Graduate Course Descriptions

AMS 500, Responsible Conduct of Research and Scholarship (RCRS)
This course is designed to introduce students to the major issues in the ethics of science and research. Using a combination of readings - written and web-based - videos, and case discussion, students will investigate the moral values intrinsic to science and the professional and social values with which scientists must comply. Each class will begin with an introductory lecture or video followed by discipline-based, small group discussions with the participation of an AMS faculty member.
Spring/Fall, 0 credits, S/U grading
AMS 500 Webpage

AMS 501 Differential Equations and Boundary Value Problems I 
Examples of initial and boundary value problems in which differential equations arise. Existence and uniqueness of solutions, systems of linear differential equations, and the fundamental solution matrix. Power series solutions, Sturm-Liouville theory, eigenfunction expansion, Green's functions. 
Fall, 3 credits, ABCF grading 
AMS 501 Webpage

AMS 502 Differential Equations and Boundary Value Problems II 
Analytic solution techniques for, and properties of solutions of, partial differential equations, with concentration on second order PDEs. Techniques covered include: method of characteristics, separation of variables, eigenfunction expansions, spherical means, GreenÕs functions and fundamental solutions, and Fourier transforms. Solution properties include: energy conservation, dispersion, dissipation, existence and uniqueness, maximum and mean value principles. 
Prerequisite: AMS 501 
Spring, 3 credits, ABCF grading 
AMS 502 Webpage 

AMS 503 Applications of Complex Analysis 
A study of those concepts and techniques in complex function theory that are of interest for their applications. Pertinent material is selected from the following topics: harmonic functions, calculus of residues, conformal mapping, and the argument principle. Application is made to problems in heat conduction, potential theory, fluid dynamics, and feedback systems. 
Fall, 3 credits, ABCF grading 
AMS 503 Webpage

AMS 504 Foundations of Applied Mathematics 
An introductory course for the purpose of developing certain concepts and techniques that are fundamental in modern approaches to the solution of applied problems. An appropriate selection of topics is based on the concepts of metric spaces, compactness, sequences and convergence, continuity, differentiation and integration, function sequences, contraction mapping theorem. Strong emphasis on proofs.
Fall, 3 credits, ABCF grading 
AMS 504 Webpage

AMS 505 Applied Linear Algebra 
Review of matrix operations. Elementary matrices and reduction of general matrices by elementary operations, canonical forms, and inverses. Applications to physical problems. Coscheduled as AMS 505 or HPH 695. 
Fall, 3 credits, ABCF grading 
AMS 505 Webpage 

AMS 506 Finite Structures 
Problem solving in combinatorial analysis and graph theory using generating functions, recurrence relations, PolyaÕs enumeration formula, graph coloring, and network flows.
3 credits, ABCF grading 
AMS 506 Webpage

AMS 507 Introduction to Probability 
The topics include sample spaces, axioms of probability, conditional probability and independence, discrete and continuous random variables, jointly distributed random variables, characteristics of random variables, law of large numbers and central limit theorem, Markov chains. Note: Crosslisted with HPH 696.
Fall, 3 credits, ABCF grading 
AMS 507 Webpage 

AMS 510 Analytical Methods for Applied Mathematics and Statistics 
Review of techniques of multivariate calculus, convergence and limits, matrix analysis, vector space basics, and Lagrange multipliers. 
Fall, 3 credits, ABCF grading
Prerequisites:  A course in linear algebra and in multivariate calculus
AMS 510 Webpage

AMS 511, Foundation of Quantitative Finance 
Introduction to capital markets, securities pricing, and modern portfolio theory, including the organization and operation of securities market, the Efficient Market Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing Theory, and more general factor models. Common stocks and their valuation, statistical analysis, and portfolio selection in a single-period, mean-variance context will be explored along with its solution as a quadratic program. Fixed income securities and their valuation, statistical analysis, and portfolio selection. Discussion of the development and use of financial derivatives. Introduction to risk neutral pricing, stochastic calculus, and the Black-Scholes Formula. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned.
3 credits, ABCF grading 
AMS 511 Webpage 

AMS 512 Capital Markets and Portfolio Theory 
Development of capital markets and portfolio theory in both continuous time and multi-period settings. Utility theory and its application to the determination of optimal consumption and investment policies. Asymptotic growth under conditions of uncertainty. Applications to problems in strategic asset allocation over finite horizons and to problems in public finance. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned. 
Prerequisite: AMS 511 
3 credits, ABCF grading 
AMS 512 Webpage 

AMS 513 Financial Derivatives and Stochastic Calculus 
Foundations of stochastic modeling for finance applications, starting with general probability theory leading up to basic results in pricing exotic and American derivatives.  We will cover filtrations and generalized conditional expectation, Girsanov theorem and the Radon-Nikodym process, martingales, Brownian motion, Ito integration and processes, Black-Scholes formula, risk neutral pricing, Feynman-Kac theorem, exotic options such as barrier and lookback, and the perpetual American put.  If time permits we will discuss term structure modeling, volatility estimation, and mortgage backed securities.
Prerequisite: AMS 511
3 credits, ABCF grading 
AMS 513 Webpage 

