertoire of analytical and numerical tools to solve a broad swath of mathematical problems. We focus on solutions to both single equations and systems of equations, both linear and nonlinear. We address the following types of equations: algebraic equations, ordinary differential equations, parabolic, hyperbolic and elliptic partial differential equations, and integral equations. Our approach is to examine analytical solutions where available then move to numerical solutions. For each type of numerical algorithm, we present examine the advantages and disadvantages of the approach.

ChE 548: Transport Phenomena via Molecular Dynamics (3)
This course focuses on heat and mass transport. We examine some traditional ways of generating transport properties like diffusivity and thermal conductivity. Then we perform Molecular Dynamics simulation to generate transport properties. We also derive systems of coupled material, momentum and energy balances describing engineering processes. We use numerical techniques for solving systems of coupled nonlinear parabolic PDEs to solve these systems of PDEs.
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Earth and Planetary Sciences


Departmental Liaison: Dr. Edmund Perfect (eperfect@utk.edu)

Courses

Geology 401: Quantitative Methods in Geology (3 credits, Masters)
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.
Recommended background: introductory geology and calculus or consent of instructor.

Geology 425, 525: Data Analysis for Geoscientists (3 credits, Masters and Ph.D.)
Overview of sampling schemes, data analysis and statistical methods as applicable to earth sciences.
Recommended background: introductory geology and introductory calculus.

Geology 473: Principles of Near Surface Geophysics (3 credits, Masters)
Basics of several standard near-surface geophysics techniques (for example, seismic reflection, seismic refraction, surface wave and GPR, electrical resistivity, magnetics, and EM), use state-of-the-art field equipment, and develop the skills necessary to process and interpret the data. Includes a significant field component.
Recommended background: introductory calculus.

Geology 501: Fractal Models in Earth Sciences (3 credits, Masters and Ph.D.)
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 coursework in earth sciences, calculus, or consent of instructor.

Geology 539: Geologic Applications of Remote Sensing (3 credits, Masters and Ph.D.)
An introduction to the use of visible, infrared, microwave/radio, and nuclear remote sensing techniques in the geologic study of 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.
Recommended background: mineralology, calculus and physics or consent of instructor.

Geology 590: Special Problems in Geology (1-3 credits, Masters and Ph.D.)
Student- or instructor-initiated course offered at the convenience of the department, with specialized topics in geological sciences.
Registration permission: consent of instructor.

Geology 675: Seminar in Geophysics (3 credits, Masters and Ph.D.)
Advanced treatment of selected topics in geophysics.
Registration permission: consent of instructor.

Geology 685: Seminar in Hydrogeology (3 credits, Masters and Ph.D.)
Advanced treatment of selected topics in hydrogeology.
Registration permission: consent of instructor.
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Ecology & Evolutionary Biology


Departmental Liaison: Dr. Lou Gross (gross@tiem.utk.edu)

Courses

EEB 514: Foundations: Readings in Mathematical and Computational Ecology (2 credits)
R eadings and discussion of classic papers in the field. This is a basic summary for those without an advanced math/computing background, and includes computational labs.

Math 527: Stochastic Modeling.
Mathematical and computational models in probability applied to real-world situations. This is an introduction for those with advanced undergrad math background (e.g. calculus, DE, linear algebra, Advanced DE or Advanced Calculus) but without requiring previous background in probability.

Math 581-2 (also EEB 581-2): Mathematical Ecology (3 credits each semester)
Deterministic and stochastic models in ecology with computational projects. Requires advanced undergrad math background (e.g. calculus, DE, linear algebra, Advanced DE or Advanced Calculus)

Math 583 (also EEB 583): Mathematical Evolutionary Theory (3 credits)
Deterministic and stochastic models in evolution and population genetics. Requires advanced undergrad math background (e.g. calculus, DE, linear algebra, Advanced DE or Advanced Calculus)

Math 681-2 (also EEB 681-2): Advanced Mathematical Ecology (3 credits each semester)
Selected topics in computational and theoretical modeling in ecology, topics including epidemiology, spatial modeling, ecotoxicology and resource management. Requires Math 581-2.
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Electrical Engineering and Computer Science


Departmental Liaison: Dr. Jack Dongarra (dongarra@eecs.utk.edu)

Courses

CS 594 Special Topics in Computer Science - The following are preliminary courses to be offered under 594:

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.

