Mathematical Prin For Scientific Computing And Visualization Pdf
Twin Cities campus
 | Twin Cities Campus Scientific Computation M.S.Chemical Engineering & Materials Science Link to a list of faculty for this program. Scientific Computation Program, University of Minnesota, 151 Amundson Hall, 421 Washington Ave S.E., Minneapolis, MN 55455 (612-625-6345; fax: 612-626-7246)
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
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:
International applicants must submit score(s) from one of the following tests:
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 Plan A: Plan A requires 14 major credits, 6 credits outside the major, and 10 thesis credits. The final exam is oral. 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 2.80 is required for students to remain in good standing. The program is offered under Plan A (thesis), which requires a minimum of 20 course credits and 10 thesis credits. The course credits must include at least 6 credits from the scientific computation core and at least 6 credits in a minor. The remaining 8 credits may be taken as additional graduate-level courses in the core or in subjects that support computational science. Many minor programs have greater requirements in terms of credits for a Master�s minor; in such cases the greater requirements will be in effect. 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 - Engineering Model Fitting (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 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 5607 - Fundamentals of Computer Graphics 1 (3.0 cr) CSCI 5608 - Fundamentals of Computer Graphics II (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 (3.0 cr) EE 8231 - Optimization Theory (3.0 cr) EPSY 8221{Inactive} (3.0 cr) EPSY 8222 - Advanced Measurement: Theory and Application (4.0 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 - Statistical Computing (3.0 cr) Thesis Credits Take 10 thesis credits. SCIC 8777 - Thesis Credits: Master's (1.0-18.0 cr) | | | |
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 8361 - Engineering Model Fitting
| Credits: | 3.0 [max 3.0] |
| Prerequisites: | CSE grad student or # |
| Grading Basis: | A-F or Aud |
| Typically offered: | Fall Even Year |
Parameter estimation and inverse modeling for civil and geological engineering. Formulating engineering model fitting problems; comparing and selecting various fit criteria; implementing numerical algorithms; analyzing and interpreting results using both statistical and qualitative tools; designing future measurement plans. prereq: CSE grad student 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
| Credits: | 3.0 [max 3.0] |
| Course Equivalencies: | EE 5561/EE 8541 |
| Typically offered: | Every Spring |
Two-dimensional digital filtering/transforms. Application to image enhancement, restoration, compression, and segmentation. 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: | 4.0 [max 4.0] |
| Course Equivalencies: | EPsy 8222/Psy 5865 |
| Typically offered: | Spring Odd Year |
Generalizability theory, item response theory, factor models for test items, binomial model. Application to problems of designing, linking assessments. Includes computer lab. 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
STAT 8711 - Statistical Computing
| Credits: | 3.0 [max 3.0] |
| Typically offered: | Periodic Fall |
Basic numerical analysis for statisticians. Numerical methods for linear algebra, eigen-analysis, integration, and optimization and their statistical applications. prereq: 8701 or instr consent
SCIC 8777 - Thesis Credits: Master's
| Credits: | 1.0 -18.0 [max 50.0] |
| Grading Basis: | No Grade |
| Typically offered: | Every Fall, Spring & Summer |
(No description) prereq: Max 18 cr per semester or summer; 10 cr total required [Plan A only]
Mathematical Prin For Scientific Computing And Visualization Pdf
Source: https://onestop2.umn.edu/pcas/viewCatalogProgram.do?programID=7020
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