AMS 514 Computational Finance 
Review of foundations: stochastic calculus, martingales, pricing, and arbitrage. Basic principles of Monte Carlo and the efficiency and effectiveness of simulation estimators. Generation of pseudo- and quasi-random numbers with sampling methods and distributions. Variance reduction techniques such as control variates, antithetic variates, stratified and Latin hypercube sampling, and importance sampling. Discretization methods including first and second order methods, trees, jumps, and barrier crossings. Applications in pricing American options, interest rate sensitive derivatives, mortgage-backed securities and risk management. Whenever practical, examples will use real market data. Extensive numerical exercises and projects in a general programming environment will also be assigned. 
Prerequisite: AMS 512 and AMS 513
3 credits, ABCF grading 
AMS 514 Webpage 

AMS 515, Case Studies in Machine Learning and Finance 
The course will cover applications of Quantitative Finance to risk assessment, portfolio management, cash flow matching, securities pricing and other topics. Particular attention will be paid to machine learning approaches, such as neural networks and support vector machines, data collection and analysis, the design and implementation of software. We will study differences between theory and practice in model application, including in-sample and out-of-sample analysis.
Prerequisite:  No formal prerequisites. 
3 credits, ABCF grading 
AMS 515 Webpage 

AMS 516, Statistical Methods in Finance
The course introduces statistical methodologies in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. The course will cover regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, statistical methods for financial time series; value at risk, smoothing techniques and estimation of yield curves, and estimation and modeling of volatilities.
3 credits, ABCF grading 
Prerequisite:  AMS 507
AMS 516 Webpage

AMS 517, Quantitative Risk Management
The course will cover structural and reduced-form approach to pricing credit default, Markovian models (or rating-based) pricing methods, statistical inference of relative risks, counting process, correlated (or dependent) default times, copula methods and pricing models for CDOs.
3 credits, ABCF grading 
Prerequisite: AMS 507 and AMS 511
AMS 517 Webpage

AMS 518, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization
The course provides a thorough treatment of advance risk measurement and portfolio optimization, extending the traditional approaches to these topics by combining distributional models with risk or performance measures into one framework. It focuses on, among others, the fundamentals of probability metrics and optimization, new approaches to portfolio optimization and a variety of essential risk measures. Numerical exercises and projects in a high-level programming environment will be assigned. 
Offered Fall semester 
Prerequisite: AMS 512 or AMS 516 or AMS 522
3 credits, ABCF grading 
AMS 518 Webpage

AMS 519, Internship in Quantitative Finance
Supervised internship in financial institution. Students will typically work at a trading desk, in an asset management group, or in a risk management group. Students will be supervised by a faculty member and a manager at their internship site. Written and oral reports will be made to both supervisors.
Offered every semester, 3-6 credits, ABCF grading
AMS 519 Webpage

AMS 520, Machine Learning in Quantitative Finance
This course will merge ML and traditional quantitative finance techniques employed at investment banks, asset management, and securities trading firms. It will provide a systematic introduction to statistical learning and machine learning methods applied in Quantitative Finance. The topics discussed in the course fall broadly into four categories which (as time permits) will be discussed in this order: (1) Probabilistic Modeling:  Bayesian vs. frequentist estimation, bias-variance tradeoff, sequential Bayesian updates, model selection and model averaging; Probabilistic graphical models and mixture models; Multiplicative Weights Update Method Bayesian regression and Gaussian processes.  (2) Feedforward neural networks: Feedforward architecture; Stochastic gradient descent and backpropagation algorithm; Non-Linear Factor Modeling and applications in asset pricing; Convolutional neural networks; Autoencoders.  (3) Sequential Learning: Linear time series models; Probabilistic sequence modeling – Hidden Markov Models and particle filtering; Recurrent Neural Networks; Applications in finance.  (4) Reinforcement Learning: Markov decision process and dynamic programming methods (Bellman equations and Bellman optimality); Reinforcement learning methods (Monte-Carlo methods, policy-based learning, TD-learning, SARSA, and Q-learning); Deep reinforcement learning; Applications of reinforcement learning in finance.
Prerequisites:  AMS 572 and AMS 595; or AMS 561; or based on Python knowledge per instructor's consent
Fall, 3 credits, ABCF grading
AMS 520 Webpage

AMS 521, Data Management
This course teaches how to manage databases, covering core concepts such as database architecture, data storage, querying, and transaction management. Students will learn how to design and build databases, work with distributed systems, and manage multiple concurrent processes. Topics include data warehousing, data cleaning, and data mining, with hands-on practice using R and SQL to prepare real-world datasets for analysis. The course also introduces modern database technologies, including graph databases for modeling complex relationships, vector databases for AI-driven similarity search on unstructured data, and AI-powered database management systems that apply machine learning to optimize performance and automate data processing tasks.
Prerequisite:  There are no prerequisites for this course, and we will start learning R and SQL from the very beginning.  However, having some prior experience would be helpful.
Spring, 3 credits; ABCF grading
AMS 521 Webpage

AMS 522, Bayesian Methods in Finance
The course explores in depth the fundamentals of the Bayesian methodology and the use of the Bayesian theory in portfolio and risk management. It focuses on, among other topics incorporating the prior views of analysts and investors into the asset allocation process, estimating and predicting volatility, improving risk forecasts, and combining the conclusions of different models. Numerical exercises and projects in a high-level programming environment will be assigned. 
SPRING 3 credits, ABCF grading
Prerequisite: AMS 512 or instructor consent
AMS 522 Webpage 

