Glossary UW Bothell Course Descriptions UW Tacoma Course Descriptions
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# COLLEGE OF ARTS & SCIENCES APPLIED MATHEMATICS

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To see the detailed Instructor Class Description, click on the underlined instructor name following the course description.

AMATH 301 Beginning Scientific Computing (4) NW
Introduction to the use of computers to solve problems arising in the physical, biological, and engineering sciences. Application of mathematical judgment, programming architecture, and flow control in solving scientific problems. Introduction to MATLAB routines for numerical programming, computation, and visualization. Prerequisite: either MATH 125, Q SCI 292, or MATH 135. Offered: AWSpS.

AMATH 351 Introduction to Differential Equations and Applications (3) NW
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125. Offered: AWSpS.

AMATH 352 Applied Linear Algebra and Numerical Analysis (3) NW
Analysis and application of numerical methods and algorithms to problems in the applied sciences and engineering. Applied linear algebra, including eigenvalue problems. Emphasis on use of conceptual methods in engineering, mathematics, and science. Extensive use of MATLAB package for programming and solution techniques. Prerequisite: either MATH 126 or Q SCI 293. Offered: AWSpS.

AMATH 353 Fourier Analysis and Partial Differential Equations (3) NW
Heat equation, wave equation, and Laplace's equation. Separation of variables. Fourier series in context of solving heat equation. Fourier sine and cosine series; complete Fourier series. Fourier and Laplace transforms. Solution of partial differential equations on infinite domains. D' Alembert's solution for wave equation. Prerequisite: either AMATH 351 or MATH 307. Offered: Sp.

AMATH 383 Introduction to Continuous Mathematical Modeling (3) NW
Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results. Prerequisite: either AMATH 351 or MATH 307. Offered: AWS.

AMATH 401 Vector Calculus and Complex Variables (4)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: either MATH 126 or MATH 136. Offered: A.

AMATH 402 Introduction to Dynamical Systems and Chaos (4)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology. Prerequisite: either AMATH 351 or MATH 307. Offered: W.

AMATH 403 Methods for Partial Differential Equations (4)
Applications of partial differential equations; linear and quasilinear first order equations, characteristics, shocks; classification of linear second order equations; basic solution techniques for parabolic, elliptic, and hyperbolic equations; Green's functions and integral transform methods. Prerequisite: AMATH 401; either AMATH 351 or MATH 307. Offered: Sp.

AMATH 422 Computational Modeling of Biological Systems (3)
Examines fundamental models that arise in biology and their analysis through modern scientific computing. Covers discrete and continuous-time dynamics, in deterministic and stochastic settings, with application from molecular biology to neuroscience to population dynamics; statistical analysis of experimental data; and MATLAB programming from scratch. Prerequisite: either MATH 307 or AMATH 351. Offered: W.

AMATH 423 Mathematical Analysis in Biology and Medicine (3)
Focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications drawn from many branches of biology and medicine. Provides experiences in applying differential equations, difference equations, and dynamical systems theory to biological problems. Prerequisite: either AMATH 351 or MATH 307, MATH/STAT 390. Offered: Sp.

AMATH 460 Mathematical Methods for Quantitative Finance (3) NW,QSR
Covers selected mathematical methods needed to begin a master's program in quantitative finance. Topics include applications of calculus, linear algebra, and constrained optimization methods to fixed income, portfolio optimization, futures, options, and risk management.

AMATH 461 Probability and Statistics for Computational Finance (3)
Covers basic concepts and methods of probability and statistical analysis and modeling for computational and quantitative finance. Coverage is carefully aligned with leading problems concerning prices and returns of individual assets and portfolios of assets. Key applications include financial risk management and portfolio performance analysis.

AMATH 462 Introduction to Computational Finance and Financial Econometrics (5) Zivot
Covers probability models, data analysis, quantitative, and statistical methods using applications in finance, and introduction to and use of the R programming system for data analysis and statistical modeling. Prerequisite: calculus through multivariate calculus; introductory probability and statistics. Offered: AS.
Instructor Course Description: Eric W Zivot

AMATH 463 R Programming for Quantitative Finance (2)
Introduction to R Programming language for applications in quantitative finance. Intended for students with no prior exposure to R and prepares them with the computing skills needed to progress effectively in an MS degree program in computational finance.

