Catalog Index Course Descriptions
Search the 1997-1998 Catalog: |
Computational Sciences and Informatics
650 Bioinformatics I (3:3:0). Prerequisites: General chemistry, general physics, organic chemistry, and calculus. An intensive review of those aspects of organic chemistry and biochemistry necessary to begin research in bioinformatics and to enter graduate courses in biology. Covalent bonding, quantum mechanical basis of bond formation, three-dimensional structure of molecules, reaction mechanisms, catalysis, polymers, enzymes, thermodynamic and kinetic foundations, metabolic pathways, sequence and structure of macromolecules. This course makes extensive use of computer approaches to convey the essential computational and visual nature of the material to be covered.
651 Bioinformatics II (3:3:0). Prerequisites: Bioinformatics I, general chemistry, general physics, organic chemistry, calculus, or permission of instructor. An intensive review of those aspects of biochemistry, molecular biology and cell biology necessary to begin research in bioinformatics and to enter graduate courses in biology. The areas covered include cell structure, intracellular sorting, cellular signalling (i.e. receptors), cytoskeleton, cell cycle, DNA replication, transcription, translation. This course makes extensive use of computer approaches to convey the essential computational and visual nature of the material to be covered.
652 Bioinformatics III/Global Change IV: Global Ecology (3:3:0). Prerequisites: General chemistry, general physics, introductory statistics, and calculus. Research in global change and global ecology is an inherently information-and informatics-rich field. The challenge is how to make scientific inferences/forecasts when confronted with large incomplete and weakly validated data sets. To approach these problems, the student needs a firm foundation in ecological concepts and theory. Therefore this course provides the necessary review of ecology and population dynamics for graduate students to begin research in Bioinformatics and Global Change.
655/PHYS 575 Introduction to Physics and Chemistry of the Atmosphere (3:3:0). Prerequisites: PHYS 305, 352, and 350. Introduction to basic physical and chemical processes that operate in the earth's atmosphere. Emphasis on those concepts that provide a global description of the current atmospheric state and those processes that relate to global change and atmospheric evolution. Topics include equilibrium structure, radiative transfer models, thermodynamics of various atmospheric layers, and the various processes defining these layers.
660/ASTR 535 Space Instrumentation and Exploration (3:3:0). Prerequisites: PHYS 352, MATH 213 or equivalent, or permission of instructor. Survey of the instruments, devices, and methods used for space and planetary exploration. Remote sensing of Earth and other solar system bodies. Planned manned and unmanned missions by United States and other countries.
687/PHYS 512 Solid State Physics and Applications (3:3:0). Prerequisites: PHYS 502 or equivalent. Crystal structures, binding, lattice vibrations, the free electron model, metals, semiconductors, semiconductor devices, superconductivity, magnetism.
700/MATH 685 Numerical Methods (3:3:0). Prerequisites: MATH 214, MATH 303, and some programming experience. Computational techniques for the solution of problems arising in science and engineering. Algorithms are developed for the treatment of typical problems in applications with special emphasis on the type of data encountered in practice. This includes theoretical development as well as implementation, efficiency, and accuracy issues in using algorithms and interpreting the results. When applicable, computer graphical techniques are used to enhance interpretation of results through visualization.
709 Topics in Computational Sciences and Informatics (3:3:0). Prerequisites: Admission to Ph.D. program and permission of instructor. Selected topics in computational sciences and informatics not covered in fixed-content computational sciences and informatics courses. May be repeated for credit as needed.
711/CHEM 633 Chemical Thermodynamics and Kinetics (3:3:0). Prerequisites: CHEM 331 and 332. Advanced study of thermodynamics and kinetics. The course covers application of kinetics to the elucidation of reaction mechanisms, and application of statistical thermodynamics to the theory of elementary reaction rates.
712/CHEM 728 Introduction to Solid Surfaces (3:3:0). Prerequisites: CHEM 422 or equivalent. Introduction to the properties of solid surfaces. Topics include gas absorption isotherms, surface area measurement techniques, real and clean surfaces, physisorption and chemisorption, methods of gas absorption and desorption, measurement of heats of adsorption, desorption kinetics, electron spectroscopies and their surface sensitivities, instrumentation needed, and principles of vacuum technology.