AMS 523, Mathematics of High Frequency Finance
The course explores Elements of real and complex linear spaces. Fourier series and transforms, the Laplace transform and z-transform. Elements of complex analysis including Cauchy theory, residue calculus, conformal mapping and Möbius transformations. Introduction to convex sets and analysis in finite dimensions, the Legendre transform and duality. Examples are given in terms of applications to high frequency finance. 
Fall 3 credits, ABCF grading
AMS 523 Webpage

AMS 524, Modern Computational Data Analytics
This course introduces the tools for the analysis of big data sets on server machines. It teaches how to store, preprocess, analyze and visualize data arriving at high volume and velocity. In the first part of the course, we will cover programming in Python, from its basic libraries to more advanced methods for big data analytics, and machine learning. Emphasis will be on the implementation in Python and practical hands-on examples.  Next, we will learn essential Shell scripting and terminal window commands for computations on server machines.  We will introduce database management systems and SQL querying.  In the second part of the course, we will discuss code version control and collaboration solutions in GitHub and GitHub Actions, microservices, containers (Docker and Kubernetes), API gateways, and other tools necessary in a professional data science pipeline.
Summer, 3 credits, ABCF grading
Note:  Instructor consent
AMS 524 Webpage

AMS 525, Geometric Deep Learning
In the first part of the course, we will cover programming in Python, from its basic libraries up to the implementation of advanced deep learning models such as CNNs, RNNs, GNNs and Transformer networks.  The practical success of many of these models in high dimensional problems such as image processing, playing GO, or protein folding comes from the predefined regularities in the underlying low-dimensional geometric structure of the data.  Therefore in the second part of the course, we will extend the aforementioned deep learning models and their implementations to graphs and manifolds in spatial and spectral domains. The focus will be on the implementation of the models in Python and their practical applications.
Summer, 3 credits, ABCF grading
Note:  Instructor consent
AMS 525 Webpage

AMS 526 Numerical Linear Algebra
Introduction to key concepts and algorithms in numerical linear algebra and their applications in computational and data sciences. Topics include direct and iterative methods for solving simultaneous linear equations, least squares problems, computation of eigenvalues and eigenvectors, and singular value decomposition.
Prerequisite:  AMS 510 and AMS 595
Fall, 3 credits, ABCF grading
AMS 526 Webpage

AMS 527 Numerical Analysis II 
Numerical methods based upon functional approximation: polynomial interpolation and approximation; and numerical differentiation and integration. Solution methods for ordinary differential equations. AMS 527 may be taken whether or not the student has completed AMS 526. 
Spring, 3 credits, ABCF grading 
AMS 527 Webpage

AMS 528 Numerical Methods for PDEs
Introduction to key concepts and algorithms for finding numerical solutions to partial differential equations (PDEs). Topics include analysis of consistency, stability and convergence, and finite difference and/or finite volume methods for the three major classes of PDEs: parabolic, elliptic, and hyperbolic. Practical implementations, important packages of scientific software algorithms, and examples of modern scientific and engineering applications are also discussed.
Co-requisite:  AMS 502
Spring, 3 credits, ABCF grading 
AMS 528 Webpage

AMS 530 Principles in Parallel Computing 
This course is designed for both academic and industrial scientists interested in parallel computing and its applications to large-scale scientific and engineering problems. It focuses on the three main issues in parallel computing: analysis of parallel hardware and software systems, design and implementation of parallel algorithms, and applications of parallel computing to selected problems in physical science and engineering. The course emphasizes hands-on practice and understanding of algorithmic concepts of parallel computing. 
Prerequisite: A course in basic computer science such as operating systems or architectures or some programming experience 
Fall, 3 credits, ABCF grading 
AMS 530 Webpage 

AMS 531 Laboratory Rotations in Computational Biology
This is a two-semester course in which first year Ph.D. students spend at least 8 weeks in each of three different laboratories actively participating in the research of participating Computational Biology faculty.  At the end of each rotation, students give a presentation of their lab activates and accomplishments.  The primary goal of rotations is to help students choose a research advisor and to help faculty members choose students.  Students register for AMS 531 in both the Fall and Spring semesters of the first year.
Offered in Fall and Spring semesters; 0-3 credits, S/U grading
AMS 531 Webpage

AMS 532 Journal Club in Computational Biology
he goal of this course is for students to hone critical reading and analytic skills through discussions of literature in the area of Computational Biology. Participants take turn being a "discussion leader" who informally guides the group through a peer-reviewed manuscript for which all Journal Club members will have to read in advance of the meeting. Meetings in the Spring semester will include in Person Training (IPT) in Responsible conduct of Research and Scholarship (RCRS) on topics that comprise (1)Integrity in Scholarship, (2) Scientific Misconduct, (3) Mentoring, (4) Ownership and Authorship, (5) Plagiarism, (6) Data Management, (7) Journalism and Science, (8) Human Subjects, and (9) Laboratory Animals.
Offered in Fall and Spring semesters; 0-1 credits, S/U grading
AMS 532 Webpage 

