Twin Cities campus

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Twin Cities Campus

Scientific Computation Ph.D.

Chemical Engineering & Materials Science
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Scientific Computation Program, University of Minnesota, 151 Amundson Hall, 421 Washington Ave S.E., Minneapolis, MN 55455 (612-625-6345; fax: 612-626-7246)
Email: wentz002@umn.edu
Website: http://www.scicomp.umn.edu
  • Students will no longer be accepted into this program after Spring 2018. Program requirements below are for current students only.
  • Program Type: Doctorate
  • Requirements for this program are current for Fall 2023
  • Length of program in credits: 48
  • This program does not require summer semesters for timely completion.
  • Degree: Doctor of Philosophy
Along with the program-specific requirements listed below, please read the General Information section of this website for requirements that apply to all major fields.
The graduate degree program in scientific computation encompasses course work and research on the fundamental principles necessary to use intensive computation to support research in the physical, biological, and social sciences and engineering. There is a special emphasis on research issues, state-of-the-art methods, and the application of these methods to outstanding problems in science, engineering, and other fields that use scientific computation, numerical analysis and algorithm development, symbolic and logic analysis, high-performance computing tools, supercomputing and heterogeneous networks, and visualization.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
A bachelor's degree in a field that uses scientific computation is required for admission.
Other requirements to be completed before admission:
All application materials must be submitted electronically through the online Graduate Admissions system. Three letters of recommendation and a statement of research and career goals are required for all applications. GRE General Test scores are required for consideration of financial support and recommended for all applicants. International applicants are required to submit TOEFL scores. January 1 is the application deadline for applicants who wish to be considered for financial aid. Applications received after January 1 will be considered on a space and funds available basis.
Applicants must submit their test score(s) from the following:
  • GRE
International applicants must submit score(s) from one of the following tests:
  • TOEFL
    • Internet Based - Total Score: 79
    • Internet Based - Writing Score: 21
    • Internet Based - Reading Score: 19
    • Paper Based - Total Score: 550
  • IELTS
    • Total Score: 6.5
  • MELAB
    • Final score: 80
Key to test abbreviations (GRE, TOEFL, IELTS, MELAB).
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
12 credits are required in the major.
12 credits are required outside the major.
24 thesis credits are required.
This program may be completed with a minor.
Use of 4xxx courses toward program requirements is permitted under certain conditions with adviser approval.
A minimum GPA of 3.00 is required for students to remain in good standing.
The PhD requires 24 course credits, including a minimum of 12 credits in core courses, and 24 thesis credits. The remaining 12 course credits may be taken from the core list, in a minor, or in subjects that support computational science, and should give the degree plan an interdisciplinary character.
Core Courses
Core courses may be chosen from the following list; other courses with a significant computation component may be used with approval of the Director of Graduate Studies.
AEM 8251 - Finite-Volume Methods in Computational Fluid Dynamics (3.0 cr)
CEGE 8022 - Numerical Methods for Free and Moving Boundary Problems (3.0 cr)
CEGE 8361 {Inactive} (3.0 cr)
CEGE 8401 - Fundamentals of Finite Element Method (3.0 cr)
CEGE 8402 - Nonlinear Finite Element Analysis (3.0 cr)
CEGE 8561 - Analysis and Modeling of Aquatic Environments I (3.0 cr)
CEGE 8562 - Analysis and Modeling of Aquatic Environments II (3.0 cr)
CEGE 8572 - Computational Environmental Fluid Dynamics (4.0 cr)
CHEM 8021 - Computational Chemistry (4.0 cr)
CHEM 8541 - Dynamics (4.0 cr)
CHEM 8551 - Quantum Mechanics I (4.0 cr)
CHEM 8552 - Quantum Mechanics II (2.0 cr)
CHEM 8561 - Thermodynamics, Statistical Mechanics, and Reaction Dynamics I (4.0 cr)
CHEM 8562 - Thermodynamics, Statistical Mechanics, and Reaction Dynamics II (4.0 cr)
CSCI 5302 - Analysis of Numerical Algorithms (3.0 cr)
CSCI 5304 - Computational Aspects of Matrix Theory (3.0 cr)
CSCI 5403 {Inactive} (3.0 cr)
CSCI 5421 - Advanced Algorithms and Data Structures (3.0 cr)
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming (3.0 cr)
CSCI 5461 - Functional Genomics, Systems Biology, and Bioinformatics (3.0 cr)
CSCI 5481 - Computational Techniques for Genomics (3.0 cr)
CSCI 5561 - Computer Vision (3.0 cr)
