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Mechanical and Aerospace Engineering |
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MAE 879 - Advanced Topics in Mechanical Design College of Engineering and Computer Science
3 credit(s) Irregularly
Selected topics dealing with problems in mechanical design, such as theory of lubrication and bearings, balancing problems, high-speed mechanisms.
Repeatable 1 time(s), 6 credits maximum
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MAE 889 - Selected Topics College of Engineering and Computer Science
3 credit(s) Irregularly
Selected topics dealing with the theory and design of steam and gas turbines, centrifugal and axial flow compressors.
Repeatable 1 time(s), 6 credits maximum
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MAE 990 - Independent Study College of Engineering and Computer Science
1-6 credit(s) Every semester
In-depth exploration of a problem or problems. Individual independent study upon a plan submitted by the student. Admission by consent of supervising instructor or instructors and the department.
Repeatable
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MAE 994 - Capstone Project College of Engineering and Computer Science
0 credit(s)
Review technical papers or reports in the open literature related to student’s field of interest. Students prepare oral presentation to the faculty summarizing the technical content of the document.
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MAE 995 - Graduate Seminar College of Engineering and Computer Science
0 credit(s) Every semester
Crosslisted with: AEE 995
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MAE 997 - Master’s Thesis College of Engineering and Computer Science
1-9 credit(s) Every semester
Repeatable
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MAE 999 - Dissertation College of Engineering and Computer Science
1-15 credit(s) Every semester
Repeatable
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Magazine |
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MAG 500 - Selected Topics S.I. Newhouse School of Public Communications
1-6 credit(s) Irregularly
Exploration of a topic (to be determined) not covered by the standard curriculum but of interest to faculty and students in a particular semester.
Repeatable
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MAG 518 - Critical Writing S.I. Newhouse School of Public Communications
3 credit(s) At least 1x fall or spring
Criticism and its function in journalism. Reviewing books, plays, motion pictures, and other art forms.
PREREQ: (NEW 205 AND MAG 205) OR MNO 617
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MAG 538 - Travel Writing S.I. Newhouse School of Public Communications
3 credit(s) At least 1x fall or spring
Writing and selling magazine articles about traveling and specific geographic areas. Students will write in a variety of styles, especially exploring the narrative form.
PREREQ: NEW 305 OR MNO 617
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Marketing Management |
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MAR 600 - Selected Topics Martin J. Whitman School of Management
1-6 credit(s) Irregularly
Exploration of a topic (to be determined) not covered by the standard curriculum but of interest to faculty and students in a particular semester.
Repeatable
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MAR 653 - Marketing Analytics Martin J. Whitman School of Management
3 credit(s) Every semester
Marketing analytics techniques including discriminant analysis, logit, cluster analysis, factor analysis, and conjoint analysis. Marketing decision support models such as new product diffusion, test-market, price and sales promotion decision models.
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MAR 655 - Customer Relationship Management with Systems Applications and Products Martin J. Whitman School of Management
3 credit(s)
Crosslisted with: MIS 655 , SCM 655
Integration of marketing, supply-chain and technology management aspects of customer relationship management. Operational, analytical and collaborative processes supported by SAP’s integrated software. Actual use of SAP software, including Business Data Warehouse, with best-practice processes.
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MAR 721 - Marketing and the Internet Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
The course focuses on how traditional marketing approaches have to be modified to take advantage of the reach and capabilities of the internet, from understanding customer needs to after sales customer services.
PREREQ: (MBC 603 AND MBC 604 ) OR MBC 636
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MAR 741 - Marketing Community and Public Service Agencies Martin J. Whitman School of Management
3 credit(s) Irregularly
Design, implementation, and control of marketing programs for community and public service agencies: performing arts, health care, urban planning, police, educational, scientific, and technical organizations
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MAR 745 - Strategic Brand Management Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Concepts and tools acquired from various marketing courses to develop analytical and decision-making skills for planning and implementing a marketing strategy from the brand manager’s point of view.