AMATH 481 Scientific Computing (5)
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results. Prerequisite: AMATH 301; either AMATH 351 or MATH 307; either AMATH 352 or MATH 308. Offered: A.

AMATH 482 Computational Methods for Data Analysis (5)
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression. Prerequisite: AMATH 301; either AMATH 352 or MATH 308. Offered: W.

AMATH 483 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Prerequisite: either CSE 142 or AMATH 301. Offered: Sp.

AMATH 490 Special Topics (1-5, max. 15)
Topics of current interest in applied mathematics not covered by other undergraduate courses.

AMATH 498 Senior Project or Thesis (1-6, max. 6)
Intended for Honors students and other advanced undergraduates completing a special project or senior thesis in applied mathematics. Offered: AWSpS.

Credit/no-credit only. Offered: AWSpS.

AMATH 500 Special Studies in Applied Mathematics (*, max. 24)
Lectures and discussions of topics of current interest in applied mathematics. May not be offered every quarter; content may vary from one offering to another. Prerequisite: permission of instructor.

AMATH 501 Vector Calculus and Complex Variables (5)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: either a course in vector calculus or permission of instructor.

AMATH 502 Introduction to Dynamical Systems and Chaos (5)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology. Prerequisite: either a course in differential equations or permission of instructor.

AMATH 503 Methods for Partial Differential Equations (5)
Applications of partial differential equations; linear and quasilinear first order equations, characteristics, shocks; classification of linear second order equations; basic solution techniques for parabolic, elliptic, and hyperbolic equations; Green's functions and integral transform methods. Prerequisite: either AMATH 501 and a course in differential equations or permission of instructor.

AMATH 504 Mathematical Epidemiology (5)
Focuses on the construction and analysis of mathematical models for infectious disease transmission and control. Emphasizes evaluation and comparison of vaccination programs. Applications are presented for a variety of diseases such as measles, rubella, smallpox, rabies, etc. Prerequisite: either a course in differential equations or permission of instructor. Offered: Sp, odd years.

AMATH 505 Introduction to Fluid Dynamics (4)
Eulerian equations for mass-motion; Navier-Stokes equation for viscous fluids, Cartesion tensors, stress-strain relations; Kelvin's theorem, vortex dynamics; potential flows, flows with high-low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory. Prerequisite: either a course in partial differential equations or permission of instructor. Offered: jointly with ATM S 505/OCEAN 511; A, odd years.

AMATH 506 Applied Probability Statistics (4)
Discrete and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Prerequisite: some advanced calculus and linear algebra. Offered: jointly with STAT 506.

AMATH 507 Calculus of Variations (5)
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods. Prerequisite: either AMATH 351 or MATH 307; MATH 324; MATH 327. Offered: W, odd years.

AMATH 509 Theory of Optimal Control (3)
Trajectories from ordinary differential equations with control variables. Controllability, optimality, maximum principle. Relaxation and existence of solutions. Techniques of nonsmooth analysis. Prerequisite: real analysis on the level of MATH 426; background in optimization corresponding to MATH 515. Offered: jointly with MATH 509.

AMATH 510 Financial Data Access and Analysis with SQL, VBA, and Excel (4)
Provides skills in retrieving and manipulating financial data and in creating computational solutions to quantitative finance problems using SQL, VBA, and Excel. Also teaches skills in leveraging the powerful financial data modeling and analysis capabilities of R in conjunction with SQL, VBA, and Excel. Offered: A.

AMATH 512 Methods of Engineering Analysis (3)
Applications of mathematics to problems in chemical engineering; vector calculus; properties and methods of solution of first and second order partial differential equations; similarity transforms, separation of variables, Laplace and Fourier transforms. Prerequisite: MATH 308, either MATH 307 or AMATH 351, MATH 324, or permission of instructor. Offered: jointly with CHEM E 512; A.