CSCI 5607 - Fundamentals of Computer Graphics 1 (3.0 cr)
CSCI 5608 - Fundamentals of Computer Graphics II (3.0 cr)
CSCI 5609 - Visualization (3.0 cr)
CSCI 5707 - Principles of Database Systems (3.0 cr)
CSCI 5801 - Software Engineering I (3.0 cr)
CSCI 5802 - Software Engineering II (3.0 cr)
CSCI 8314 - Sparse Matrix Computations (3.0 cr)
CSCI 8725 - Databases for Bioinformatics (3.0 cr)
EE 5239 - Introduction to Nonlinear Optimization (3.0 cr)
EE 5531 - Probability and Stochastic Processes (3.0 cr)
EE 5561 - Image Processing and Applications: From linear filters to artificial intelligence (3.0 cr)
EE 8231 - Optimization Theory (3.0 cr)
EPSY 8221 {Inactive} (3.0 cr)
EPSY 8222 - Advanced Measurement: Theory and Application (3.0 cr)
ESCI 5201 - Time-Series Analysis of Geological Phenomena (3.0 cr)
HINF 5430 - Foundations of Health Informatics I (3.0 cr)
HINF 5431 - Foundations of Health Informatics II (3.0 cr)
HINF 8434 {Inactive} (3.0 cr)
IE 5531 - Engineering Optimization I (4.0 cr)
LING 5801 - Introduction to Computational Linguistics (3.0 cr)
MATH 5467 - Introduction to the Mathematics of Image and Data Analysis (4.0 cr)
MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
MATH 5705 - Enumerative Combinatorics (4.0 cr)
MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
MATH 8441 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8442 - Numerical Analysis and Scientific Computing (3.0 cr)
MATH 8445 - Numerical Analysis of Differential Equations (3.0 cr)
MATH 8450 - Topics in Numerical Analysis (1.0-3.0 cr)
MATH 8571 - Theory of Evolutionary Equations (3.0 cr)
ME 5228 - Introduction to Finite Element Modeling, Analysis, and Design (4.0 cr)
ME 5351 - Computational Heat Transfer (4.0 cr)
ME 8228 - Finite Elements in Multidisciplinary Flow/Thermal/Stress and Manufacturing Applications (4.0 cr)
ME 8229 - Finite Element Methods for Computational Mechanics: Transient/Dynamic Problems (4.0 cr)
ME 8345 - Computational Heat Transfer and Fluid Flow (3.0 cr)
NSC 5202 - Theoretical Neuroscience: Systems and Information Processing (3.0 cr)
PHYS 5041 - Mathematical Methods for Physics (4.0 cr)
PHYS 5042 {Inactive} (4.0 cr)
PSY 5036W - Computational Vision [WI] (3.0 cr)
PSY 5038W - Introduction to Neural Networks [WI] (3.0 cr)
PSY 5960 - Topics in Psychology (1.0-4.0 cr)
SCIC 8001 - Parallel High-Performance Computing (3.0 cr)
SCIC 8011 - Scientific Visualization (3.0 cr)
SCIC 8021 - Advanced Numerical Methods (3.0 cr)
SCIC 8031 - Modeling, Optimization, and Statistics (3.0 cr)
SCIC 8041 - Computational Aspects of Finite Element Methods (3.0 cr)
SCIC 8095 - Problems in Scientific Computation (1.0-3.0 cr)
SCIC 8190 - Supercomputer Research Seminar (1.0 cr)
SCIC 8253 - Computational Nanomechanics (3.0 cr)
SCIC 8551 - Multiscale Methods for Bridging Length and Time Scales (3.0 cr)
SCIC 8594 - Scientific Computation Directed Research (1.0-4.0 cr)
STAT 8701 - Computational Statistical Methods (3.0 cr)
STAT 8711 {Inactive} (3.0 cr)
Thesis Credits
Take 24 credits after passing preliminary oral exam
SCIC 8888 - Thesis Credit: Doctoral (1.0-24.0 cr)
 
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AEM 8251 - Finite-Volume Methods in Computational Fluid Dynamics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Development of finite-volume computational methods for solution of compressible Navier-Stokes equations. Accuracy, consistency, and stability of numerical methods; high-resolution upwind shock-capturing schemes; treatment of boundary conditions; explicit and implicit formulations; considerations for high performance computers; recent developments and advanced topics. prereq: 4201 or 8201 or equiv, CSci 1107 or equiv
CEGE 8022 - Numerical Methods for Free and Moving Boundary Problems
Credits: 3.0 [max 3.0]
Prerequisites: 8401 or #
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Examples of free and moving boundary problems: metal solidification, filling, polymer molding, flow in porous media, ground freezing. Solutions: analytical, fixed finite difference, fixed finite element, front tracking schemes, general deforming finite element methods. prereq: 8401 or instr consent
CEGE 8401 - Fundamentals of Finite Element Method
Credits: 3.0 [max 3.0]
Prerequisites: 4411 or #
Grading Basis: A-F or Aud
Typically offered: Every Spring
Elements of calculus of variations; weak and strong formulations of linear continuum and structural problems. Isoparametric elements and numerical integration. Basic concepts of error analysis and convergence. Analysis of plates and shells. Introduction to mixed methods and time dependent problems. prereq: 4411 or instr consent
CEGE 8402 - Nonlinear Finite Element Analysis
Credits: 3.0 [max 3.0]
Prerequisites: 8401 or #; offered alt yrs
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Large strains and work conjugate stresses. Equilibrium and principle of virtual work for nonlinear problems. Nonlinear elasticity and plasticity. Finite element discretization and nonlinear algebraic equations. Linearization and solution algorithms for nonlinear problems. Structural stability. prereq: 8401 or instr consent; offered alt yrs
