## Undergraduate Course Listing in Applied Mathematics and Statistics

**AMS 102-C Elements of Statistics**

The use and misuse of statistics in real life situations; basic statistical measures
of central tendency and of dispersion, frequency distributions, elements of probability,
binomial and normal distributions, small and large sample hypothesis testing, confidence
intervals, chi square test, and regression. May not be taken by students with credit
for AMS 110, 310, 311, 312; ECO 320; POL 201; PSY 201; or SOC 202. This course has been designated as a
High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses
for the first time will have priority to do so.

Prerequisite: Satisfaction of entry skill in mathematics requirement (Skill 1) or
satisfactory completion of D.E.C. C or SBC: QPS; Non AMS majors only

Antirequisite: May not be taken by students with credit for AMS 110 or AMS 310.

3 credits

AMS 102 Webpage

**AMS 103 Applied Mathematics in Modern Technology**

Technologies that drive our modern world rely critically on applied mathematics. This
course explores "How does it work?" for selected technologies that rely on mathematics
and statistics, e.g., internet search, social networking, financial markets, online
auctions, cell phones, DNA sequencing, GPS, Wii, Google maps, and more.*Prerequisite:* Level 3 or higher on the mathematics placement examination; SBC: QPS, TECH

3 credits

AMS 103 Webpage

**AMS 104 Introduction to Spreadsheets**

Spreadsheets are a critically important tool in many careers, particularly in quantitative
fields. This course explores how to use spreadsheets and how to use them to model
real-world situations, such as project management, optimization, budgeting, finance,
and more.

3 credits

AMS 104 Webpage

**AMS 110 Probability and Statistics in the Life Sciences**

A survey of probability theory and statistical techniques with applications to biological
and biomedical situations. Topics covered include Markov chain models; binomial, Poisson,
normal, exponential, and chi square random variables; tests of hypotheses; confidence
intervals; t tests; and analysis of variance, regression, and contingency tables.
May not be taken for credit in addition to AMS 310. This course has been designated
as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA
courses for the first time will have priority to do so. SBC: QPS

Prerequisite: AMS 151 or MAT 125 or 131 or 141.

Antirequisite: May not be taken by students with credit for AMS 102 or AMS 310

3 credits

AMS 110 Webpage**AMS 151 Applied Calculus I**

A review of functions and their applications; analytic methods of differentiation;
interpretations and applications of differentiation; introduction to integration.
Intended for CEAS majors. Not for credit in addition to MAT 125 or 126 or 131 or 141.
This course has been designated as a High Demand/Controlled Access (HD/CA) course.
Students registering for HD/CA courses for the first time will have priority to do
so.

Prerequisite: B or higher in MAT 123, or level 5 on the mathematics placement examination.
DEC: C or SBC: QPS

3 credits

AMS 151 Webpage **AMS 161 Applied Calculus II**

Analytic and numerical methods of integration; interpretations and applications of
integration; differential equations models and elementary solution techniques; phase
planes; Taylor series and Fourier series. Intended for CEAS majors. Not for credit
in addition to MAT 126 or 127 or 132 or 142. This course has been designated as a
High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses
for the first time will have priority to do so.

Prerequisite: C or higher in AMS 151 or MAT 131 or 141, or level 7 on the mathematics placement examination. DEC: C or
SBC: QPS

3 credits

AMS 161 Webpage

**AMS 210 Applied Linear Algebra**

An introduction to the theory and use of vectors and matrices. Matrix theory including
systems of linear equations. Theory of Euclidean and abstract vector spaces. Eigenvectors
and eigenvalues. Linear transformations. May not be taken for credit in addition to
MAT 211. SBC: STEM+

Prerequisite: AMS 151 or MAT 131 or 141, or corequisite MAT 126 or level 7 or higher on the MPE

3 credits

AMS 210 Webpage **AMS 261 Applied Calculus III**

Vector algebra and analytic geometry in two and three dimensions; multivariable differential
calculus and tangent planes; multivariable integral calculus; optimization and Lagrange
multipliers; vector calculus including GreenÕs and StokesÕs theorems. May not be taken
for credit in addition to MAT 203 or 205.