PREREQ: MBC 604 OR MBC 636
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MAR 751 - Environmental Influences on Innovation Martin J. Whitman School of Management
3 credit(s) Irregularly
Major environmental forces that shape innovation policy from a technology, market, international, economic, social, and political-legal perspective. Managerial response to environmental forces.
PREREQ: MBC 636
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MAR 752 - Introduction to Innovation Management Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
The process of converting ideas, technology, and customer needs into new products, services, and processes. Environmental and organizational influences on the innovation process.
PREREQ: MBC 636
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MAR 753 - Marketing Channel Management Martin J. Whitman School of Management
3 credit(s) Irregularly
Marketing channels as both economic and social systems. Channel change and evolution, channel membership, structural and functional relationships, interorganizational behavior, and channel information management.
PREREQ: MBC 636
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MAR 754 - Seminar in Marketing Research Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Collection, analysis, and interpretation of data. Problem definition, questionnaire design, attitude measurement, data analysis, and demand forecasting. For those interested in conducting marketing research or using research information for marketing decision making.
PREREQ: MBC 636 , MBC 638
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MAR 755 - Marketing Communications Strategy Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Managerial aspects. Determination of promotional budgets, planning and building promotional effectiveness, scheduling and monitoring promotional impact.
PREREQ: MBC 636
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MAR 756 - Market Measurement and Analysis Martin J. Whitman School of Management
3 credit(s) Irregularly
Application of analytical and quantitative techniques to market measurement. Product-market strategy.
PREREQ: MBC 636 AND MBC 638
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MAR 757 - Managing Innovative Products and New Ventures Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Problems in developing new products and new corporate ventures. Designing innovation strategies, risk taking, technology planning, evaluation of new product proposals, and managing the innovation team.
PREREQ: MBC 636
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MAR 759 - Seminar in Marketing Martin J. Whitman School of Management
3 credit(s) Irregularly
Selected topics in marketing. Current issues and problems in marketing.
PREREQ: MBC 636
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MAR 761 - Marketing Strategies for Innovations Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Commercializing new products, services, and technologies. Introduction and diffusion of innovations, market planning, product strategy design, and marketing decision making.
PREREQ: MBC 636
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MAR 777 - Global Supply Chain Strategy Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Crosslisted with: SCM 777
Topics include: design of global facility networks, containerization and logistical planning across borders, benefits and risks of outsourcing and offshoring while integrating financial and accounting-related matters such as exchange rates, duties, drawbacks and tax differentials.
PREREQ: MBC 616 , MBC 638
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MAR 930 - Seminar in Marketing Theory Martin J. Whitman School of Management
3 credit(s) Irregularly
Current marketing theory as developed by contemporary writers.
PREREQ: MBC 636
Repeatable
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MAR 960 - Doctoral Seminar in Marketing Martin J. Whitman School of Management
3 credit(s) Irregularly
Repeatable
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MAR 962 - Marketing and Supply Chain Models Martin J. Whitman School of Management
3 credit(s) Irregularly
Crosslisted with: SCM 962
Statistical/econometric and management science modeling approaches to marketing/supply chain management problem solving.
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Managerial Statistics |
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MAS 653 - Accelerated Managerial Statistics Martin J. Whitman School of Management
3 credit(s) Irregularly
Survey of statistics for managerial decision making. Applications and problem identification. Descriptive statistics, probability, sampling, estimation, hypothesis testing, time-series analysis, simple and multiple regression, and statistical decision theory.
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MAS 723 - Nonparametric Statistics Martin J. Whitman School of Management
3 credit(s) Irregularly
Statistical methods that make no assumptions about the probability distribution sampled. Methods based on signs, ranks, and order statistics, related aspects of probability theory, statistical inference, special procedures, and case examples.