713/CHEM 732 Quantum Chemistry (3:3:0). Prerequisites: CHEM 332. Illustration of the fundamental concepts of quantum mechanics with applications to chemical systems, including atomic and molecular electronic structure and properties, molecular symmetry, and intermolecular forces.
714/CHEM 737 Spectroscopy and Structure (3:3:0). Prerequisites: CHEM 332. Quantum mechanics of the interaction of atoms and molecules with electromagnetic radiation. Modern specroscopic methods as applied to the elucidation of molecular structure and dynamics are surveyed.
719 Topics in Computational Chemistry (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational chemistry not covered in fixed-content computational chemistry courses. May be repeated for credit as needed.
721 Computational Fluid Dynamics I (3:3:0). Prerequisites: Course in partial differential equations such as MATH 678 or equivalent, knowledge of linear algebra (i.e. MATH 603 or CSI 740/MATH 625), coding experience in FORTRAN or C; or permission of instructor. This course teaches the fundamentals of computational fluid dynamics, including: spatial and temporal approximation techniques for partial differential equations, solution of large systems of equations, data structures, solvers of the Laplace/full potential equation, and simple Euler solvers. There are two major projects: a Laplace solver, and a 2-D Euler solver on unstructured grids. Students are expected to write their own codes.
722 Computational Fluid Dynamics II (3:3:0). Prerequisites: CSI 721 or permission of instructor. This course teaches some of the more advanced topics of CFD, including: high resolution schemes for hyperbolic PDE's, advanced Euler solvers, Navier-Stokes solvers, grid generation, adaptive mesh refinement, efficient use of supercomputing hardware, and future trends. Projects include topics in grid generation and adaptive refinement. Students are expected to write their own codes.
729 Topics in Continuum Systems (3:3:0). Prerequisite: Permission of instructor. Selected topics in the computational aspects of continuum systems not covered in fixed-content courses in dynamical systems. May be repeated for credit as needed. The following are possible topics that may be considered for offering under this course: smooth-particle hydrodynamics; radiation hydrodynamics; algorithms for continuum systems; adaptive grids for continuum computations; spectral methods in CFD; algorithms for concurrent machines; formation of high-energy particle jets in astrophysical applications; application to Earth atmospheric problems; flow considerations in molten materials.
734 Computational Neurobiology (3:3:0). Prerequisites: CSI 651 or permission of instructor. An intense review of neurobiology for graduate students interested in studying how nerve cells integrate and transmit signals, and how higher functions emerge from the integrated actions of populations or circuits of nerve cells. The course covers electrical properties of single neurons; electrical and chemical communications between neurons; and the biophysical basis of sensory perception; motor systems and learning. Emphasis is on mathematical descriptions of neurons and neuronal systems, and how computational techniques are used to study and understand neurons and neuronal systems.
739 Topics in Bioinformatics (3:3:0). Prerequisites: Permission of instructor. Selected topics in bioinformatics not covered in fixed-content bioinformatics courses. May be repeated for credit as needed.
740/MATH 625 Numerical Linear Algebra (3:3:0). Prerequisites: MATH 203 and some programming experience. Study of computational methods for matrix systems. Theory and development of numerical algorithms for the solution of linear systems of equations including direct and iterative methods. Analysis of sensitivity of system to computer roundoff. Solution of least squares problems using orthogonal matrices. Computation of eigenvalues and eigenvectors, singular value decomposition and applications.
741/ECE 721 Nonlinear Dynamical Systems (3:3:0). Prerequisites: Knowledge of linear algebra, advanced calculus, and differential equations. Contemporary topics in the field of nonlinear dynamical systems are illustrated in mathematical models from the natural sciences and engineering. Traditional qualitative analysis of difference and differential equations provides the background for understanding chaotic behavior when it occurs in these models. Topics include stability of equilibria and periodic orbits, bifurcation theory, Hamiltonian systems, Lyapunov exponents, and chaotic attractors.