Prerequisite: AMS 161 or MAT 127 or 132 or 142 or MPE level 9. SBC: STEM+

4 credits

AMS 261 Webpage **AMS 300 Writing in Applied Mathematics**

See Requirements for the Major in Applied Mathematics and Statistics, Upper Division
Writing Requirement.

Prerequisites: WRT 102; AMS major; U3 or U4 standing. SBC: SPK, WRTD

1 credit, S/U grading

AMS 300 Webpage **AMS 301 Finite Mathematical Structures **

An introduction to graph theory and combinatorial analysis. The emphasis is on solving
applied problems rather than on theorems and proofs. Techniques used in problem solving
include generating functions, recurrence relations, and network flows. This course
develops the type of mathematical thinking that is fundamental to computer science
and operations research. SBC: STEM+

Prerequisite: AMS 210 or MAT 211 or AMS 361 or MAT 303.

3 credits

AMS 301 Webpage **AMS 303 Graph Theory**

Paths and circuits, trees and tree based algorithms, graph coloring, digraphs, network
flows, matching theory, matroids, and games with graphs.

Prerequisite: AMS 301

3 credits

AMS 303 Webpage **AMS 310 Survey of Probability and Statistics**

A survey of data analysis, probability theory, and statistics. Stem and leaf displays,
box plots, schematic plots, fitting straight line relationships, discrete and continuous
probability distributions, conditional distributions, binomial distribution, normal
and t distributions, confidence intervals, and significance tests. May not be taken
for credit in addition to ECO 320. SBC: STEM+

Prerequisite: AMS 161 or MAT 127, 132, 142.

3 credits

AMS 310 Webpage **AMS 311 Probability Theory**

Probability spaces, random variables, moment generating functions, algebra of expectations,
conditional and marginal distributions, multivariate distributions, order statistics,
law of large numbers.

Prerequisites: AMS 301 and 310 or permission of instructor Corequisites: MAT 203 or 205 or AMS 261.

3 credits

AMS 311 Webpage**AMS 315 Data Analysis**

A continuation of AMS 310 that covers two sample t-tests, contingency table methods,
the one-way analysis of variance, and regression analysis with one and multiple independent
variables. Student projects analyze data provided by the instructor and require the
use of a statistical computing package such as SAS or SPSS. An introduction to ethical
and professional standards of conduct for statisticians will be provided.

Prerequisite: AMS 310

3 credits

AMS 315 Webpage **AMS 316 Introduction to Time Series Analysis**

Trend and seasonal components of time series models, autoregressive and moving average
(ARMA) models, Box-Jenkins methodology, Portmanteau test, unit-root, generalized autoregressive
conditionally heteroskedasticity (GARCH) models, exponential GARCH, stochastic volatility
models. This course is offered as both AMS 316 and AMS 586.

Prerequisites: AMS 311 and 315

3 credits

AMS 316 Webpage**AMS 317 Introduction to Linear Regression Analysis**Basic inference procedures and linear regression, model adequacy checking, transformations
and weighted least squares, handling with influential observations and outliers, polynomial
regression modeling, use of indicator variables, multicollinearity, variable selection,
introduction of logistic regression, conventional and less common uses of linear regression
in today's cutting-edge scientific research. Understanding of the basic principles
for applied regression model-building techniques in various fields of study, including
engineering, management and the health sciences.

*Prerequisite:*AMS 315

3 credits

AMS 317 Webpage

**AMS 318 Financial Mathematics**

This course will focus on accumulation functions, yield rates, annuities, loan repayment, term structure of interest rates/spot rates/forward rates, options, duration/convexity. This course follows the syllabus for the Financial Mathematics (FM) Exam of the Society of Actuaries and prepares students to pass the FM Exam.

Prerequisite: AMS 310

3 credits

AMS 318 Webpage

**AMS 320 Introduction to Quantitative Finance**

The course introduces the main classes of financial securities, the mathematical tools employed to model their prices, and common models for risk and investment management. Building realistic models relies on having a working knowledge of the empirical properties of financial asset returns which is another focus of the course. R is used as an environment for modeling.