CEGE 8561 - Analysis and Modeling of Aquatic Environments I
Credits: 3.0 [max 3.0]
Prerequisites: One sem grad work or #
Grading Basis: A-F or Aud
Typically offered: Every Spring
Introduction to hydrologic transport and water quality simulation in natural water systems. Deterministic, process-oriented water quality model development. Mixed cell models, advection, turbulent diffusion/dispersion. Chemical/biological kinetics in water quality models. Application of water quality models to management problems. prereq: One sem grad work or instr consent
CEGE 8562 - Analysis and Modeling of Aquatic Environments II
Credits: 3.0 [max 6.0]
Prerequisites: One sem grad work or #
Typically offered: Periodic Fall & Spring
Models for transport/transformation of pollutants, nutrients, particulates, ecosystems, etc., from recently completed theses, articles, or research in progress. Students review assigned recent papers, make presentations, and analyze a topic of their choice. prereq: One sem grad work or instr consent
CEGE 8572 - Computational Environmental Fluid Dynamics
Credits: 4.0 [max 4.0]
Prerequisites: grad student in CSE or COAFES or #
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Finite difference methods, their application to solution of one-/two-dimensional problems in environmental fluid dynamics. Stability, convergence, consistency, and accuracy of numerical schemes. Navier-Stokes equations, their physical meaning, and their numerical solution. Turbulence modeling: RANS and LES. prereq: grad student in CSE or COAFES or instr consent
CHEM 8021 - Computational Chemistry
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Modern theoretical methods used in study of molecular structure, bonding, reactivity. Concepts/practical applications. Determination of spectra, relationship to experimental techniques. Molecular mechanics. Critical assessment of reliability of methods. prereq: 4502 or equiv
CHEM 8541 - Dynamics
Credits: 4.0 [max 4.0]
Course Equivalencies: Chem 5541/8541
Typically offered: Periodic Fall
Mathematical methods for physical chemistry. Classical mechanics/dynamics, normal modes of vibration. Special topics such as rotational motion, Langevin equation, Brownian motion, time correlation functions, collision theory, cross sections, energy transfer, molecular forces, potential energy surfaces, classical electrostatics, Shannon entropy. prereq: Undergrad physical chem course
CHEM 8551 - Quantum Mechanics I
Credits: 4.0 [max 4.0]
Course Equivalencies: Chem 5551/8551
Typically offered: Every Fall
Review of classical mechanics. Postulates of quantum mechanics with applications to determination of single particle bound state energies and scattering cross-sections in central field potentials. Density operator formalism with applications to description of two level systems, two particle systems, entanglement, and Bell inequality. prereq: undergrad physical chem course
CHEM 8552 - Quantum Mechanics II
Credits: 2.0 [max 4.0]
Typically offered: Every Spring
Second Quantization;Density matrices; Molecular Electronic Structure Theory; Hartree-Fock Theory; Electron Correlation; Configuration Interaction; Perturbation Theory; Energy Derivatives; Coupled-Cluster;Density Functional Theory; Relativistic Quantum Chemistry; prereq: 8551
CHEM 8561 - Thermodynamics, Statistical Mechanics, and Reaction Dynamics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Two-part sequence. Thermodynamics, equilibrium statistical mechanics, ensemble theory, partition functions. Applications, including ideal gases/crystals. Theories of simple liquids, Monte Carlo, and molecular dynamics simulations. Reaction dynamics from microscopic viewpoint. prereq: undergrad physical chem course
CHEM 8562 - Thermodynamics, Statistical Mechanics, and Reaction Dynamics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Two-part sequence. Thermodynamics, equilibrium statistical mechanics, ensemble theory, partition functions. Applications, including ideal gases/crystals. Theories of simple liquids, Monte Carlo, and molecular dynamics simulations. Reaction dynamics from microscopic viewpoint. prereq: 8561
CSCI 5302 - Analysis of Numerical Algorithms
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Additional topics in numerical analysis. Interpolation, approximation, extrapolation, numerical integration/differentiation, numerical solutions of ordinary differential equations. Introduction to optimization techniques. prereq: 2031 or 2033 or instr consent
CSCI 5304 - Computational Aspects of Matrix Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Perturbation theory for linear systems and eigenvalue problems. Direct/iterative solution of large linear systems. Matrix factorizations. Computation of eigenvalues/eigenvectors. Singular value decomposition. LAPACK/other software packages. Introduction to sparse matrix methods. prereq: 2031 or 2033 or instr consent