742/MATH 687 The Mathematics of the Finite Element Method (3:3:0). Prerequisites: MATH 446 or 685 or permission of instructor. The finite element method is a commonly used technique for developing numerical approximations to problems involving ordinary and partial differential equations. This course develops the underlying mathematical foundation for the method, examine several specific types of finite elements, analyze the convergence rates and approximation properties of the method, and use it to solve a number of important equations. Students develop their own codes and are expected to complete independent projects.
744 Linear and Nonlinear Modeling in the Natural Sciences (3:3:0). Prerequisites: Permission of instructor. This course develops the tools of mathematical modeling, while simultaneously carrying out numerical simulations of the models. Examples from across the sciences are considered throughout the course. Topics include basic issues (models, simplification, linearity and nonlinearity); dimensionless parameters, dimensional analysis; models involving differential equations; examples from population growth, chemical kinetics; models involving partial differential equations; diffusion; transport; nonlinearity and shocks; probabilistic modelling; perturbation methods; extrapolation; introduction to stability.
745 Mathematical Tomography (3:3:0). Prerequisites: MATH 675. Physical principles of tomography; the Radon transform in Euclidean space, inversion formulas, the Radon transform on distributions; integral geometry and generalized Radon transforms, the Radon transform on symmetric spaces; applications to CAT, PET, radar imaging and synthetic aperture radar.
746 Wavelet Theory (3:3:0). Prerequisites: Knowledge of convolution and Fourier transforms of sequences; some familiarity with Hilbert space theory helpful but not required: knowledge of a scientific programming language. Study of the theory and computational aspects of wavelets and the wavelet transform. The course first emphasizes computational aspects of wavelets, defining the Fast Wavelet Transform in one and two dimensions and developing the appropriate numerical algorithms. Then the course will develop the theory of wavelet bases on the real line, discussing multiresolution analysis, splines, time-frequency localization, and wavelet packets.
747/MATH 676 Spectral Theory of Linear Operators (3:3:0). Prerequisites: MATH 675. Linear operators arise throughout mathematics, physics, engineering, and elsewhere. Topics covered include examples in finite dimensions; examples in infinite-dimensional spaces; spectral theory of bounded self-adjoint operators; unbounded operators, adjoints, closures, domains; spectral theory of self-adjoint operators; functional calculus; approximation of operators arising in numerical methods; perturbation methods, including iterative algorithms for numerical evaluation; applications.
748/MATH 629 Symbolic Computation (3:3:0). Prerequisites: Undergraduate degree in a scientific discipline, and a course in abstract algebra. The course provides the mathematical and computational background for computational algebraic geometry and its applications. This includes notions of algebra, geometry, algorithms, the concept of Groebner bases, automatic theorem proving, and serial and parallel algorithms and their complexity. These topics are related to applications in engineering and computer science. Students are expected to complete a project.
749 Topics in Computational Mathematics (3:3:0). Prerequisite: Permission of instructor. Selected topics in computational mathematics not covered in fixed-content computational mathematics courses. May be repeated for credit as needed.
750 Earth Systems and Global Changes (Global Change I) (3:3:0). Prerequisites: Undergraduate degree in physical or biological or environmental sciences or permission of instructor. This course provides an introduction to the global system interactions responsible for global environmental change. The course discusses the natural causes of past and present global changes, how human activities affect these global system changes, and the ecological and human consequences of these global changes. Topics to be discussed include climate and hydrological systems, global warming, deforestation, ozone depletion, ecological system dynamics, introduction to climate and global change monitoring, satellite instrumentation and calibration, and model predictions.
751 Global Change II: Introduction to Physical Climate System (3:3:0). Prerequisite: CSI 750 or permission of instructor. This course provides the student with a modern understanding of the system of ocean, atmosphere, and land, based on fundamental physical laws. The course describes, the current climate and its past changes, the physical processes by which a current climate is maintained, the sensitivity of climate, the mechanisms that have produced climate change in the past, and possible mechanisms whereby humans will produce climate change in the future.