PREREQ: MBC 638 OR MAS 653
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MAS 765 - Sample Survey Methods and Theory Martin J. Whitman School of Management
3 credit(s) Irregularly
Simple random, stratified, systematic, cluster, and multistage sampling methods. Cost and precision. Methods of estimation; simple, unbiased, ratio, regression, and composite methods of measuring and controlling nonsampling errors.
PREREQ: MBC 638
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MAS 766 - Linear Statistical Models I: Regression Models Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
General regression model, estimation methods, general linear hypothesis tests, residual analysis, indicator variables, multicollinearity, autoregressive model, weighted least squares, variable-screening procedures.
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MAS 767 - Linear Statistical Models II: Variance Martin J. Whitman School of Management
3 credit(s) Irregularly
Single and multiclassification analysis of variance for fixed, random, and mixed effects models, simultaneous estimation method implementation of ANOVA models, analysis of covariance.
PREREQ: MAS 766
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MAS 777 - Time Series Modeling and Analysis Martin J. Whitman School of Management
3 credit(s) At least 1x fall or spring
Fundamental concepts and procedures for forecasting discrete time series for planning and control. Regression analysis, ARIMA methods, econometric modeling, transfer functions, intervention analysis, Kalman filters, univariate and multivariate methods.
PREREQ: MBC 638
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MAS 788 - Causal Modeling and Analysis Martin J. Whitman School of Management
3 credit(s) Irregularly
Multivariate Statistical techniques and analysis strategies for formulating and testing causal models using both experimental and nonexperimental data sources Path analysis, correlation and causality, sources of estimation-bias interpretation and limitations simultaneous equation models, confirmator, factor analysis, measurement error and latent variable models, and structural equatrons.
PREREQ: MBC 638
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Mathematics |
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MAT 503 - Matrix Methods for Data Science College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Matrix methods required for data analysis with an emphasis on applications and using software. Matrix norms, orthogonality, eigendecomposition, SVD, LS, QRD, LDA, PCA. Not for math majors or minors. Additional work required of graduate students.
PREREQ: MAT 397
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MAT 511 - Advanced Calculus College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Partial derivatives, implicit functions, integration in several variables, line and surface integrals.
PREREQ: (MAT 331 AND 397) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 512 - Introduction to Real Analysis II College of Arts and Sciences
3 credit(s) Every semester
Real-number system, set theory and elementary topological properties of the real line, continuity and differentiability, sequences and series, uniform convergence, Riemann integration, and improper integrals.
PREREQ: MAT 412 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 513 - Introduction to Complex Analysis College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Complex number system and its arithmetic, geometric representation. Linear transformations. Analytic functions and the Cauchy-Riemann equations. Integration and Cauchy’s theorem, Taylor and Laurent series, singularities, poles, and residues. Applications.
PREREQ: MAT 412 OR MAT 511 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 517 - Partial Differential Equations and Fourier Series College of Arts and Sciences
3 credit(s) Every semester
Partial differential equations, boundary-value problems, Fourier series and orthogonal expansions, Bessel functions, and Legendre polynomials.
PREREQ: MAT 485 OR 414 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 518 - Fourier Series, Transforms and Wavelets College of Arts and Sciences
3 credit(s) Irregularly
Orthogonal functions, Fourier series, Fourier transforms-continuous and discrete, Haar wavelets and multiresolution analysis, applications to signal processing. Additional work required of graduate students.
PREREQ: MAT 331 OR MAT 485 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 521 - Introduction to Probability College of Arts and Sciences
3 credit(s) Every semester
Algebra of sets. Probability in finite sample spaces. Binomial and multinomial coefficients. Random variables. Expected value and standard deviation. Density functions. Statistical applications.
PREREQ: MAT 397 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 523 - Statistical Methods for Data Science College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Statistical methods (such as hypothesis testing, parameter estimation, regression, ANOVA, sampling, experimental design) required for data science. Emphasis on applications and using software. Additional work required for graduate students.