CSCI 5421 - Advanced Algorithms and Data Structures
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent
CSCI 5461 - Functional Genomics, Systems Biology, and Bioinformatics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Computational methods for analyzing, integrating, and deriving predictions from genomic/proteomic data. Analyzing gene expression, proteomic data, and protein-protein interaction networks. Protein/gene function prediction, Integrating diverse data, visualizing genomic datasets. prereq: 3003 or 4041 or instr consent
CSCI 5481 - Computational Techniques for Genomics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Techniques to analyze biological data generated by genome sequencing, proteomics, cell-wide measurements of gene expression changes. Algorithms for single/multiple sequence alignments/assembly. Search algorithms for sequence databases, phylogenetic tree construction algorithms. Algorithms for gene/promoter and protein structure prediction. Data mining for micro array expression analysis. Reverse engineering of regulatory networks. prereq: 4041 or instr consent
CSCI 5561 - Computer Vision
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Issues in perspective transformations, edge detection, image filtering, image segmentation, and feature tracking. Complex problems in shape recovery, stereo, active vision, autonomous navigation, shadows, and physics-based vision. Applications. prereq: CSci 5511, 5521, or instructor consent.
CSCI 5607 - Fundamentals of Computer Graphics 1
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081
CSCI 5608 - Fundamentals of Computer Graphics II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent
CSCI 5609 - Visualization
Credits: 3.0 [max 3.0]
Typically offered: Fall Even Year
Fundamental theory/practice in data visualization. Programming applications. Perceptual issues in effective data representation, multivariate visualization, information visualization, vector field/volume visualization. prereq: [1913, 4041] or equiv or instr consent
CSCI 5707 - Principles of Database Systems
Credits: 3.0 [max 3.0]
Course Equivalencies: CSci 4707/CSci 5707/INET 4707
Typically offered: Every Fall
Concepts, database architecture, alternative conceptual data models, foundations of data manipulation/analysis, logical data models, database designs, models of database security/integrity, current trends. prereq: [4041 or instr consent], grad student
CSCI 5801 - Software Engineering I
Credits: 3.0 [max 3.0]
Prerequisites: 2041 or #
Typically offered: Every Fall
Advanced introduction to software engineering. Software life cycle, development models, software requirements analysis, software design, coding, maintenance. prereq: 2041 or instr consent
CSCI 5802 - Software Engineering II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Introduction to software testing, software maturity models, cost specification models, bug estimation, software reliability models, software complexity, quality control, and experience report. Student groups specify, design, implement, and test partial software systems. Application of general software development methods and principles from 5801. prereq: 5801 or instr consent
CSCI 8314 - Sparse Matrix Computations
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Sparsity and sparse matrices. Data structures for sparse matrices. Direct methods for sparse linear systems. Reordering techniques to reduce fill-in such as minimal degree ordering and nested dissection ordering. Iterative methods. Preconditioning algorithms. Algorithms for sparse eigenvalue problems and sparse least-squares. prereq: 5304 or numerical linear algebra course or instr consent
CSCI 8725 - Databases for Bioinformatics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
DBMS support for biological databases, data models. Searching integrated public domain databases. Queries/analyses, DBMS extensions, emerging applications. prereq: 4707 or 5707 or instr consent
EE 5239 - Introduction to Nonlinear Optimization
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Nonlinear optimization. Analytical/computational methods. Constrained optimization methods. Convex analysis, Lagrangian relaxation, non-differentiable optimization, applications in integer programming. Optimality conditions, Lagrange multiplier theory, duality theory. Control, communications, management science applications. prereq: [3025, Math 2373, Math 2374, CSE grad student] or dept consent
EE 5531 - Probability and Stochastic Processes
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Probability, random variables and random processes. System response to random inputs. Gaussian, Markov and other processes for modeling and engineering applications. Correlation and spectral analysis. Estimation principles. Examples from digital communications and computer networks. prereq: [3025, CSE grad student] or dept consent