753 Global Change V: Observational Methods (3:3:0). Prerequisites: GECA 579, or ASTR 535/CSI 660, or an introductory graduate remote sensing course and earth science or physics course, or chemistry or environmental science or space science undergraduate background, or permission of instructor. Provides the requisite material to understand techniques of remote sensing and other observational methods as applicable to earth science and global change. The course surveys methodologies and their applications including a systematic study of how each part of the electromagnetic spectrum is used to gather data about the Earth. The limitations imposed by satellite engineering, sensor limitations on data gathering, and a survey of data reduction specific to remote sensing applications are described along with current research issues, including examples pertaining to the atmosphere, land masses, and oceans. The current efforts by agencies such as NASA and NOAA to provide integrated data gathering and dissemination systems are discussed.
755 Introduction to Atmospheric Dynamics (3:3:0). Prerequisites: CSI 655/PHYS 575 or permission of instructor. The first part of the course covers the basic conservation laws of mass, momentum, and energy, and a scaling analysis of the equation of motion and the thermodynamic equation. Discussion of balanced flows in the atmosphere, e.g., the geotropic wind and its vertical shear, the thermal wind relationship. The concepts of circulation and vorticity, the role of the atmospheric boundary layer in mass, momentum, and energy transfer, synoptic scale motions, and the role of gravity and Rossby waves in controlling the general circulation of the atmosphere will be discussed.
756 Ocean Dynamics and Ocean Modeling (3:3:0). Prerequisite: CSI 755 or permission of instructor. The course is a mix of formal lectures, computer laboratory work with ocean models and reading of published papers on ocean dynamics and ocean modeling. The topics include ocean observations, ocean dynamics, tropical wave dynamics, ocean modeling, ocean data assimilations, and coupled ocean-atmosphere models.
758 Visualization and Modeling of Complex Systems (3:3:0). Prerequisites: CSI 803 or permission of instructor. The course covers elements of modeling and analysis of earth and space sciences data and systems. It concentrates on both sample projects and student-initiated projects as a means of using visualization and graphical analysis techniques as they apply to the modeling of complex data sets and systems. Several different analysis and visualization packages are used. Spacecraft data sets from the Naval Research Laboratory (NRL) Backgrounds Data Center and other NRL data sets are available for course projects. These data include a number of current and past satellite missions. A perusal of data sets from the World Wide Web is also possible. The modeling and analysis will be accompanied by appropriate readings from the current literature.
759 Topics in Earth Systems and Global Changes (3:3:0). Prerequisites: Permission of instructor. Selected topics in earth systems and global changes not covered in fixed-content earth systems/global changes courses. May be repeated for credit as needed.
761 N-Body Methods and Particle Simulations (3:3:0). Prerequisites: PHYS 613/CSI 780 and CSI 700 or permission of instructor. Study of particle methods as a tool in solving a variety of physical systems. Study and development of the numerical results and visualization of these results in complex physical systems are emphasized. Applications and projects include stellar and galaxy dynamics, smoothed particle hydrodynamics, plasma simulations, and semiconductor device theory algorithms on parallel and vectorized systems will be included.
763 Statistical Methods in Space Sciences (3:3:0). Prerequisites: ASTR 530 or permission of instructor. Study of statistical and data analysis methods applicable to problems in space science, remote sensing, and astrophysics. Course includes parametric and non-parametric hypothesis testing, parameter estimation, correlation analysis, time series analysis, spatial analysis, and image reconstruction. Emphasis is placed on the imperfect nature of actual data sets and hypotheses. Examples are drawn from areas of current space science research.
764 Computational Astrophysics (3:3:0). Prerequisites: ASTR 530. Study of statistical mechanical concepts important in astrophysics. Presentation of unified approach to particle acceleration and inter-action theory based on analytical and numerical analysis of Boltzmann and Liouville equations. Discussion of computational methods relevant for particle transport problems, with emphasis on Fokker-Planck and Monte-Carlo solution techniques. Applications from space sciences include studies of cosmic ray acceleration, photon Comptonization, particle transport in the near-Earth environment, energy transport in stellar atmospheres, and self-gravitating system dynamics.
