## 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 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 Analysis I **

Direct and indirect methods for solving simultaneous linear equations and matrix inversion,
conditioning, and round-off errors. Computation of eigenvalues and eigenvectors.

Co-requisite: 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 Analysis III **

An introduction to scientific computation, this course considers the basic numerical
techniques designed to solve problems of physical and engineering interest. Finite
difference methods are covered for the three major classes of partial differential
equations: parabolic, elliptic, and hyperbolic. Practical implementation will be discussed.
The student is also introduced to the important packages of scientific software algorithms.
AMS 528 may be taken whether or not the student has completed AMS 526 or AMS 527.

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. This course is offered as both ECO 605
and AMS 555.

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 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.

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