EE 5561 - Image Processing and Applications: From linear filters to artificial intelligence
Credits: 3.0 [max 3.0]
Course Equivalencies: EE 5561/EE 8541
Typically offered: Every Spring
Image enhancement, denoising, segmentation, registration, and computational imaging. Sampling, quantization, morphological processing, 2D image transforms, linear filtering, sparsity and compression, statistical modeling, optimization methods, multiresolution techniques, artificial intelligence concepts, neural networks and their applications in classification and regression tasks in image processing. Emphasis is on the principles of image processing. Implementation of algorithms in Matlab/Python and using deep learning frameworks. prereq: [4541, 5581, CSE grad student] or instr consent
EE 8231 - Optimization Theory
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Introduction to optimization in engineering; approximation theory. Least squares estimation, optimal control theory, and computational approaches. prereq: instr consent
EPSY 8222 - Advanced Measurement: Theory and Application
Credits: 3.0 [max 4.0]
Course Equivalencies: EPsy 8222/Psy 5865
Typically offered: Spring Odd Year
Topics in test theory. Classical reliability/validity theory/methods, generalizability theory. Linking, scaling, equating. Item response theory, methods for dichotomous/polytomous responses. Comparisons between classical, item response theory methods in instrument construction. prereq: [5221 or PSY 5862 or equiv], [8252 or equiv]
ESCI 5201 - Time-Series Analysis of Geological Phenomena
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall
Time-series analysis of linear and nonlinear geological and geophysical phenomena. Examples drawn from ice age cycles, earthquakes, climatic fluctuations, volcanic eruptions, atmospheric phenomena, thermal convection and other time-dependent natural phenomena. Modern concepts of nonlinear dynamics and complexity theory applied to geological phenomena. prereq: Math 2263 or instr consent
HINF 5430 - Foundations of Health Informatics I
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
An introductory survey of health informatics, focusing on foundational concepts. Topics covered include: conceptualizations of data, information, and knowledge; current terminologies, coding, and classification systems for medical information; ethics, privacy, and security; systems analysis, process and data modeling; human-computer interaction and data visualization. Lectures, readings, and exercises highlight the intersections of these topics with electronic health record systems and other health information technology. prereq: Junior, senior, grad student, professional student, or instr consent
HINF 5431 - Foundations of Health Informatics II
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
An introductory survey of health informatics, focusing on applications of informatics concepts and technologies. Topics covered include: health informatics research, literature, and evaluation; precision medicine; decision models; computerized decision support systems; data mining, natural language processing, social media, rule-based system, and other emerging technologies for supporting 'Big Data' applications; security for health care information handling. Lectures, readings, and exercises highlight the intersections of these topics with current information technology for clinical care and research. prereq: Junior, senior, grad student, professional student, or instr consent
IE 5531 - Engineering Optimization I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Linear programming, simplex method, duality theory, sensitivity analysis, interior point methods, integer programming, branch/bound/dynamic programming. Emphasizes applications in production/logistics, including resource allocation, transportation, facility location, networks/flows, scheduling, production planning. prereq: Upper div or grad student or CNR
LING 5801 - Introduction to Computational Linguistics
Credits: 3.0 [max 3.0]
Typically offered: Spring Odd Year
Methods/issues in computer understanding of natural language. Programming languages, their linguistic applications. Lab projects. prereq: [4201 or 5201] or programming experience or instr consent
MATH 5467 - Introduction to the Mathematics of Image and Data Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5588 - Elementary Partial Differential Equations II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5705 - Enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707
MATH 8441 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation. prereq: [4xxx analysis, 4xxx applied linear algebra] or instr consent
MATH 8442 - Numerical Analysis and Scientific Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods. prereq: 8441 or instr consent; 5477-5478 recommended for engineering and science grad students