765 High-Energy and Accretion Astrophysics (3:3:0). Prerequisites: PHYS 502, ASTR 530, PHYS 613/CSI 780, or permission of instructor. Overview of the field, including atomic and nuclear physics; nuclear reactions of use to high-energy astrophysics; radiation processes in cosmic plasmas emphasizing quantum mechanical calculations; stellar evolution and nucleosynthesis; computational models of stellar evolution; binary stars and accretion disks; numerical models of the structure of accretion disks; compact stars, white dwarfs, neutron stars and black holes; acceleration processes and cosmic rays; interstellar medium and propagation of cosmic rays; high-energy processes in the center of galaxies; and ground and space-based techniques and observations.
766 Relativity and Cosmology (3:3:0). Prerequisites: ASTR 530 and MATH 314, or permission of instructor. Special relativity, four-dimensional space-time, general relativity, non-Euclidean geometries, geodesic and field equations, test of general relativity theory, black holes, cosmic background radiation, thermodynamic considerations in cosmology, and cosmological models.
769 Topics in Space Sciences (3:3:0). Prerequisites: Permission of instructor. Selected topics in space sciences not covered in fixed-content space sciences courses. May be repeated for credit as needed.
771 /STAT 751 Computational Statistics (3:3:0). Prerequisites: STAT 544, STAT 554, and STAT 652. Covers the basic computationally intensive statistical methods and related methods, which would not be feasible without modern computational resources. Covers nonparametric density estimation including kernel methods, orthogonal series methods and multivariate methods, recursive methods, cross-validation, nonparametric regression, penalized smoothing splines, the jackknife and bootstrapping, computational aspects of exploratory methods including the grand tour, projection pursuit, alternating conditional expectations, and inverse regression methods.
773/STAT 663 Statistical Graphics and Data Exploration (3:3:0). Prerequisites: 300-level course in statistics; STAT 554 strongly recommended. Exploratory data analysis provides a reliable alternative to classical statistical techniques, which are designed to be the best possible when stringent assumptions apply. Topics covered include graphical techniques such as scatter plots, box plots, parallel coordinate plots and other graphical devices, re-expression and transformation of data, influence and leverage, dimensionality reduction methods such as projection pursuit.
776/INFT 746 Stochastic Calculus (3:3:0). Prerequisites: STAT 652 or ECE 630 or ECE 632 or permission of instructor. Introduction to modern theory of stochastic calculus such as stochastic integrals, martingales, counting processes, diffusion processes and Ito-type processes in general. Applications of these methods to engineering, biology, and economics are considered in some detail.
778/INFT 776 Real Analysis and Statistics (3:3:0). Prerequisites: STAT 652 or ECE 620 or 621 or 630 or permission of instructor. Advanced calculus and linear algebra needed for doctoral work in statistics and related fields. Topology, vector spaces, matrices, continuity, differentiation, sequences and series of real numbers and real-valued functions, Riemann and Riemann-Stieltjes integrals, and multidimensional calculus. Applications in probability and statistics including response surface methodology.
779 Topics in Computational Statistics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational statistics not covered in fixed-content computational statistics courses. May be repeated for credit as needed.
780/PHYS 613 Computational Physics and Applications (3:3:0). Prerequisites: PHYS 510; FORTRAN, C or C++ programming; PHYS 502 or equivalent recommended, or permission of instructor. Study of diverse physical systems with emphasis on modeling and simulation. Development of numerical algorithms and application of numerical methods to gain understanding of the mechanisms and processes taking place in the physical system. Several projects will be undertaken, which are drawn from such areas as atomic and molecular interactions, molecular dynamics, quantum systems, chaos, percolation, random walks, and aggregation mechanisms.