PREREQ: MAT 397 AND (MAT 222 OR CIS 321 OR MAT 421 OR MAT 521)
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MAT 525 - Mathematical Statistics College of Arts and Sciences
3 credit(s) Every semester
Estimation and confidence intervals. Normal distribution and central limit theorem. Testing hypotheses, chi-square, t, and F distributions. Least squares, regression, and correlation.
PREREQ: MAT 521 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 526 - Introduction to Stochastic Processes College of Arts and Sciences
3 credit(s) Every semester
Discrete time Markov chains, Poisson process, continuous time Markov chains and other selected stochastic processes.
PREREQ: MAT 521 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 528 - Probability Models for Actuarial Science College of Arts and Sciences
3 credit(s) Irregularly
Applied probability focusing on distributions for actuarial applications. Conditional expectation. Moment generating functions. Limit theorems. Loss and Survival models. Parametric and Non-Parametric estimation. Model assessment. Benefit reserves and risk measures. Additional work required of graduate students.
PREREQ: MAT 521
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MAT 531 - Second Course in Linear Algebra College of Arts and Sciences
3 credit(s) Every semester
Abstract vector spaces and inner product spaces, linear transformations and linear operators, eigenvalues and diagonalization. Primarily for mathematics majors.
PREREQ: ((MAT 375 OR CIS 275) AND MAT 331) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 532 - Applied Linear Algebra College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Factorization of matrices, eigenvalues and eigenvectors, orthogonality. Applications of matrices to such topics as least-squares approximation, fast Fourier transform, difference and differential equations, linear programming, networks, game theory.
PREREQ: MAT 331 OR 485 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 534 - Introduction to Abstract Algebra College of Arts and Sciences
3 credit(s) Every semester
Theory of groups, rings, and fields, including the integers and polynomail rings.
PREREQ: MAT 531 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 541 - Introduction to Number Theory College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Prime numbers, greatest common divisors, congruences. Euler’s function, Fermat’s theorem, primitive roots, indices, quadratic residues, Legendre and Jacobi symbols, and the quadratic reciprocity law.
PREREQ: ((MAT 375 OR CIS 275) AND MAT 331) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 545 - Introduction to Combinatorics College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Crosslisted with: CIS 545
Permutations, combinations, recurrence relations, generating functions, inclusion-exclusion and applications, introductory graph theory.
PREREQ: MAT 375 OR CIS 275 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 551 - Fundamental Concepts of Geometry College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Synthetic projective geometries. Coordinate systems for projective spaces. Algebraic representation of projective transformations; euclidean, non-euclidean, and affine geometries as real cases of projective geometry.
PREREQ: ((MAT 375 OR CIS 275) AND MAT 331) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 554 - Differential Geometry College of Arts and Sciences
3 credit(s) Irregularly
Theory of curves in three-dimensional space, including Frenet’s formula, Gaussian and mean curvature, geodesics, developable surfaces, special conformal mappings.
PREREQ: MAT 412 OR MAT 511 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 562 - Elementary Topology College of Arts and Sciences
3 credit(s) Irregularly
Metrics and metric spaces, topologies and topological spaces, separation properties, compactness, connectedness, and continuity.
PREREQ: ((MAT 375 OR CIS 275) AND MAT 412) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 581 - Numerical Methods with Programming College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Approximation methods for solution of nonlinear equations. Interpolation problems. Numerical integration. Solution of ordinary differential equations. Error analysis and writing computer programs. Primarily for mathematics and engineering students.
PREREQ: MAT 397 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 593 - History of Mathematics College of Arts and Sciences
3 credit(s) Irregularly
Mathematical concepts in their historical perspective. Character and contributions of the great mathematicians and relation of mathematics to other sciences.
PREREQ: (MAT 397 AND AT LEAST TWO 500-LEVEL MATH COURSES) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 599 - Senior Seminar in Mathematics College of Arts and Sciences
3 credit(s) Irregularly
Topic Chosen by the instructor. Permission of department.