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

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.

Scripting Languages (3)
An introduction to scripting and markup languages, including Perl, Python, Matlab, and XML. This course will examine how scripting languages can be used to 1) quickly extract, analyze, organize, and summarize data, and 2) write simple programs that use pre-existing modules from other languages, such as C or C++, to accomplish specific tasks.
Prerequisites: Some programming.

Computer Systems Organization (3)
Architectures and systems organization for serial and parallel machines. Prereq: Architecture or machine organization. (Currently, CS530)

Scientific Computing for Engineers
This course will provide an introduction to high-performance scientific computing tools, methods, and environments for the solution of problems in science and engineering.
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Genome Science and Technology


Departmental Liaison: Dr. Cynthia Peterson (cbpeters@utk.edu)

Courses

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.

510 Special Topics in Life Sciences (1-3)
Specializations in biotechnology; cellular, molecular, and developmental biology; environmental toxicology; ethology; plant, physiology and genetics; and physiology. Repeatability: May be repeated. Maximum 9 hours.

520 Genome Science and Technology I (4)
Overview of genomics, advanced genetics principles.

521 Genome Science and Technology II (4)
Analytical technologies and special techniques.

550 Mammalian Genetics and Genomics (3)
Genetic variation, inheritance, phenotypic traits, molecular genetics and genomics, mutagenesis in laboratory rodents and other mammals. (DE) Prerequisite(s): 520 and 521.

595 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.

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.

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.

696 Advanced Topics in Genome Science and Technology (1-3)
Tutorialsor lectures on variety of advanced topics to be chosen by instructor. Repeatability: May be repeated. Maximum 12 hours.
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Geography


Departmental Liaison: Dr. Bruce Ralston (bralston@utk.edu)

Courses

M.S. Level: 411 Introduction to Geographic Information Science (3)
Concepts and methods of spatial analysis and their application to geographic information systems software and techniques. Emphasizes both theoretical and applied aspects of GIS. 2 hours lecture and 2 hours lab. Prereq: Geography 310 or consent of instructor.

414 Spatial Databases and Data Management (3) Types, sources, acquisition, and documentation of spatial data. Spatial database management methods and strategies for data sharing. 2 hours lecture and 2 hours lab. Prereq: 411.

510 Geographic Software Design (3)
Algorithms for spatial analysis, software design, and program implementation in stand alone and distributed computing environments. Prereq: consent of instructor.

517 Geographic Information Management and Processing (3)
Concepts and methods in management of geographic information. Database desgin, manipulation, sampling and analysis. Prereq: consent of instructor.

Ph.D. Level: 611 Seminar in Geographic Information Science (3)
Prereq: 517, 518 or Consent of Instructor. May be repeated. Maximum 6 hours.
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Information Science


Departmental Liaison: Dr. Peiling Wang (peilingw@utk.edu)

Courses

Domain Science/Software

IS 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.

IS 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.

IS 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.

Hardware/Software

IS 585: Information Technologies (3)
Evolution, trends, capabilities, and limitations of technologies applied to information capture, storage, preservation, access, and distribution.

IS 589: Information Networking Technologies (3)
Concepts and terminology of information transmission. Information network architectures and standards. Contemporary and emerging information networking technologies.

Internship

IS 594: Graduate Research Participation (3)
Advanced research techniques under supervision of faculty member whose area coincides with interests of the student. Prereq: Consent of advisor and research director. May be repeated. Maximum 6 hours. Satisfactory/No Credit grading only.

IS 599: Practicum (3-6)
Opportunity to translate theory into practice under guidance of qualified information professionals. Prereq: Completion of required and pertinent advanced courses relevant to student’s practicum design. Minimum 3.0 cumulative GPA. Written consent of advisor and approval of practicum coordinator. May be repeated. Maximum 6 hours. S/NC only.
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Mathematics


Departmental Liaison: Dr. Chuck Collins (ccollins@math.utk.edu)

Courses

We've divided the math courses into three categories:

Mathematics for Modeling - basic mathematics courses covering the content needed to develop and understand mathematical models. Theses courses typically do not have any computation nor much application content.