781 Plasma Science (3:3:0). Prerequisites: PHYS 513 or PHYS 722/CSI 785, PHYS 711/CSI 782/CHEM 730; or permission of instructor. Study of ionized matter, theory, and some computation; with application to astrophysics, industrial plasma processing, magnetosphere and ionosphere problems. Vlasov and fluid equations are derived and applied in Plasma Science, including the study of waves in plasmas, with and without magnetic fields.
782/PHYS 711 Statistical Mechanics (3:3:0). Prerequisites: PHYS 502 and 613 or permission of instructor. Microcanonical, canonical, and grand canonical ensembles and fluctuations. Fermi-Dirac and Bose-Einstein statistics, the ideal monoatomic gas and diatomic gas, the Liouville equation, equipatition of energy, crystals, imperfect gases, kinetic theory, quantum statistics, and transport processes.
783/PHYS 736 Computational Quantum Mechanics (3:3:0). Prerequisites: PHYS 502 and 613/CSI 780, or permission of instructor. Study of the fundamental concepts of quantum mechanics from a computational point of view, review of systems with spherically symmetric potentials, many electron-atom solutions to Schroedinger's equation, electron spin in many-electron systems, atomic structure calculations, algebra of many-electron calculations, Hartree-Fock self-consistent field method, molecular structure calculations, scattering theory computations, and solid-state computations.
784/PHYS 732 Quantum Mechanics (3:3:0). Prerequisite: PHYS 502 or permission of instructor. Study of the fundamental concepts of quantum mechanics, time evolution, Schroedinger and Heisenberg formalism, harmonic oscillators, propagators, Feynman path integrals, rotations and angular momentum, angular momentum eigenvalues and eigenstates, Bell's inequality, symmetries, conservation laws, degeneracy, perturbation theory, WKB methods, and scattering theory.
785/PHYS 722 Electromagnetic Theory (3:3:0). Prerequisites: PHYS 513 and PHYS 613/CSI 780, or permission of instructor. Advanced study of electric and magnetic fields; topics include electrostatic fields, magnetostatic fields, boundary-value problems in field theory, multipoles, simple radiating systems, relativistic electrodynamics, and radiation by moving charges.
786 Molecular Dynamics Modeling (3:3:0). Prerequisites: PHYS 613/CSI 780 or CHEM 633/CSI 711, or permission of instructor. An introduction to simulation methods used in the physical chemistry sciences. Computational approaches to model molecular and condensed matter systems including interatomic and molecular potentials, molecular dynamics, time averages, ensemble distributions, numerical sampling, thermodynamic functions, response theory, transport coefficients, dynamic structure. Stochastic simulations such as Brownian motion, Langevin dynamics, Monte Carlo methods and random walks, and an introduction to cellular automata are included.
787 Computational Materials Science (3:3:0). Prerequisites: PHYS 512/CSI 687 and PHYS 736/CSI 783, or permission of instructor. Selected topics in the computational aspects of condensed matter such as methods of electronic structure calculations, surface science, molecular clusters, lattice dynamics, nanomaterials, semiconductors, superconductivity, quantum Hall effect, magnetism, Hubbard model, mesoscopic systems, liquids.
788/PHYS 728 Simulation of Large-Scale Physical Systems (3:3:0). Prerequisites: PHYS 613/CSI 780 and CSI 700, or permission of instructor. Study of diverse large-scale physical systems with emphasis on the modeling and simulation of these multifaceted systems. Several projects are undertaken, which are drawn from such areas as many-body dynamics, atmospheric structure and dynamics, high-temperature plasmas, stellar structure, hydrodynamical systems, galactic structure and interactions, and cosmology.
789 Topics in Computational Physics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational physics not covered in fixed-content computational physics courses. May be repeated for credit as needed.
796 Directed Reading and Research (3:3:0). Prerequisites: Permission of instructor. Reading and research on a specific topic in computational sciences and informatics under the direction of a faculty member. May be repeated as necessary.