AMS 533 Numerical Methods and Algorithms in Computational Biology
This class will survey many of the key techniques used in diverse aspects of computational biology. We will focus on how to successfully formulate a statement of the problem to be solved, and how that formulation can guide in selecting the most suitable computational approach. A set of problems from a diverse range of problems in biology will be used as examples. Note: Informatic methods for genomic analysis (such as data mining and analysis of nucleic acid and protein sequences) will not be covered. These topics are covered thoroughly in CSE 549.
3 credits, ABCF grading 
AMS 533 Webpage 

AMS 534 Introduction to Systems Biology
A detailed introduction to essential concepts and computational skills for doing research in Systems Biology. The class will be centered upon two key programming languages: Matlab for modeling applications and the R language for statistical analysis and sequence manipulation. Examples will come from a broad range of biological applications ranging from theoretical population genetics, metabolic and gene network dynamics to analysis of high-throughput data. No prior knowledge of biology or mathematical/computational techniques is required.
Note: Crosslisted with BGE 534.
3 credits, ABCF grading
AMS 534 Webpage

AMS 535 Introduction to Computational Structural Biology and Drug Design
This course will provide an introduction to Computational Structural Biology with application to Drug Design. Methods and applications that use computation to model biological systems involved in human disease will be emphasized. The course aims to foster collaborative learning and will consist of presentations by the instructor, guest lecturers, and by course participants with the goal of summarizing key methods, topics, and papers relevant to Computational Structural Biology.  AMS 535 is cross-listed with CHE 535.
3 credits, ABCF grading, may be repeated for credit 
AMS 535 Webpage

AMS 536 Molecular Modeling of Biological Molecules 
This course is designed for students who wish to gain hands-on experience modeling biological molecules at the atomic level. In conjunction with the individual interests, Molecular Mechanics, Molecular Dynamics, Monte Carlo, Docking (virtual screening), or Quantum Mechanics software packages can be used to study relevant biological systems(s). Projects will include setup, execution, and analysis. Course participants will give literature presentations relevant to the simulations being performed and a final project report will be required. Familiarity with UNIX (Linux) is desirable.   Note:  This course is cross-listed with CHE 536.
Prerequisite: AMS 535/CHE 535; or permission of the instructor
3 credits, ABCF grading, may be repeated for credit 
AMS 536 Webpage 

AMS 537 Biological Dynamics and Networks
This course will provide a solid foundation in key theoretical concepts for the study of dynamics in biological systems and networks at different scales ranging from the molecular level to metabolic and gene regulatory networks. Topics of this course include but are not limited to: Physical kinetics; Diffusion/Smoluchowskii; Random flights; Waiting times; Poisson; Brownian ratchets; Chemical kinetics; Transition states; Stability, bifurcations, pattern development; Noise in cells: intrinsic and Extrinsic; Feedback; Biological Osciillators; Recurrence, period doubling, chaos; Networks; Topologies; Degree distribution, betweenness; Models of nets: Erdos-Renyi, scale-free, social, Watts-Strogatz, agents; Robustness, highly-optimized tolerance, bowties, epidemics; Biological networks: Protein-protein nets, regulatory and metabolic nets; Known biological circuits and their behaviors; How networks evolve: Preferential attachment, rewiring; Power laws; Fluxed through networks; Information and communication, entropy; Metabolic flux analysis; Artificial and Natural selection for traits; Darwinian evolution; Population dynamics.
Offered in the Spring semester, 3 credits, ABCF grading
Crosslisted with PHY 559 and CHE 559
AMS 537 Webpage

AMS 539 Introduction to Physical and Quantitative Biology
This course is a seminar series organized by the Laufer Center for Physical and Quantitative Biology and is aimed at any incoming graduate students who might be interested in doing research in computational, mathematical or physical biology. Each seminar will be given by a different faculty member about their research and will span a range of topics including computational cell biology and evolutionary models.
0-1 credits, S/U grading
AMS 539 Webpage

AMS 540 Linear Programming 
Formulation of linear programming problems and solutions by simplex method. Duality, sensitivity analysis, dual simplex algorithm, decomposition. Applications to the transportation problem, two-person games, assignment problem, and introduction to integer and nonlinear programming. This course is offered as both MBA 540 and AMS 540.
Prerequisite: A course in linear algebra 
3 credits, ABCF grading 
AMS 540 Webpage

AMS 542 Analysis of Algorithms 
Techniques for designing efficient algorithms, including choice of data structures, recursion, branch and bound, divide and conquer, and dynamic programming. Complexity analysis of searching, sorting, matrix multiplication, and graph algorithms. Standard NP-complete problems and polynomial transformation techniques. This course is offered as both AMS 542 and CSE 548.
Spring, 3 credits, ABCF grading 
AMS 542 Webpage

AMS 544 Discrete and Nonlinear Optimization 
Theoretical and computational properties of discrete and nonlinear optimization problems: integer programming, including cutting plane and branch and bound algorithms, necessary and sufficient conditions for optimality of nonlinear programs, and performance of selected nonlinear programming algorithms. This course is offered as both MBA 544 and AMS 544. 
Prerequisite: AMS 540 or MBA 540 
3 credits, ABCF grading 
AMS 544 Webpage 

AMS 545 Computational Geometry 
Study of the fundamental algorithmic problems associated with geometric computations, including convex hulls, Voronoi diagrams, triangulation, intersection, range queries, visibility, arrangements, and motion planning for robotics. Algorithmic methods include plane sweep, incremental insertion, randomization, divide-and-conquer, etc. This course is offered as both AMS 545 and CSE 555. 
Spring, 3 credits, ABCF grading 
AMS 545 Webpage 