MATH 8445 - Numerical Analysis of Differential Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Finite element and finite difference methods for elliptic boundary value problems (e.g., Laplace's equation) and solution of resulting linear systems by direct and iterative methods. prereq: 4xxx numerical analysis, 4xxx partial differential equations or instr consent
MATH 8450 - Topics in Numerical Analysis
Credits: 1.0 -3.0 [max 12.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Selected topics. prereq: Grad math major or instr consent; offered as one year or one semester course as circumstances warrant
MATH 8571 - Theory of Evolutionary Equations
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Infinite dimensional dynamical systems, global attractors, existence and robustness. Linear semigroups, analytic semigroups. Linear and nonlinear reaction diffusion equations, strong and weak solutions, well-posedness of solutions. prereq: 8502 or instr consent
ME 5228 - Introduction to Finite Element Modeling, Analysis, and Design
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Finite elements as principal analysis tool in computer-aided design (CAD); theoretical issues and implementation aspects for modeling and analyzing engineering problems encompassing stress analysis, heat transfer, and flow problems for linear situations. One-, two-, and three-dimensional practical engineering applications. prereq: CSE upper div or grad, 3221, AEM 3031, CSci 1113, MatS 2001
ME 5351 - Computational Heat Transfer
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Numerical solution of heat conduction/analogous physical processes. Develop/use computer program to solve complex problems involving steady/unsteady heat conduction, flow/heat transfer in ducts, flow in porous media. prereq: 3333, CSE upper div or grad student
ME 8228 - Finite Elements in Multidisciplinary Flow/Thermal/Stress and Manufacturing Applications
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Fall & Spring
Multidisciplinary and coupled effects involving flow/heat transfer/stress. In-depth understanding of modeling and analysis in each discipline. Coupling multi-disciplines for engineering problems. Applications to manufacturing and process modeling of, e.g., metals, alloys, polymers. prereq: 3222, 5341, AEM 3031, CSci 1113
ME 8229 - Finite Element Methods for Computational Mechanics: Transient/Dynamic Problems
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Computational mechanics involving transient or dynamic situations; development and analysis of computational algorithms. Stability and accuracy of algorithms, convergence issues; linear/nonlinear situations. Implicit, explicit, mixed, and variable time discretization approaches; modal-based methods for engineering problems prereq: 5228 or equiv, 5341, AEM 3031, CSci 1113
ME 8345 - Computational Heat Transfer and Fluid Flow
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Finite volume method for solution of governing equations for heat transfer and fluid flow. Mathematical models of turbulence. Construction of general computer program. Practical applications. prereq: CSE grad student
NSC 5202 - Theoretical Neuroscience: Systems and Information Processing
Credits: 3.0 [max 3.0]
Course Equivalencies: NSc 5202/Phsl 5202
Typically offered: Every Spring
Concepts of computational/theoretical neuroscience. Distributed representations and information theory. Methods for single-cell modeling, including compartmental/integrate-and-fire models. Learning rules, including supervised, unsupervised, and reinforcement learning models. Specific systems models from current theoretical neuroscience literature. Lecture/discussion. Readings from current scientific literature. prereq: [3101, 3102W] recommended
PHYS 5041 - Mathematical Methods for Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Survey of mathematical techniques needed in analysis of physical problems. Emphasizes analytical methods. prereq: 2601 or grad student
PSY 5036W - Computational Vision (WI)
Credits: 3.0 [max 3.0]
Typically offered: Fall Even Year
Applications of psychology, neuroscience, computer science to design principles underlying visual perception, visual cognition, action. Compares biological/physical processing of images with respect to image formation, perceptual organization, object perception, recognition, navigation, motor control. prereq: [[3031 or 3051], [Math 1272 or equiv]] or instr consent
PSY 5038W - Introduction to Neural Networks (WI)
Credits: 3.0 [max 3.0]
Typically offered: Fall Odd Year
Parallel distributed processing models in neural/cognitive science. Linear models, Hebbian rules, self-organization, non-linear networks, optimization, representation of information. Applications to sensory processing, perception, learning, memory. prereq: [[3061 or NSC 3102], [MATH 1282 or 2243]] or instr consent
PSY 5960 - Topics in Psychology
Credits: 1.0 -4.0 [max 8.0]
Typically offered: Periodic Fall, Spring & Summer