AMATH 514 Networks and Combinatorial Optimization (3)
Mathematical foundations of combinatorial and network optimization with an emphasis on structure and algorithms with proofs. Topics include combinatorial and geometric methods for optimization of network flows, matching, traveling salesmen problem, cuts, and stable sets on graphs. Special emphasis on connections to linear and integer programming, duality theory, total unimodularity, and matroids. Prerequisite: either MATH 308 or AMATH 352 any additional 400-level mathematics course. Offered: jointly with MATH 514.

AMATH 515 Fundamentals of Optimization (5)
Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Prerequisite: linear algebra and advanced calculus. Offered: jointly with IND E 515/MATH 515.

AMATH 516 Numerical Optimization (3)
Methods of solving optimization problems in finitely many variables, with or without constraints. Steepest descent, quasi-Newton methods. Quadratic programming and complementarity. Exact penalty methods, multiplier methods. Sequential quadratic programming. Cutting planes and nonsmooth optimization. Prerequisite: AMATH 515. Offered: jointly with MATH 516.

AMATH 521 Special Topics in Mathematical Biology (5, max. 15)
DNA-folding, patter-forming systems, stochastic analysis. Prerequisite: permission of instructor. Offered: Sp.

AMATH 522 Introduction to Mathematical Biology (5)
Modeling biological systems with differential and difference equations. Examples from: ecology (population growth, disease dynamics); biochemistry and cell biology; and neurobiology (Hodgkin-Huxley and neural networks). Methods include linear stability analyses, phase-plane analyses, and perturbation theory. Prerequisite: either a course in differential equations or permission of instructor.

AMATH 523 Mathematical Analysis in Biology and Medicine (5)
Focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications drawn from many branches of biology and medicine. Provides experiences in applying differential equations, difference equations, and dynamical systems theory to biological problems. Prerequisite: either courses in differnential equations and statistics and probability, or permission of instructor. Offered: W.

AMATH 524 Mathematical Biology: Spatiotemporal Models (5)
Examines partial differential equations for biological dynamics in space and time. Draws examples from molecular and cell biology, ecology, epidemiology, and neurobiology. Topics include reaction-diffusion equations for biochemical reactions, calcium wave propagation in excitable medium, and models for invading biological populations. Prerequisite: either courses in partial differential equations and statistics and probability, or permission of instructor. Offered: Sp.

AMATH 531 Mathematical Theory of Cellular Dynamics (3)
Develops a coherent mathematical theory for processes inside living cells. Focuses on analyzing dynamics leading to functions of cellular components (gene regulation, signaling biochemistry, metabolic networks, cytoskeletal biomechanics, and epigenetic inheritance) using deterministic and stochastic models. Prerequisite: either courses in dynamical systems, partial differential equations, and probability, or permission of instructor.

AMATH 532 Mathematics of Genome Analysis and Molecular Modeling (5)
Covers genome analysis, including bioinformatics and molecular modeling in terms of molecular dynamics. Prerequisite: either AMATH 506 or permission of instructor. Offered: A.

AMATH 533 Neural Control of Movement: A Computational Perspective (3)
Systematic overview of sensorimotor function on multiple levels of analysis, with emphasis on the phenomenology amenable to computational modeling. Topics include musculoskeletal mechanics, neural networks, optimal control and Bayesian inference, learning and adaptation, internal models, and neural coding and decoding. Prerequisite: vector calculus, linear algebra, MATLAB, or permission of instructor. Offered: jointly with CSE 529; W.

AMATH 534 Dynamics of Neurons and Networks (5)
Covers mathematical analysis and simulation of neural systems - singles cells, networks, and populations - via tolls of dynamical systems, stochastic processes, and signal processing. Topics include single-neuron excitability and oscillations; network structure and synchrony; and stochastic and statistical dynamics of large cell populations. Prerequisite: either CSE 528 or permission of instructor.