AMS 546 Network Flows 
Theory of flows in capacity-constrained networks. Topics include maximum flow, feasibility criteria, scheduling problems, matching and covering problems, minimum-length paths, minimum-cost flows, and associated combinatorial problems.  
Spring, 3 credits, ABCF grading 
AMS 546 Webpage 

AMS 547 Discrete Mathematics 
This course introduces such mathematical tools as summations, number theory, binomial coefficients, generating functions, recurrence relations, discrete probability, asymptotics, combinatorics, and graph theory for use in algorithmic and combinatorial analysis. This course is offered as both CSE 547 and AMS 547. 
Spring, 3 credits, ABCF grading 
AMS 547 Webpage 

AMS 548 Optimization Techniques in Biomolecular Simulations
This practical hands-on course will teach basic techniques for building mathematical models, algorithms, and software for biomolecular simulations of macromolecular interactions.  The topics of this course include, but are not limited to: the basics of statistical mechanics and its connection to the sampling algorithms, the origin of and approximations for the computation of molecular forces; geometry of the molecular configuration search space and multidimensional optimization; basics of software development and programming for high performance computing (HPC).  During the course, the students will develop a multiscale approach for modeling protein-protein interactions from the ground up.
Spring, 0-3 credits, ABCF grading
AMS 548 Webpage

AMS 549 Computational Biology
This course focuses on current problems in computational biology and bioinformatics. Our emphasis will be algorithmic, on discovering appropriate combinatorial algorithm problems and the techniques to solve them. Primary topics will include DNA sequence assembly, DNA/protein sequence comparison, hybridization array analysis, RNA and protein folding, and phylogenic trees.
Spring/Fall, 3 credits, ABCF grading
AMS 549 Webpage

AMS 550 Operations Research: Stochastic Models 
Includes Poisson processes, renewal theory, discrete-time and continuous-time Markov processes, Brownian motion, applications to queues, statistics, and other problems of engineering and social sciences. 
Prerequisite: AMS 507 
Spring, 3 credits, ABCF grading 
AMS 550 Webpage

AMS 552 Game Theory I 
Elements of cooperative and noncooperative games. Matrix games, pure and mixed strategies, and equilibria. Solution concepts such as core, stable sets, and bargaining sets. Voting games, and the Shapley and Banzhaff power indices. This course is offered as both ECO 604 and AMS 552.
Prerequisite: Admission to graduate AMS program or permission of instructor 
3 credits, ABCF grading 
AMS 552 Webpage 

AMS 553 Simulation and Modeling 
A comprehensive course in formulation, implementation, and application of simulation models. Topics include data structures, simulation languages, statistical analysis, pseudorandom number generation, and design of simulation experiments. Students apply simulation modeling methods to problems of their own design. This course is offered as CSE 529, AMS 553, and MBA 553.
Prerequisite: CSE 214 or equivalent; AMS 310 or AMS 507 or equivalent; or permission of instructor 
Fall, 3 credits, ABCF grading 
AMS 553 Webpage 

AMS 554 Queuing Theory 
Introduction to the mathematical aspects of congestion. Birth and death processes. Queues with service priorities and bulk-service queues. Analysis of transient- and steady-state behavior. Estimation of parameters. Applications to engineering, economic, and other systems. This course is offered as both MBA 554 and AMS 554. 
3 credits, ABCF grading 
AMS 554 Webpage 

AMS 555 Game Theory II 
Refinements of strategic equilibrium, games with incomplete information, repeated games with and without complete information, and stochastic games. The Shapley value of games with many players, and NTU-values.
Note: This course is offered as both ECO 605 and AMS 555.
Prerequisite: AMS 552/ECO 604
Spring, 3 credits, ABCF grading 
AMS 555 Webpage 

AMS 556 Dynamic Programming 
Stochastic and deterministic multistage optimization problems. Stochastic path problems. Principle of optimality. Recursive and functional equations. Method of successive approximations and policy iteration. Applications to finance, economics, inventory control, maintenance, inspection, and replacement problems. This course is offered as both MBA 556 and AMS 556. 
Prerequisite: AMS 507
3 credits, ABCF grading 
AMS 556 Webpage

AMS 559 Smart Energy in the Information Age 
Energy and sustainability have become critical issues of our generation. While the abundant potential of renewable energy sources, such as solar and wind, provides a real opportunity for sustainability, their intermittency and uncertainty present a daunting operational challenge. This course studies how to use Information Technology (IT) to improve sustainability in our energy-hungry society. In particular, topics include the applications of mathematical modeling, algorithm design, optimization, game theory, and control theory in real systems. The goal of the course is to provide rigorous foundations for the study of smart energy management for sustainability. 
3 credits, Letter graded (A, A-, B+, etc.)  Note:  Cross-listed with CSE 551.
AMS 559 Webpage

AMS 560 Big Data Systems, Algorithms and Networks

Recent progress on big data systems, algorithms and networks. Topics include the web graph, search engines, targeted advertisements, online algorithms and competitive analysis, and analytics, storage, resource allocation, and security in big data systems. 
3 credits, Letter graded (A, A-, B+, etc.)  Note:  Cross-listed with CSE 542.
AMS 560 Webpage