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MAT 601 - Fundamentals of Analysis I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Real and complex numbers, elementary point set topology, sequences and series, continuity, differentiation.
PREREQ: MAT 512 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 602 - Fundamentals of Analysis II College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Riemann-Stieltjes integration, functional sequences and series, functions of several variables.
PREREQ: (MAT 601 AND MAT 631 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 631 - Introduction to Algebra I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Linear algebra, linear transformations, eigenvectors, diagonalization, inner product spaces, groups, quotient groups, group actions, Sylow theorems, finitely generated Abelian groups, rings, unique factorization domains, finitely generated modules over principal ideal domains, fields, Galois theory.
PREREQ: (MAT 531 AND MAT 534 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 632 - Introduction to Algebra II College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Continuation of MAT 631 .
PREREQ: MAT 631 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 645 - Graph Theory College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Crosslisted with: CIS 645
Fundamentals of graph theory and special topics including networks, matching, connectivity, planarity, and automorphism groups.
PREREQ: MAT 531 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 646 - Enumeration, Designs, and Matroids College of Arts and Sciences
3 credit(s) Irregularly
Crosslisted with: CIS 646
Generating functions, Polya enumeration, set systems, design parameters, finite projective planes, matroids.
PREREQ: MAT 531 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 651 - Probability and Statistics I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Calculus of probabilities, univariate and multivariate random variables and distribution functions, expectations and variance, conditional distributions, transformations of random variables, characteristic functions, basic limit theorems including Borel-Cantelli, Khinchin, Lindeberg- Feller.
PREREQ: MAT 521 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 652 - Probability and Statistics II College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Point and interval estimation, consistent, efficient, and sufficient statistics, Rao-Blackwellization, hypothesis testing, brief treatment of ranking and selection, decision theory.
PREREQ: MAT 651 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 653 - Statistical Simulation and Nonstandard Data Analysis College of Arts and Sciences
3 credit(s) Irregularly
Simulation and Monte Carlo techniques appropriate where statistical theory does not yet provide a solution. Design and analysis of experiments under nonstandard conditions.
PREREQ: MAT 651 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 654 - Linear Models College of Arts and Sciences
3 credit(s) Irregularly
Point estimation by least squares, regression, curve fitting, testing a linear hypothesis, analysis of variance, simple experimental designs.
PREREQ: (MAT 525 AND MAT 531 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 661 - Introduction to Topology College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Topological spaces, continuous mappings, compactness, connectedness, path connectedness, separation axioms, metric spaces, quotient spaces, CW complexes, the fundamental group, and the classification of 2-dimensional manifolds.
PREREQ: MAT 512 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 682 - Numerical Linear Algebra College of Arts and Sciences
3 credit(s) Odd academic yr e.g. 2007-8
Solution of linear equations. Norms and conditioning. Calculation of eigenvalues and eigenvectors. Least squares approximation and orthogonal functions. Error analysis and writing computer programs.
PREREQ: MAT 511 AND MAT 531
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MAT 683 - Methods of Numerical Analysis I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Numerical methods of interpolation, approximation, integration, and differentiation, solutions of nonlinear equations.
PREREQ: MAT 512 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 684 - Methods of Numerical Analysis II College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Analysis of numerical methods for approximating solutions of ordinary and partial differential equations.
PREREQ: MAT 683 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 687 - Introduction to Applied Mathematics College of Arts and Sciences
3 credit(s) Irregularly
Mathematical model building, dimensional analysis, scaling, and perturbation theory. Models selected from the natural and social sciences according to the interests of instructor and students. Examples are: planetary orbits, fluid flow, isomers in organic chemistry, biological competition, biochemical kinetics, and physiological flow.