AMATH 535 Mathematical Ecology (5)
Considers models, methods, and issues in population ecology. Topics include the effects of density dependence, delays, demographic stochasticity, and age structure on population growth; population interactions (predation, competition, and mutualism); and application of optimal control theory to the management of renewable resources. Prerequisite: either a course in differential equations or permission of instructor. Offered: Sp.

AMATH 536 Spatial Models in Ecology and Epidemiology (5)
Considers models for growth and dispersal of biological populations. Topics include population persistence, climate-induced range shifts, and rates of spread of invading organisms. Considers reaction-diffusion equations, integrodifference equation, branching random walks, and other relevant classes of models. Prerequisite: either a course in partial differential equations or permission of instructor. Offered: Sp.

AMATH 540 Capital Markets and Data for Computational Finance (2) Golbeck
Introduces students to the language and terminology of finance, capital markets, and data through selected textbook and financial news readings. Also teaches students how to access, manipulate, and analyze complex financial data from various repositories available through the internet.

AMATH 541 Investment Science (4) Martin, Tung
Introduces the mathematical, statistical, and financial foundations of investment science. Topics include: Mean-Variance Portfolio Theory, efficient frontiers, expected tail loss, futures and forwards, no arbitration and risk-neutral pricing, and binomial tree derivate pricing. Prerequisite: coursework in introductory probability and statistics, and advanced calculus. Offered: A.

AMATH 542 Financial Data Modeling and Analysis in R (4)
Introduces the R statistical programming language for computational finance application. Focuses on use of R packages for quantitative finance and R scripts development for statistical analysis and modeling methods in key quantitative finance areas including factor modeling, financial time series, and portfolio analytics. Prerequisite: AMATH 541. Offered: A.

AMATH 543 Portfolio Optimization and Asset Management (4)
Covers long-only and long-short portfolio optimization with real-world constraints and costs using industrial strength optimization softwar; classical mean-variance and modern mean-versus downside risk optimization for dealing with fat-tailed skewed asset returns; optimization and risk analysis with factor models; and equity, mixed asset class, and fund-of-hedge portfolios. Prerequisite: AMATH 541 and AMATH 542, or permission of instructor. Offered: S.

AMATH 544 Options and Derivatives (4)
Covers financial instrument options and derivatives. Explores how to price options and other derivatives and use them to hedge investment risk. Involves theory, statistical modeling, numerical methods, and computation using the R programming language. Prerequisite: AMATH 540; co-requisite: AMATH 541 or permission of instructor. Offered: A.

AMATH 545 Financial Risk Management I (4)
Introduces the concepts and methodologies of financial risk management. Uses derivatives for hedging risk, emphasizing fixed income and exchange rate derivatives. Includes models, credit derivatives, mortgage backed securities, and asset backed securities. First in a sequence of three on financial risk management. Prerequisite: AMATH 541 or permission of instructor. Offered: W.

AMATH 546 Financial Risk Management II (4)
Provides a comprehensive treatment of the theoretical concepts and modeling techniques of quantitative risk management focusing on practical tools to solve real-work problems. Covers methods for market, credit, and operational risk modeling. Prerequisite: AMATH 545 or permission of instructor. Offered: S.

AMATH 547 Credit Risk Management (4) Henniger
Theory, applications & computational methods for credit risk measurement & management. Statistical and mathematical modeling of credit risk, emphasizing numerical methods & R programming. Methods include logistic regression, Monte Carlo simulation, & portfolio cash flow modeling. Covers default risk regression, analytics, & portfolio models of credit risk. Offered: A.

AMATH 548 Monte Carlo Methods in Finance (4) Marting
Monte Carlo simulations in quantitative finance for portfolio assembly and financial risk management. Students learn theory and methods of tracking the behavior of underlying securities in an option or portfolio and determine the derivative's value by taking the expected value of the discounted payoffs at maturity. Prerequisite: AMATH 540. Offered: A.

AMATH 551 Introduction to Trading Systems (4)
Introduces electronic trading systems. Uses the R programming language to develop, evaluate, and optimize quantitative trading strategies. Students apply trading strategies through a live paper-trading account with an online broker using real time market data.