AMS 561 Introduction to Computational and Data Science
This course provides a foundation of knowledge and basic skills for the successful application in graduate research of modern techniques in computational and data science relevant to engineering, the humanities, and the physical, life and social sciences. It is consciously crafted to provide a rich, project-oriented, multidisciplinary experience that establishes a common vocabulary and skill set. Centered around the popular programming language Python, the course will serve as an introduction to programming including data structures, algorithms, numerical methods, basic concepts in computer architecture, and elements of object-oriented design.  Also introduced will be important concepts and tools associated with the analysis and management of data, both big and small, including basic statistical modeling in R, aspects of machine learning and data mining, data management, and visualization. No previous computing experience is assumed. Students are assumed to have taken some introductory courses in two of these three math subjects: linear algebra, calculus, and probability. 3 credits, ABCF grading
Antirequisite: AMS 595
Pre-requisite: Instructor Consent Required
Offered in the Spring Semester
AMS 561 Webpage

AMS 562 Introduction to Scientific Programming in C++
This course provides students with foundational skills and knowledge in practical scientific programming relevant for scientists and engineers. The primary language is C++ since it is a widely-used object-oriented language, includes C as a subset, and is a powerful tool for writing robust, complex, high-performance software. Elements of Python, Bash, and other languages will be introduced to complement the capabilities of C++, and essential tools for software development and engineering will be employed throughout the course (e.g., makefiles, version control, online code repositories, debugging, etc.)  This course is controlled and owned by the Institute for Advanced Computational Science (IACS).
3 credits, ABCF grading
Offered in the Fall Semester
AMS 562 Webpage

AMS 563, Medical Image Analysis 
This course explores the fundamental principles and algorithms used in medical image processing and analysis. Key topics include interpolation, registration, enhancement, feature extraction, classification, segmentation, quantification, shape analysis, motion estimation, and visualization, including traditional and machine learning techniques. Both anatomical and functional image analysis will be covered, using data from common medical imaging modalities. Through projects and assignments, students will gain hands-on experience working with real medical imaging data.
Prerequisites:  Listed on webpage
AMS 563 Webpage

AMS 565 Wave Propagation 
Theory of propagation of vector and scalar waves in bounded and unbounded regions. Development of methods of geometrical optics. Propagation in homogeneous and anisotropic media. 
Fall, 3 credits, ABCF grading 
AMS 565 Webpage 

AMS 566 Compressible Fluid Dynamics 
Physical, mathematical, and computational description in compressible fluid flows. Integral and differential forms of the conservation equations, one-dimensional flow, shocks and expansion waves in two and three dimensions, quasi-one-dimensional flow, transient flow, numerical methods for steady supersonic flow, numerical methods for transient flow. 
Spring, 3 credits, ABCF grading 
Prerequisite: AMS 510
AMS 566 Webpage 

AMS 569 Probability Theory I 
Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli lemmas. Expectation using simple functions. Monotone and dominated convergence theorems. Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers and the central limit theorem. 
Prerequisite: AMS 510 
AMS 569 Webpage
3 credits, ABCF grading

AMS 570 Introduction to Mathematical Statistics 
Probability and distributions; multivariate distributions; distributions of functions of random variables; sampling distributions; limiting distributions; point estimation; confidence intervals; sufficient statistics; Bayesian estimation; maximum likelihood estimation; statistical tests.
Prerequisite: AMS 507
Spring, 3 credits, ABCF grading 
AMS 570 Webpage 

AMS 571 Mathematical Statistics 
Sampling distribution; convergence concepts; classes of statistical models; sufficient statistics; likelihood principle; point estimation; Bayes estimators; consistency; Neyman-Pearson Lemma; UMP tests; UMPU tests; Likelihood ratio tests; large sample theory. 
Prerequisite: AMS 570
Fall, 3 credits, ABCF grading
AMS 571 Webpage 

AMS 572 Data Analysis I 
Introduction to basic statistical procedures. Survey of elementary statistical procedures such as the t-test and chi-square test. Procedures to verify that assumptions are satisfied. Extensions of simple procedures to more complex situations and introduction to one-way analysis of variance. Basic exploratory data analysis procedures (stem and leaf plots, straightening regression lines, and techniques to establish equal variance). Coscheduled as AMS 572 or HPH 698. 
Fall, 3 credits, ABCF grading
AMS 572 Webpage 

AMS 573 Design and Analysis of Categorical Data 
Measuring the strength of association between pairs of categorical variables. Methods for evaluating classification procedures and inter-rater agreement. Analysis of the associations among three or more categorical variables using log linear models. Logistic regression. 
Spring, 3 credits, ABCF grading
Prerequisites: AMS 572
AMS 573 Webpage 

AMS 575 Internship in Statistical Consulting 
Directed quantitative research problem in conjunction with currently existing research programs outside the department. Students specializing in a particular area work on a problem from that area; others work on problems related to their interests, if possible. Efficient and effective use of computers. Each student gives at least one informal lecture to his or her colleagues on a research problem and its statistical aspects. 
Prerequisite: Permission of instructor 
Fall and Spring, 1-9 credits, ABCF grading 
AMS 575 Webpage 