801 Foundations of Computational Science (3:3:0). Prerequisite: CSI 700 or permission of instructor. Investigation methods for scientific questions in the presence of teraops computation, gigabyte memory, and gigabit transmission. Mapping of mathematical models to parallel algorithm and architectures, associated data structures, languages, operating systems, networks, and visualization methods. Case studies in bioinformatics, space science, physics, and global change will demonstrate important scientific accomplishments enabled by computation. Class projects involve work in teams to learn the mathematical models, abstract algorithms, and concrete algorithms for these cases, and conduct experiments and simulations with them.
803/INFT 875 Scientific and Statistical Visualization (3:3:0). Prerequisites: STAT 554 or CS 651 or permission of instructor. Visualization methods used to provide new insights and intuition concerning measurements of natural phenomena and scientific and mathematical models. Present case study examples from a variety of disciplines to illustrate what can be done. Topics include human perception and cognition, an introduction to the graphics laboratory, elements of graphing data, representation of space-time and vector variables, representation of 3-D and higher dimensional data, dynamic graphical methods, and virtual reality. Students are required to work on a visualization project. Emphasizes software tools on the Silicon Graphics workstation, but other workstations and software may be used for the project.
810 Scientific Databases (3:3:0). Prerequisites: INFS 714 or equivalent or permission of instructor. Study of database support for scientific data management. Requirements and properties of scientific databases, data models for statistical and scientific databases, semantic and object-oriented modeling of application domains, statistical database query languages and query optimization, advanced logic query languages, and case studies such as the human genome project and Earth-orbiting satellite.
876/INFT 876 Measure and Linear Spaces (3:3:0). Prerequisites: INFT 776/CSI 778 or permission of instructor. Measure theory and integration, convergence theorems, and the theory of linear spaces and functional analysis, including normed linear spaces, inner product spaces, Banach and Hilbert spaces, Sobelev spaces, and reproducing kernels. Topics in wavelets, applications to stochastic processes, and nonparametric functional inference.
877/INFT 877 Geometric Methods in Statistics (3:3:0). Prerequisites: STAT 751 or permission of instructor. Modern multivariate statistical methods including visualization of multivariable data rely on geometric insight and methods. Course develops the foundations of geometric methods for statistics. Topics include n-dimension Euclidian geometry, projective geometry; differential geometry including curves, surfaces and n-dimensional differentiable manifolds; and computational geometry including computation of convex hulls, tessellations of 2-, 3- and n-dimensional spaces, and finite element grid generation. Examples include applications to scientific visualization.
888 Topics in Quantum Systems (3:3:0). Prerequisites: PHYS 736/CSI 783 or PHYS 732/CSI 784, or permission of instructor. Selected topics in quantum systems in physics and chemistry not covered in fixed-content courses in quantum mechanics. May be repeated for credit as needed. The following are possible topics that may be considered for offering under this course: new spectroscopic methods, density functional theory, energy transfer and fluorescence; nuclear magnetic resonance, Mossbauer spectroscopy, advanced computational considerations in atomic and/or molecular structure, nuclear scattering theory, quantum considerations in condensed matter problems, and quantum gravity.
898 Research Colloquia in Computational Sciences and Informatics (1:1:0). Prerequisites: Admission to the doctoral program or permission of instructor. Attendance of colloquium presentations in research areas in computational sciences and informatics by Institute faculty, staff, and professional visitors. May be repeated for credit; however, a maximum of 3 credits of CSI 898 and CSI 899 may be applied towards the Ph.D.
899 Colloquium in Computational Sciences and Informatics (1:1:0). Prerequisites: Admission to doctoral candidacy or permission of instructor. Attendance of colloquium presentations in computational sciences and informatics by institute faculty, staff, and professional visitors. May be repeated for credit; however, a maximum of 3 credits of CSI 899 and 898 may be applied towards the Ph.D.
909 Advanced Topics in Computational Sciences and Informatics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational sciences and informatics not covered in fixed-content courses. May be repeated for credit as necessary.
919 Advanced Topics in Computational Chemistry (3:3:0). Prerequisite: Permission of instructor. Selected topics in computational chemistry not covered in fixed-content computational chemistry courses. May be repeated for credit as needed.