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MAT 690 - Independent Study College of Arts and Sciences
1-6 credit(s) Upon sufficient interest
In-depth exploration of a problem or problems. Individual independent study upon a plan submitted by the student. Admission by consent of supervising instructor or instructors and the department.
Repeatable
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MAT 695 - Fundamentals of Data Science College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Double Numbered with: MAT 495
Fundamental methods for data science, such as regression, linear discriminant analysis, k-nearest neighbors, support vector machine, k-means, principal component analysis, and nonlinear dimension reduction. Performance evaluation and model selection. Additional work required of graduate students.
PREREQ: (MAT 331 AND MAT 521 ) OR (MAT 503 AND MAT 523 )
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MAT 701 - Real Variables I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Measure and integration, including basic theorems on integration and differentiation of sequences of functions; modes of convergence, product measures.
PREREQ: MAT 602 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 702 - Functional Analysis I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Norms, seminorms, and inner products on linear spaces. Standard theorems on linear functionals and operations. Dual spaces and weak topologies, classical spaces and their duals. Applications.
PREREQ: (MAT 631 AND MAT 661 AND MAT 701 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 704 - Differential Equations College of Arts and Sciences
3 credit(s) Irregularly
Existence theorems for ordinary differential equations, linear differential equations and systems, Euler variational equations, typical Cauchy and boundary-value problems for partial differential equations.
PREREQ: (MAT 632 AND MAT 701 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 705 - Calculus on Manifolds College of Arts and Sciences
3 credit(s) Irregularly
Differentiable manifolds, differential forms, exterior calculus, integration over manifolds, Stokes’ Theorem, other selected topics.
PREREQ: (MAT 602 AND MAT 632 AND MAT 661 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 712 - Functions of a Complex Variable I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Cauchy theory, power series, analytic continuation, entire functions, the residue theorem, contour integration, maximum modulus theorem and applications, conformal representation. Dirichlet series, special functions.
PREREQ: MAT 602 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 721 - Probability I College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Measure and integration. Random variables, their distributions and transforms. Modes of convergence. Classical limit laws. Markov chains.
PREREQ: (MAT 602 AND MAT 701 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 722 - Probability II College of Arts and Sciences
3 credit(s) Irregularly
Conditional expectation. Martingales. Brownian motion. Ergodic theorem. Random walks.
PREREQ: MAT 721 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 731 - Rings and Modules College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Submodules, factor modules, chain conditions, Hilbert basis theorem, division rings, Schur’s lemma, Jacobson density theorem, semi-simple modules, socles, Jacobson radical, semi primitive rings, Artin-Wedderburn theorem, integral extensions, completions, localization.
PREREQ: (MAT 631 AND MAT 632 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 732 - Homological Algebra College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Projective and injective resolutions, Tor and Ext, flatness, homology, derived categories, spectral sequences.
PREREQ: MAT 731 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 733 - Commutative Algebra College of Arts and Sciences
3 credit(s) Irregularly
Localization, primary decomposition, and dimension theory; Nullstellensatz; Artin-Rees lemma and completion; integral and flat extensions; Koszul complex, Cohen-Macaulay and regular rings.
PREREQ: MAT 731
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MAT 737 - Representations of Groups and Algebras College of Arts and Sciences
3 credit(s) Irregularly
The course covers representations of finite groups and finite-dimensional algebras. Topics will come from: ordinary and modular representations of finite groups, Auslander-Reiten theory, representations of quivers, Koszul algebras, Hopf algebras and Frobenius algebras.
PREREQ: MAT 731
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MAT 738 - Introduction to Algebraic Geometry College of Arts and Sciences
3 credit(s) Irregularly
The study of the zeros of polynomials. Classical algebraic varieties in affine and projective space, followed by introduction to modern theory of sheaves, schemes, and cohomology.
PREREQ: MAT 632 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 750 - Statistical Consulting College of Arts and Sciences
3 credit(s) Irregularly
Crosslisted with: STT 750
Working with real data taken from case studies, published papers, and current projects in the statistical laboratory.