AMS 577 Multivariate Analysis 
The multivariate distribution. Estimation of the mean vector and covariance matrix of the multivariate normal. Discriminant analysis. Canonical correlation. Principal components. Factor analysis. Cluster analysis. 
Prerequisites: AMS 572 and AMS 578 
3 credits, ABCF grading
AMS 577 Webpage 

AMS 578 Regression Theory 
Classical least-squares theory for regression including the Gauss-Markov theorem and classical normal statistical theory. An introduction to stepwise regression, procedures, and exploratory data analysis techniques. Analysis of variance problems as a subject of regression. Brief discussions of robustness of estimation and robustness of design. 
Prerequisite: AMS 572
Spring, 3 credits, ABCF grading 
AMS 578 Webpage 

AMS 580 Statistical Learning
This course teaches the following fundamental topics: (1) General and Generalized Linear Models; (2) Basics of Multivariate Statistical Analysis including dimension reduction methods, and multivariate regression analysis; (3) Supervised and unsupervised statistical learning.
Spring, 3 credits, ABCF grading
AMS 580 Webpage

AMS 582 Design of Experiments 
Discussion of the accuracy of experiments, partitioning sums of squares, randomized designs, factorial experiments, Latin squares, confounding and fractional replication, response surface experiments, and incomplete block designs. Coscheduled as AMS 582 or HPH 699.
Prerequisite: AMS 572  
Fall, 3 credits, ABCF grading 
AMS 582 Webpage 

AMS 583 Applied Longitudinal Data Analysis
Longitudinal data takes the form of repeated measurements of the same subject (humans, animals, plants, samples, etc) over time (or other conditions). This type of data has a broad range of applications, including public health, medical research, pharmaceutical studies, life sciences, agriculture, engineering and physical sciences.  Longitudinal data analysis allows one to study the changes in mean response over time and answer other scientific questions pertaining to the relationship between the response and time.  This course aims to introduce statistical models and methods for the analysis of longitudinal data.  Both the classical (univariate and multivariate repeated analysis of variance) and more recent approaches (1) general linear models for correlation, random coefficient models, linear mixed effect models for normal repeated measurements; (2) generalized linear models for non-normal response and population-averaged models (generalized estimating equations) for non-normal repeated measurements, of analyzing longitudinal data be covered in this course. 
Prerequisite: AMS 572 and AMS 578
Spring semester, 3 credits, ABCF grading
AMS 583 Webpage

AMS 585 Internship in Data Science 
Directed data science problem in conjunction with currently existing research programs outside the department. Students specializing in a particular area work on a problem from that area; others work on problems related to their interests, if possible. Efficient and effective use of computers. Each student gives at least one informal lecture to his or her colleagues on a research problem and its statistical aspects.
3 credits, ABCF grading
AMS 585 Webpage

AMS 586 Time Series 
Analysis in the frequency domain. Periodograms, approximate tests, relation to regression theory. Pre-whitening and digital fibers. Common data windows. Fast Fourier transforms. Complex demodulation, GibbsÕ phenomenon issues. Time-domain analysis.
Prerequisites: AMS 570 or AMS 572
Spring or Fall semester, 3 credits, ABCF grading
AMS 586 Webpage 

AMS 587 Nonparametric Statistics 
This course covers the applied nonparametric statistical procedures: one-sample Wilcoxon tests, two-sample Wilcoxon tests, runs test, Kruskal-Wallis test, KendallÕs tau, SpearmanÕs rho, Hodges-Lehman estimation, Friedman analysis of variance on ranks. The course gives the theoretical underpinnings to these procedures, showing how existing techniques may be extended and new techniques developed. An excursion into the new problems of multivariate nonparametric inference is made.
Prerequisites: AMS 412 and AMS 572 or equivalent
3 credits, ABCF grading
AMS 587 Webpage 

AMS 588 Failure and Survival Data Analysis
Statistical techniques for planning and analyzing medical studies. Planning and conducting clinical trials and retrospective and prospective epidemiological studies. Analysis of survival times including singly censored and doubly censored data. Quantitative and quantal bioassays, two-stage assays, routine bioassays. Quality control for medical studies. 
3 credits, ABCF grading
AMS 588 Webpage 

AMS 589 Quantitative Genetics 
Definition of relevant terminology. Statistical and genetic models for inheritance of quantitative traits. Estimation of effects of selection, dominance polygenes, epistatis, and environment. Linkage studies and threshold characteristics. 
3 credits, ABCF grading 
AMS 589 Webpage 

AMS 591 Topics for M.S. Students 
Various topics of current interest in applied mathematics will be offered if sufficient interest is shown. Several topics may be taught concurrently in different sections. 
Prerequisite: Permission of instructor 
3 credits, ABCF grading, may be repeated for credit
AMS 591 Webpage 

AMS 593 Mathematical Theory of Interest and Portfolio Pricing 
Calculation of simple and compound interest poses elementary arithmetic or algebraic problems. Variable interest rates (including indexing), inflation, changes in the exchange rates of foreign currency, and changes in the laws, such as income tax, create investment risks. The course is intended to develop problem-solving skills and adopts both deterministic and stochastic approaches. The perspectives of the consumer and the investor are taken into account. The material helps students prepare for the actuarial examinations. Topics are selected from the following: simple and compound interest, fixed-rate loans and mortgages, annuities and capital budgeting of pension plans, variable interest rates, bonds, prepayment and default scenarios, and currency baskets. 
Prerequisite: AMS 512
Fall, 3 credits, ABCF grading
AMS 593 Webpage 