939 Advanced Topics in Bioinformatics (3:3:0). Prerequisites: Permission of instructor. Selected topics in bioinformatics not covered in fixed-content bioinformatics courses. May be repeated for credit as needed.
949 Advanced Topics in Computational Mathematics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational mathematics not covered in fixed-content computational mathematics courses. May be repeated for credit as needed.
959 Advanced Topics in Earth Systems and Global Changes (3:3:0). Prerequisites: Permission of instructor. Selected topics in earth systems and global changes not covered in fixed-content earth systems and global changes courses. May be repeated for credit as needed.
969 Advanced Topics in Space Sciences (3:3:0). Prerequisites: Permission of instructor. Selected topics in space sciences not covered in fixed-content space sciences courses. May be repeated for credit as needed.
972/INFT 972 Mathematical Statistics I (3:3:0). Prerequisite: STAT 652 or equivalent. Focuses on the theory of estimation. The principles of estimation are explored including the method of moments, least squares, maximum likelihood, and maximum entropy methods. The methods of minimum variance unbiased estimation are covered in detail. Other topics include sufficiency and completeness of statistics, Fisher information, Cramer-Rao bounds, Bhattacharyya bounds, asymptotic consistency and distributions, statistical decision theory, minimax and Bayesian decision rules, and applications to engineering and scientific problems.
973/INFT 973 Mathematical Statistics II (3:3:0). Prerequisite: CSI 972. Continuation of CSI 972. Concentrates on the theory of hypothesis testing. Topics include characterizing the decision process, simple versus simple hypothesis tests, Neyman Pearson Lemma, uniformly most powerful tests, unbiasedness of tests, invariance of tests, randomized tests, and sequential tests. Applications of the testing principles are made to situations in the normal distribution family and to other families of distributions.
976/INFT 976 Statistical Inference for Stochastic Processes (3:3:0). Prerequisite: CSI 776 or permission of instructor. Course covers the modern theory of parameter estimation and hypothesis testing for stochastic processes, counting processes with random intensities, and solutions to stochastic differential equations driven by martingales. Applications to engineering, biology, and economics are considered.
978/INFT 978 Statistical Analysis of Signals (3:3:0). Prerequisites: STAT 544 and 658 or equivalent. Advanced course in the analysis of discrete- and continuous-time signals using methods of stochastic differential equation and time series. Familiarity with the methods of harmonic analysis and times series modeling is presumed. Topics include state-space modeling and eigen-value processing, nonlinear modeling of signals, non-Gaussian stochastic process structure, detection and estimation of vector-valued signals, robust signal detection, array processing and target tracking.
979/INFT 979 Advanced Topics in Computational Statistics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational statistics not covered in fixed-content computational statistics courses. May be repeated for credit as needed.
986 Advanced Topics in Large-Scale Physical Simulation (3:3:0). Prerequisites: Permission of instructor. Simulation of physical systems not covered in fixed-content physical simulation courses. May be repeated for credit as needed.
989 Advanced Topics in Computational Physics (3:3:0). Prerequisites: Permission of instructor. Selected topics in computational physics not covered in fixed-content computational physics courses. May be repeated for credit as needed.
996 Doctoral Reading and Research (1-12:0:0). Prerequisites: Admission to doctoral program and permission of instructor. Reading and research on a specific topic in computational sciences and informatics under the direction of a faculty member. May be repeated as needed.
998 Doctoral Dissertation Proposal (1-6:0:0). Prerequisites: Admission to doctoral candidacy. Development of a research proposal under the guidance of a major professor and the doctoral supervisory committee, which forms the basis for a doctoral dissertation. Maybe repeated as needed; however, no more than a total of 24 hours in CSI 998 and CSI 999 may be applied toward satisfying doctoral degree requirements.
999 Doctoral Dissertation (1-24:0:0). Prerequisites: Approval of the Graduate Committee. Research on a basic or applied topics in computational sciences or informatics under the direction of a graduate faculty member. May be repeated as needed; however, no more than a total of 24 hours of CSI 998 and CSI 999 may be applied toward satisfying doctoral degree requirements.