AMATH 552 Portfolio Performance Analysis and Benchmarking (2)
Covers fundamental principles and commonly used methods in performance measurement, analysis, and benchmarking of portfolio evaluation. Prerequisite: AMATH 541, MBA level investments course, or equivalent. Offered: A.

AMATH 553 Financial Time Series Forecasting Methods (2)
Covers financial time series forecasting methods and their use in making investment decisions for asset management purposes. Asset-class specific forecasting methods. Uses the R statistical modeling and data analysis system for implementing and evaluating such forecasting methods. Prerequisite: AMATH 541 or permissions of instructor. Offered: W.

AMATH 554 Endowment and Institutional Investment Management (2)
Focuses on the endowment management process and specific challenges facing institutional fund managers. Includes evaluating the role of an endowment, portfolio construction, risk management, manager selection, and alternative asset class investing. Utilizes concepts from finance and investments, macroeconomics, and mathematical optimization. Prerequisite: AMATH 54; recommended: AMATH 543 or equivalent. Offered: S.

AMATH 555 Optimization Methods in Finance (4) Murray
Covers theory and efficient solution methods for optimization problems in finance. Includes financial solution methodologies using linear, non-linear, quadratic, and integer formulations; and dynamic and stochastic programming. Prerequisite: AMATH 540; linear algebra and matrix notation; statistics and probability; and experience with R language and MS Excel. Offered: A.

AMATH 556 Statistical Modeling for Computational Finance (4) Konis
Advanced classical and modern statistical modeling methods for computational finance including: covariance matrix, correlation matrix, and principal components estimation and analysis; least-squares, robust, nonlinear and nonparametric regression for asset return factor models; shrinkage methods; risk factors selection; and clustering and classification methods. Asset management applications and computer exercise with R. Offered: A.

AMATH 557 Financial Software Development and Integration with C++ (4)
Practical introduction to C++ programming for financial applications. Focuses on developing basic object oriented programming skills in C++ to implement computational finance solutions. Also includes integrating C++ applications with R, MATLAB, SQL, and VBA.

AMATH 558 Fixed Income Analytics and Portfolio Management (4)
Covers fixed income markets and securities, data sources, analytics and portfolio management methods, in particular the valuation, risks, and risk management of fixed income securities. Uses a hands-on data-oriented and computational focus. Offered: A.

AMATH 559 Stochastic Calculus for Quantitative Finance (4) Golbeck
Provides a systematic examination of financial derivatives pricing using stochastic calculus. Examines popular stochastic differential equation models such as Geometric Brownian motion, Vasicek, Hull-White, Cox-Ingersoll-Ross, Black-Karasinski, Heath-Jarrow-Morton, and Brace-Gatarek-Musiela, as well as Poisson and Levy processes. Applications include equity, fixed-income, and credit derivatives. Offered: S.

AMATH 567 Applied Analysis (5)
Reviews applications of metric and normed spaces, types of convergence, upper and lower bounds, and completion of a metric space; Banach spaces and Hilbert spaces, bounded linear operators, orthogonal sets and Fourier series, and the Riesz representation theorem; and the spectrum of a bounded linear operator and the Fredholm alternative. Introduces distributions. Prerequisite: either a course in real analysis or advanced calculus, or permission of instructor. Offered: A.

AMATH 568 Advanced Methods for Ordinary Differential Equations (5)
Survey of practical solution techniques for ordinary differential equations. Linear systems of equations including nondiagonable case. Nonlinear systems; stability phase plane analysis. Asymptotic expansions. Regular and singular perturbations. Prerequisite: either a course in differential equations or permission of instructor. Offered: W.

AMATH 569 Advanced Methods for Partial Differential Equations (5)
Analytical solution techniques for linear partial differential equations. Discussion of how these arise in science and engineering. Transform and Green's function methods. Classification of second-order equations, characteristics. Conservation laws, shocks. Prerequisite: either a course in partial differential equations or permission of instructor. Offered: Sp.