AMS 595 Fundamentals of Computing 
Introduction to programming in MATLAB, Python, and C/C++, including scripting, basic data structures, algorithms, scientific computing, software engineering and programming tools.  No previous programming experience is required.
Anti-requisite: AMS 561
Fall, 1-9 credits, ABCF grading 
AMS 595 Webpage 

AMS 596 Fundamentals of Large-Scale Computing 
Overview of the design and maintenance of large scale computer projects in applied mathematics, including basic programming techniques for massively parallel supercomputers. 
1 credit, ABCF grading 
AMS 596 Webpage 

AMS 597 Statistical Computing 
Introduction to statistical computing using SAS and S plus. 
3 credits, ABCF grading
AMS 597 Webpage 

AMS 598 Big Data Analysis
Introduction to the application of the supercomputing for statistical data analyses, particularly on big data.
Prerequisites: AMS 507, AMS 580 and AMS 597
Fall, 3 credits, ABCF grading
AMS 598 Webpage

AMS 599 Research 
Fall, spring, and summer, 1-12 credits, S/U grading, may be repeated for credit
AMS 599 Webpage

AMS 603 Risk Measures for Finance & Data Analysis
Risk analysis is an important to quantitative finance, insurance, commercial credit and many areas of data analysis. We emphasize risk analysis methods that capture observed features of risk, such as heavy tails, and validation of risk models against observed data. Students will be graded on the basis of projects drawn from multiple asset classes considered in the course work, including fixed income, options, portfolio optimization and foreign exchange. Professional standards for software development will be followed. Guest lectures by industry leaders will be included. Participation via conferencing software will be available as an option to class attendance.
1-3 credits;  ABCF grading
AMS 603 Webpage

AMS 676 Internship in Applied Mathematics
Directed research and/or practical experience in industry, financial and consulting firms, and research institutions. Students are required to have a department faculty adviser who coordinates and supervises the internship. Submission of the final report is required.
1-9 credits;  S/U grading; may be repeated for credit
AMS 676 Webpage

AMS 683 Biological Physics and Biophysical Chemistry: Theoretical Perspectives 
This course will survey a selected number of topics in biological physics and biophysical chemistry. The emphasis is on the understanding of physical organization principles and fundamental mechanisms involved in the biological process. The potential topics include: Protein Folding, Protein Dynamics, Biomolecular Interactions and Recognition, Electron and Proton Transfer, Motors, Membranes, Single Molecules and Single Cells, Cellular Networks, Development and Differentiation, Brains and Neural Systems, Evolution. There will be no homework or exams. The grades will be based on the performance of the term projects. Crosslisted with PHY 680 and CHE 683. 
0-3 credits, ABCF grading 
AMS 683 Webpage 

AMS 691 Topics in AMS
Varying topics selected from the list below if sufficient interest is shown. Several topics may be taught concurrently in different sections: Advanced Operational Methods in Applied Mathematics, Approximate Methods in Boundary Value Problems in Applied Mathematics, Control Theory and Optimization Foundations of Passive Systems Theory, Game Theory, Mixed Boundary Value Problems in Elasticity, Partial Differential Equations, Quantitative Genetics, Stochastic Modeling.
0-3 credits, ABCF grading, may be repeated for credit 
AMS 691 Webpage 

AMS 698 Practicum in Teaching
Undergraduate teaching to be supervised by a faculty member of the Applied Mathematics and Statistics program. Course to be identified by the student and Graduate Program Director.
Spring, 0 credits, S/U grading, may be repeated for credit.
AMS 698 Webpage

AMS 699 Dissertation Research on Campus 
Prerequisite: Must be advanced to candidacy (G5); major portion of research must take place on SBU campus, at Cold Spring Harbor, or at Brookhaven National Lab 
Fall, spring, and summer, 0-9 credits, S/U grading, may be repeated for credit
AMS 699 Webpage 

AMS 700 Dissertation Research off Campus Domestic 
Prerequisite: Must be advanced to candidacy (G5); major portion of research will take place off-campus, but in the U.S. and/or U.S. provinces (Brookhaven National Lab and Cold Spring Harbor Lab are considered on campus); all international students must enroll in one of the graduate student insurance plans and should be advised by an International Advisor 
Fall, spring, summer, 1-9 credits, S/U grading, may be repeated for credit 
AMS 700 Webpage 

AMS 701 Dissertation Research off Campus International 
Prerequisite: Must be advanced to candidacy (G5); major portion of research will take place outside of the U.S. and/or U.S. provinces; domestic students have the option of the health plan and may also enroll in MEDEX; international students who are in their home country are not covered by mandatory health plan and must contact the Insurance Office for the insurance charge to be removed; international students who are not in their home country are charged for the mandatory health insurance (if they are to be covered by another insurance plan, they must file a waiver by the second week of classes; the charge will only be removed if the other plan is deemed comparable); all international students must receive clearance from an International Advisor.
Fall, spring, summer, 1-9 credits, S/U grading, may be repeated for credit 
AMS 701 Webpage

AMS 800 Summer Research 
May be repeated for credit 
AMS 800 Webpage