Mathematical Modeling - courses that develop and solve mathematical models associated with some application area. These courses focus on the modeling process.

Numerical Analysis - courses that develop and analyze the algorithms used to solve specific mathematical problems. Typically these courses have some computational content (projects).

Unless otherwise stated, the pre-requisites for a graduate student to take these courses would be sophomore level mathematics: 241 Calculus III, 231 Differential Equations I & 251 Matrix Algebra I, or their equivalent.

Mathematics for Modeling

Math 453: Matrix Algebra II (3)
Basic matrix algebra, including eigenvalues and eigenvectors. Contains some applications (depending on the instructor) and typically does not address any computational issues. We try to offer this every semester including summer but, due to low enrollment, it may not always run.

Math 511: Methods in Applied Mathematics I (3)
Fundamental ideas and techniques associated with discrete models in physical, engineering and biological systems. Covers discrete dynamical systems, fractals, chaos, difference equations, networks and graphs, optimization and other related topics. Offered in the Fall (not every year).

Math 512: Methods in Applied Mathematics II (3)
Fundamental ideas and techniques associated with continuous models in physical, engineering and biological systems. Covers solution methods and qualitative analysis of ordinary and partial differential equations, calculus of variations and other related topics. Offered in the Spring (not every year).

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)
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. Prereq: Math 513.

Mathematical Modeling

Math 411: Mathematical Modeling (3)
Basics of mathematical modeling covering continuous and discrete (in time) models and stochastic models. Emphasis on the modeling cycle and projects. The basic mathematics is covered as needed. Offered in the Spring.

Math 475: Industrial Mathematics (3)
Focuses on a handful of interesting physical problems, going from the physical problem, to the development of the model, to the mathematical analysis of the model, to the numerical solution of the model, with hands-on computing. Mathematical and computational tools are developed as needed. Prereq: Some programming skill. Offered in the Fall.

Numerical Analysis - Basic (these all require some programming skill)

Math/CS 471: Numerical Analysis (3)
Covers interpolation and approximation of functions by polynomials & splines, numerical integration and numerical solution of ODEs. Offered in the Fall.

Math/CS 472: Numerical Algebra (3)
Covers direct and iterative methods for solving linear systems, methods for finding eigenvalues, and methods for solving nonlinear systems of equations. Offered in the Spring.

Math/CS 571: Numerical Mathematics I (3)
Covers the theory for direct and interative methods for solving linear systems of equations, methods for finding eigenvalues, and methods for solving nonlinear systems of equations. Requires some background in analysis as the course emphasises proofs. Offered in the Fall.

Math/CS 572: Numerical Mathematics II (3)
Covers the theory for numerical methods for solving ordinary differential equations, both initial value problems and two-point boundary value problems. Also introduces the finite difference and finite element methods for solving select partial differential equations. Requires some background in analysis as the course emphasises proofs. Offered in the Spring.

Numerical Analysis - Special Topic (require some programming skill and a basic numerical analysis course)

Math 576 Linear and Nonlinear Programming (3)
Covers linear programming via the Simplex and interior methods. Also covers other topics in nonlinear programming like integer, convex and stochastic programming. Discussion of applications. Offered in the Spring, irregularily.

Math 577 Optimization (3)
Covers the mathematical foundations of unconstrained and constrained optimization. Focuses on deriving and analyzing the main algorithms with some discussion of applications. Offered in the Fall, every other year.

Math 578 Numerical Solution of PDEs (3)
Covers numerical approximation of PDEs, especially conservation laws, and the methods used to solve the approximation. Includes some discussion of modeling and implementation. Requires a course in PDEs (435 or 512). Offered in the Fall, every other year.

Math 679 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).
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Mechanical, Aerospace and Biomedical Engineering


Departmental Liaison: Dr. A. J. Baker (ajbaker@utk.edu)

Courses

Engineering Science 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\u2019s degree in engineering or natural science required.

Engineering Science 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, streamfunction-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.

Engineering Science 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.

Engineering Science 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.

Mechanical Engineering 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.

Mechanical Engineering 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.