Prerequisite: AMS 311

AMS 320 Webpage

**AMS 325 Computer and Programming Fundamentals**

Introduction to programming in MATLAB and Python, including scripting, basic data
structures, algorithms, scientific computing, and software engineering. Homework
projects will focus on using computation to solve linear algebra, data analysis, and
other mathematical problems.

Prerequisite: AMS 210 or MAT 211; AMS Major

3 credits

AMS 325 Webpage

**AMS 326 Numerical Analysis**

Direct and indirect methods for the solution of linear and nonlinear equations. Computation
of eigenvalues and eigenvectors of matrices. Quadrature, differentiation, and curve
fitting. Numerical solution of ordinary and partial differential equations.

Prerequisites: CSE 101; AMS 161; basic skills in using a high-level programming language (C, C++, or Java.)

Advisory prerequisite: AMS 210 or MAT 211

3 credits

AMS 326 Webpage

**AMS 332 Computational Modeling of Physiological Systems**

Introduces students to the fundamental principles underlying computational modeling
of complex physiological systems. A major focus of the course will be on the process
by which a model of a biological system is developed. Students will be introduced
to the mathematical methods required for the modeling of complex systems (including
stochastic processes and both temporal and spatial dynamics) as well as to tools for
computational simulation. Roughly one half of the class will focus on models for general
cellular physiology, while the remaining half will focus on the development of higher-level
models of a particular physiological system (for example, the neurobiological systems
underlying learning). This course is offered as both AMS 332 and BIO 332 and is intended
for STEM majors who have already completed the foundational courses in their major.
Students who satisfy the pre-requisites but do not have a deeper background in some
STEM field may find the class very challenging and should ask the instructor for guidance
before registering.

Prerequisites: MAT 127 or MAT 132 or higher and any one of the following: BIO 202
or BIO 203 or CHE 132 or CHE 331 or PHY 127 or PHY 132

3 credits

AMS 332 Webpage

**AMS 333 Computational Biology**

This course introduces the use of mathematics and computer simulation to study a wide
range of problems in biology. Topics include the modeling of populations, the dynamics
of signal transduction and gene-regulatory networks, and simulation of protein structure
and dynamics. A computer laboratory component allows students to apply their knowledge
to real-world problems.

Prerequisites: AMS 161 or MAT 132; U3 or U4 standing; or permission of the instructor.

3 credits

AMS 333 Webpage**AMS 335 Game Theory**

Introduction to game theory fundamentals with special emphasis on problems from economics
and political science. Topics include strategic games and Nash equilibrium, games
in coalitional form and the core, bargaining theory, measuring power in voting systems,
problems of fair division, and optimal and stable matching. This course is offered
as both AMS 335 and ECO 355.

Prerequisites: MAT 126 or 131 or 141 or AMS 151; C or higher in ECO 303

3 credits

AMS 335 Webpage **AMS 341 Operations Research I: Deterministic Models**

Linear programming with a view toward its uses in economics and systems analysis.
Linear algebra and geometric foundations of linear programming; simplex method and
its variations; primal dual programs; formulation and interpretation of linear programming
models, including practical problems in transportation and production control. Optional
computer projects. AMS 341 and 342 may be taken in either order, though it is recommended that AMS 341 be taken first.

Prerequisites: AMS 210 or MAT 211

3 credits

AMS 341 Webpage **AMS 342 Operations Research II: Stochastic Models**

Methods and techniques for stochastic modeling and optimization, with applications
to queueing theory, Markov chains, inventory theory, games, and decisions. AMS 341
and 342 may be taken in either order, though it is recommended that AMS 341 be taken first.

Prerequisites: AMS 210 or MAT 211; AMS 311

3 credits

AMS 342 Webpage**AMS 345 Computational Geometry**

The design and analysis of efficient algorithms to solve geometric problems that arise
in computer graphics, robotics, geographical information systems, manufacturing, and
optimization. Topics include convex hulls, triangulation, Voronoi diagrams, visibility,
intersection, robot motion planning, and arrangements. This course is offered as both
AMS 345 and CSE 355.

Prerequisites: AMS 301; programming knowledge of C or C++ or Java.