AMATH 570 Asymptotic and Perturbation Methods (5)
Asymptotics for integrals, perturbation, and multiple-scale analysis. Singular perturbations: matched asymptotic expansions, boundary layers, shock layers, uniformly valid solutions. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or permission of instructor. Offered: A.

AMATH 572 Introduction to Applied Stochastic Analysis (5)
Introduction to the theory of probability and stochastic processes based on differential equations with applications to science and engineering. Poisson processes and continuous-time Markov processes, Brownian motions and diffusion. Prerequisite: either courses in dynamical systems, statistics, and probability, or permission of instructor. Offered: Sp, even years.

AMATH 573 Coherent Structures, Pattern Formation and Solitons (5)
Methods for nonlinear partial differential equations (PDEs) leading to coherent structures and patterns. Includes symmetries, conservations laws, stability Hamiltonian and variation methods of PDEs; interactions of structures such as waves or solitons; Lax pairs and inverse scattering; and Painleve analysis. Prerequisite: either a course in partial differential equations or permission of instructor. Offered: A, odd years.

AMATH 574 Conservation Laws and Finite Volume Methods (5)
Theory of linear and nonlinear hyperbolic conservation laws modeling wave propagation in gases, fluids, and solids. Shock and rarefaction waves. Finite volume methods for numerical approximation of solutions; Godunov's method and high-resolution TVD methods. Stability, convergence, and entropy conditions. Prerequisite: AMATH 586 or permission of instructor. Offered: W.

AMATH 575 Dynamical Systems (5)
Overview of ways in which complex dynamics arise in nonlinear dynamical systems. Topics include bifurcation theory, universality, Poincare maps, routes to chaos, horseshoe maps, Hamiltonian chaos, fractal dimensions, Liapunov exponents, and the analysis of time series. Examples from biology, mechanics, and other fields. Prerequisite: either AMATH 502 or permission of instructor. Offered: Sp, odd years.

AMATH 579 Intelligent Control through Learning and Optimization (3)
Design or near-optimal controllers for complex dynamical systems, using analytical techniques, machine learning, and optimization. Topics from deterministic and stochastic optimal control, reinforcement learning and dynamic programming, numerical optimization in the context of control, and robotics. Prerequisite: vector calculus; linear algebra, and Matlab. Recommended: differential equations; stochastic processes, and optimization. Offered: jointly with CSE 579.

AMATH 581 Scientific Computing (5)
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results. Prerequisite: either a course in numerical analysis or permission of instructor.

AMATH 582 Computational Methods for Data Analysis (5)
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression. Prerequisite: either courses in Matlab and linear algebra or permission of instructor. Offered: W.

AMATH 583 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Prerequisite: a course in linear algebra; programming experience. Offered: Sp.

AMATH 584 Applied Linear Algebra and Introductory Numerical Analysis (5)
Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations. Prerequisite: either a course in linear algebra or permission of instructor. Offered: jointly with MATH 584; A.

AMATH 585 Numerical Analysis of Boundary Value Problems (5)
Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse symmetric and non-symmetric linear systems: conjugate-gradients, preconditioners. Prerequisite: either AMATH 581, AMATH 584/MATH 584, or permission of instructor. Offered: jointly with MATH 585; W.

AMATH 586 Numerical Analysis of Time Dependent Problems (5)
Numerical methods for time-dependent differential equations, including explicit and implicit methods for hyperbolic and parabolic equations. Stability, accuracy, and convergence theory. Spectral and pseudospectral methods. Prerequisite: AMATH 581 or AMATH 584. Offered: jointly with ATM S 581/MATH 586; Sp.

AMATH 590 Special Topics (1-5, max. 30)
Topics of current interest in applied mathematics. Offered: AWSpS.

AMATH 600 Independent Research or Study (*-)
Credit/no-credit only.

AMATH 700 Master's Thesis (*-)
Credit/no-credit only.

AMATH 800 Doctoral Dissertation (*-)
Credit/no-credit only.