PREREQ: (MAT 525 OR MAT 652 ) AND (MAT 654 OR APM 630 OR MAS 766 )
Repeatable
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MAT 752 - Statistical Ranking, Selection, and Multiple Comparisons College of Arts and Sciences
3 credit(s) Irregularly
Statistical selection of the best category or population. Preference-zone and subset formulations. Multivariate preferences and populations. Applications. Recent developments, including Multiple Comparisons with the Best (MCB) and the Heteroscedastic Method (HM).
PREREQ: MAT 652 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 753 - Decision Theory College of Arts and Sciences
3 credit(s) Irregularly
Minimax theorems, completeness of the class of Bayes procedures. Invariance. Criteria for admissibility.
PREREQ: MAT 525 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 754 - Sequential Analysis College of Arts and Sciences
3 credit(s) Irregularly
General sequential decision problems, sequential probability ratio test, sequential test among three hypotheses, sequential estimation, optimal stopping, Wald’s identity. Generalized SPRT’s, Cox’s theorem, sequential regression, functional equations, dynamic programming, sequential choice of experiments.
PREREQ: MAT 525 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 755 - Multivariate Statistical Analysis College of Arts and Sciences
3 credit(s) Irregularly
Multivariate normal distribution, conditional densities, partial correlation, multiple correlation, regression coefficients, maximum likelihood estimates, Hotelling’s statistic, Wishart distribution, tests of hypotheses, and linear discriminant functions.
PREREQ: MAT 525 OR MAT 532 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 761 - Introduction to Algebraic Topology College of Arts and Sciences
3 credit(s) At least 1x fall or spring
Fundamental group covering spaces, chain complexes, simplicial or singular homology and cohomology theory, exact sequences, and the Eilenberg-Steenrod axioms.
PREREQ: (MAT 632 AND MAT 661 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 762 - Algebraic Topology College of Arts and Sciences
3 credit(s) Irregularly
Homology, cohomology ring, universal coefficient theorem, duality, homotopy, theory, selected topics.
PREREQ: (MAT 632 AND MAT 761 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 771 - Differential Geometry College of Arts and Sciences
3 credit(s) Irregularly
Differential manifolds, tensor fields and mappings, differential forms and Stokes’s theorem, affine connections, exponential mapping, covariant differentiation, torsion and curvature tensors, Riemannian connections, complete Riemannian manifolds, other modern topics.
PREREQ: (MAT 602 AND MAT 632 AND MAT 661 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 781 - Numerical Optimization I College of Arts and Sciences
3 credit(s) Irregularly
Newton methods, interior point methods, proximal point algorithms, alternating direction method of multipliers, coordinate descent method, and stochastic/randomized algorithms.
PREREQ: (MAT 682 AND MAT 683 ) OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 782 - Numerical Optimization II College of Arts and Sciences
3 credit(s) Irregularly
Continuation of MAT 781.
PREREQ: MAT 781 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 800 - Topics In Analysis College of Arts and Sciences
3 credit(s) Irregularly
Exploration of a topic (to be determined) not covered by the standard curriculum but of interest to faculty and students in a particular semester.
Repeatable
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MAT 802 - Real Variables II College of Arts and Sciences
3 credit(s) Irregularly
Topics in real variables and measure theory, such as differentiation theory in euclidean and abstract spaces, generalized derivatives and integrals, ergodic theory, martingales, surface area.
PREREQ: MAT 701 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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MAT 804 - Functional Analysis II College of Arts and Sciences
3 credit(s) Irregularly
Abstract integration, Radon-Nikodym theorem. Representation of set functions by integrals. Ergodic theorems. Duality. Weak topologies, convex sets, and extreme points. Elements of spectral theory.
PREREQ: MAT 702 OR GRADUATE STANDING IN MATHEMATICAL SCIENCES
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