3 credits

AMS 345 Webpage**AMS 351 Applied Algebra**

Topics in algebra: groups, informal set theory, relations, homomorphisms. Applications:
error correcting codes, BurnsideÕs theorem, computational complexity, Chinese remainder
theorem. This course is offered as both AMS 351 and MAT 312

Prerequisite: AMS 210 or MAT 211

Advisory Prerequisite: MAT 200 or CSE 150 or CSE 215 or equivalent

3 credits

AMS 351 Webpage**AMS 361 Applied Calculus IV: Differential Equations**

Homogeneous and inhomogeneous linear differential equations; systems of linear differential
equations; solution with power series and Laplace transforms; partial differential
equations and Fourier series. May not be taken for credit in addition to the equivalent
MAT 303.

Prerequisite: AMS 161 or MAT 127 or 132 or 142 or MPE level 9.

4 credits

AMS 361 Webpage

**AMS 380 Data Mining**

This course will teach the basic ingredients of classical and contemporary statistical
data mining methods including dimension reduction, variable selection, pattern recognition,
and predictive modeling using traditional general linear models and generalized linear
models, and modern statistical learning methods such as classification and regression
tree, random forest, neural networks, etc. We will also teach how to run these procedures
with the statistical programming language R.

Prerequisite: AMS 311

3 credits

AMS 380 Webpage

**AMS 394 Statistical Laboratory**

Designed for students interested in statistics and their applications. Basic statistical
techniques including sampling, design, regression, and analysis of variance are introduced.
Includes the use of statistical packages such as SAS and R. Students translate realistic
research problems into a statistical context and perform the analysis.

Prerequisites: AMS 310 or AMS 315

3 credits

AMS 394 Webpage**AMS 410 Actuarial Mathematics**

Integrates calculus and probability with risk assessment and insurance in a quantitative
manner to prepare students for the first actuarial examination.

Prerequisites: AMS 261 or MAT 203 or 205; AMS 310; AMS 311 or 315.

3 credits

AMS410 Webpage **AMS 412 Mathematical Statistics**

Estimation, confidence intervals, Neyman Pearson lemma, likelihood ratio test, hypothesis
testing, chi square test, regression, analysis of variance, nonparametric methods.

Prerequisite: AMS 311

3 credits

AMS 412 Webpage

**AMS 420 Investment Science Foundations**Focuses on fundamental principles of financial engineering and investment science

such as cash flow streams, arbitrage, risk aversion, pricing of finance instruments, interest

rate term structure, fixed income instruments duration, bond portfolio immunization,

Markowitz mean-variance portfolio theory, Capital Asset Pricing Model and fixed proportion investment strategy.

Prerequisite: Grade of B+ or higher in AMS 311

Advisory Prerequisite: AMS 341

3 credits

AMS 420 Webpage

**AMS 441 Business Enterprise**

Explores the strategy and technology of business enterprises. Integrates the practice of engineering and quantitative methods with the operations of a business in today's globalized environment, whether in product development, financial management, or e-commerce.

Prerequisite: U3 or U4.

3 credits

AMS 441 Webpage

**AMS 475 and AMS 476 Undergraduate Teaching Practicum**

Students assist the instructor in teaching by conducting weekly office hours, review sessions, and answering questions via electronic means. The student receives regularly scheduled supervision from the instructor. May be used as an open elective only and repeated once.

Prerequisites: A minimum GPA of 3.00 in all Stony Brook courses and demonstrated mastery of the subject at the level of "A" or "A-"; permission of department.

3 credits

AMS 475 Webpage

**AMS 487 Research in Applied Mathematics**

An independent research project with faculty supervision. Permission to register requires
a B average and the agreement of a faculty member to supervise the research. May be
repeated once. Only 3 credits of research electives (AMS 487, CSE 487, MEC 499, ESE
499, ESM 499, EST 499, ISE 487) may be counted toward engineering technical elective
requirements.

Prerequisites: Permission of instructor and department.

0-3 credits

AMS 487 Webpage **AMS 492 Topics in Applied Mathematics**

Treatment of an area of applied mathematics that expands upon the undergraduate curriculum.
Topics may include applied mathematics, statistics, or operations research and change
from semester to semester. Semester supplements to this Bulletin contain specific
description when course is offered. May be repeated for credit once, as the topic
changes.

Prerequisite: Permission of instructor.

3 credits

AMS 492 Webpage