Mechanical Engineering 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-Bénard, Taylor, Raleigh-Taylor, Kevin-Helmholtz, Görtler instability. Orr-Sommerfeld equation, bifurcation theory, and transition to turbulence. (DE) Prerequisite(s): 540 and 542.
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Physics


Departmental Liaison: Dr. Thomas Papenbrock (tpapenbr@utk.edu)

Courses

Physics 513-514 Problems in Theoretical Physics (3,3)
Fundamentals of physics: classical mechanics (Newtonian mechanics, Lagrangian and Hamiltonian dynamics), electrostatics, magnetostatics, electrodynamics, relativity, and quantum mechanics.

Physics 571-572: Mathematical Methods in Physics (3,3)
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. Prereq: Advanced calculus and differential equations. Must be taken in sequence. (Same as Mathematics 517-518.)

Physics 573: Numerical Methods in Physics (3)
Numerical methods for solution of physical problems, use of digital computers, analysis of errors.
Prereq: 571 or consent of instructor.

Physics 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.
Prereq: 521, 531, 571.

Physics 5xx: Internship in Computational Physics (To be proposed) (3)
Experience using techniques of computational science to address research problems in physics, supervised by departmental faculty. May not be used toward requirements for MS or PhD in Physics. Prereq: Consent of instructor.
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Statistics


Departmental Liaison: Dr. Hamparsum Bozdogan (bozdogan@utk.edu)

Courses

M.S. Level: 563 Introduction to Mathematical Statistics (3)
Basic probability models and theory of distributions of random variables.
Prereq: Mathematics 241.

564 Theory of Statistical Inference (3)
Introductory theory underlying common statistical procedures of hypothesis testing and estimation.
Prereq: 563.

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.
Prereq: 571 and matrix algebra.

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.
Prereq: 538 or knowledge of regression and analysis of variance.

Ph.D. Level: 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.
Prereq: Knowledge of programming language and 572 or consent of instructor.

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.
Prereq: 564, 579 or equivalent, and knowledge of programming language, or consent of instructor.

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.
Prereq: 564 and 572 or 538, or consent of instructor.

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.
Prereq: Matrix algebra and 564, or matrix-based linear models with experience in interactive computing, or consent of instructor.
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UT Space Institute (UTSI)


Departmental Liaison: Dr. Bruce Whitehead (bwhitehe@utsi.edu)

Courses

CS 594 Special Topics: Introduction to Computer Science for Computational Scientists (3)
Since UTSI has no Computer Science degree program, the main purpose of this course is to meet the needs of IGMCS students on the UTSI campus. Therefore, the course content is similar to content of CS 594 Introduction to Computer Science for Computational Scientists listed under Electrical Engineering and Computer Science above, but with greater emphasis on parallel and cluster computing. Course content includes very basic data structures, effective toolchain use, Fortran/C interoperability, concurrency, parallel computing models & APIs, and cluster computing.
Prereq: Students are expected to enter this course already proficient in either C or Fortran programming, but not necessarily both.
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Below is information for academic departments interested in joining the IGMCS program:

Academic departments with existing or planned graduate degree programs are invited to submit requests for participation to the Program Committee. Applications should indicate which degree program options (eg., Masters and/or PhD) are to be included and which courses are to be accepted for each of the options. It is expected that courses will generally be equivalent to existing graduate level courses in the participating departments. The Program Committee representative (College Representative) from the applicant's college may assist in developing the application.

Suggested program modifications that have been approved by the faculty of the participating academic unit should be sent to the College Representative, who in turn will bring them to the attention of the Program Committee for final approval.

The policies and operational guidelines approved by the Faculty Senate for the IGMCS are flexible so that approval for new programs or modification of existing ones can be given with a minimum of delay. Interested students can be admitted provisionally to the IGMCS program at the same time that the sponsoring department is applying for approval of its degree program.

For more information, contact Dr. Jack Dongarra (dongarra@cs.utk.edu).

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Claxton Complex

Contact IGMCS

413 Claxton Complex
Knoxville, TN 37996-3450
Phone: (865) 974-8295
Fax: (865) 974-8296
Email: info@igmcs.utk.edu

Sponsored by CITR