Special course or seminar. Topics listed in Class Schedule. prereq: PSY 1001, [jr or sr or grad student]
SCIC 8001 - Parallel High-Performance Computing
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Interdisciplinary overview of computer science aspects of scientific computation, both hardware and techniques. Parallel computing, architectures, programming, and algorithms; restructuring compilers and data structures. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8011 - Scientific Visualization
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Basic issues in scientific visualization, visualization software, graphics, representation of scientific data, modeling, hardware for visualization, user interface techniques, output, commonly used algorithms and techniques for visualization, animation, information visualization, higher dimensional data, case studies, and examples of successful visualizations. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8021 - Advanced Numerical Methods
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Interdisciplinary overview of advanced numerical methods of scientific computation, emphasizing computational aspects. Approximation methods for partial differential equations, numerical linear algebra, sparse matrix techniques, iterative methods, solution of eigenvalue problems, and case studies. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8031 - Modeling, Optimization, and Statistics
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Interdisciplinary overview of mathematical modeling, optimization, and statistics techniques for scientific computation. Nonlinear equations and nonlinear optimization, statistics, control theory, modeling, and simulation. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8041 - Computational Aspects of Finite Element Methods
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Fundamental concepts and techniques of finite element analysis. Variational equations and Galerkin's method; weak formulations for problems with nonsymmetric differential operators; Petrov-Galerkin methods; examples from solid and fluid mechanics; properties of standard finite element families, implementation. prereq: Undergrad degree in field using sci comp or IT grad student or instr consent
SCIC 8095 - Problems in Scientific Computation
Credits: 1.0 -3.0 [max 9.0]
Typically offered: Periodic Fall
Selected topics in interdisciplinary aspects of scientific computing. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8190 - Supercomputer Research Seminar
Credits: 1.0 [max 3.0]
Typically offered: Periodic Fall & Spring
Series of seminars by distinguished lecturers. prereq: Undergrad degree in field using sci comp or instr consent
SCIC 8253 - Computational Nanomechanics
Credits: 3.0 [max 3.0]
Course Equivalencies: ME 8253/SCIC 8253
Prerequisites: CSE graduate student
Typically offered: Every Spring
Fundamentals of mechanical properties in nanometer scale. Role of discrete structure and underlying atomic, molecular, and interfacial forces are illustrated with modern examples. Overview of computational atomistic methods. Lectures, hands-on computing using publicly available or personally developed scientific software packages. prereq: CSE graduate student
SCIC 8551 - Multiscale Methods for Bridging Length and Time Scales
Credits: 3.0 [max 3.0]
Course Equivalencies: AEM 8551/SCIC 8551
Prerequisites: Basic knowledge of [continuum mechanics, atomic forces], familiarity with partial differential equations, grad student in [engineering or mathematics or physics or scientific computation]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Classical/emerging techniques for bridging length/time scales. Nonlinear thermoelasticity, viscous fluids, and micromagnetics from macro/atomic viewpoints. Statistical mechanics, kinetic theory of gases, weak convergence methods, quasicontinuum, effective Hamiltonians, MD, new methods for bridging time scales. prereq: Basic knowledge of [continuum mechanics, atomic forces], familiarity with partial differential equations, grad student in [engineering or mathematics or physics or scientific computation]
SCIC 8594 - Scientific Computation Directed Research
Credits: 1.0 -4.0 [max 9.0]
Typically offered: Every Fall, Spring & Summer
tbd prereq: Undergrad degree in field using sci comp or instr consent
STAT 8701 - Computational Statistical Methods
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Random variate generation, variance reduction techniques. Robust location estimation and regression, smoothing additive models, regression trees. Programming projects; basic programming ability and familiarity with standard high-level language (preferably FORTRAN or C) are essential. prereq: 8311, programming exper
SCIC 8888 - Thesis Credit: Doctoral
Credits: 1.0 -24.0 [max 100.0]
Grading Basis: No Grade
Typically offered: Every Fall, Spring & Summer
(No description) prereq: Max 18 cr per semester or summer; 24 cr required