APPLIED MATHEMATICS AND STATISTICS

550.111 (E,Q)

STATISTICAL ANALYSIS I (4) Fishkind   Prereq: Four years of High School Math     First semester of a general survey of statistical methodology. Topics include descriptive statistics, probability models, random variables, expectation, sampling, the central limit theorem, classical and robust estimation of location, confidence intervals, hypothesis testing, two-sample problems, introductory analysis of variance, introductory nonparametric methods. Three lectures and a conference weekly. Some use of computer terminals and the Minitab statistical package, but prior computing experience not required. Prerequisite: four years of high school mathematics. Students who may wish to undertake more than two semesters of probability and statistics should consider 550.420-430.

Lec.

Sec. 01

02

03

04

05

MTW 1

W 2

Th 9

Th 10:30

Th 12

Th 1

550.112 (E,Q)

STATISTICAL ANALYSIS II (4) Naiman Said  Prereq: 550.111    Second semester of a general survey of statistical methodology. Topics include least squares and regression analysis, correlation, further nonparametric methods, chi-square tests, the likelihood concept, decision theory, Bayesian inference, time series, simultaneous equations, sample survey design.  Students who may wish to undertake more than two semesters of probability and statistics should consider 550.420-430.

Lec.

Sec. 01

02

03

04

MTW 12

Th 9

Th 10:30

Th 12

Th 1

550.122 (Q)

CHANCE AND RISK (3) Wierman The course will help students develop an appreciation of probability and randomness, and an understanding of its applications in real life situations involving chance and risk. Applications, controversies, and paradoxes involving risk in business and economics, health and medicine, law, politics, sports, and gambling will be used to illustrate probabilistic concepts such as independence, conditional probability, expectation, and variance. The course is intended primarily for humanities and social science majors. Not open to students who have taken two semesters of Calculus

Sec. 01

MTW 10

550.171 (E,Q)

DISCRETE MATHEMATICS (4) Torcaso   Prereq: Four years of High School Math     Introduction to the mathematics of finite systems. Logic; Boolean algebra; induction and recursion; sets, functions, relations, equivalence, and partially ordered sets; elementary combinatorics; modular arithmetic and the Euclidean algorithm; group theory; permutations and symmetry groups; graph theory. Selected applications. The concept of a proof and development of the ability to recognize and construct proofs are part of the course.

Lec.

Sec. 01

02

MTW 10

Th 10:30

Th 2

550.251 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: DETERMINISTIC MODELS (4) Castello  Prereq: Calculus I   An introduction to management science and the quantitative approach to decision making.  Focus will be on deterministic models, in which we assume that all problem parameters are known with certainty.  Covered topics may include Linear and Integer Programming, Network Models, Inventory Models (Stationary Demand), Nonlinear Programming, Goal Programming, and Dynamic Programming.  We emphasize model development and case studies, using spreadsheets and other computer software.  The applications we study occur in manufacturing and transportation systems, as well as in finance and general management.

Lec.

Sec. 01

02

MTW 11

Th 11

Th   3

550.252 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: STOCHASTIC MODELS (4) Castello  Prereq: Calculus I   An introduction to management science and the quantitative approach to decision making.  Focus will be on the formulation and analysis of stochastic models, where some problem data may be uncertain.  Covered topics may include Project Scheduling, Decision Analysis, Time Series Forecasting, Inventory Models with Stationary or Nonstationary Demand, Queuing Models, Discrete-Event Simulation, and Quality Management.  We emphasize model development and case studies, using spreadsheets and other computer software.  The applications we study occur in variety of applications.

Sec. 02 canceled 02/02/06

Lec.

Sec. 01

02

MTW 12

Th 12

Th  2

550.281 (E,Q)

COMPUTING IN APPLIED MATHEMATICS (4) Naiman   Prereq: Calculus I     Overview of some of the more common computational platforms in which to do applied mathematics. The course will cover computing in at least three general areas: numerical linear algebra using Matlab, symbolic mathematics using Maple, and statistics using R. Students will be presented with applications, basic mathematics that underlies the problems to be solved, and computational approaches to their solution.

Lec.

Sec. 01

MTW 11

Th 11

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Castello   Prereq: One year of Calculus, computing experience     An introduction to the basic concepts of linear algebra, matrix theory, and differential equations that are used widely in modern engineering and science. Intended for engineering and science majors whose program does not permit taking both 110.201 and 110.302.

Lec.

Sec. 01

02

MTW 9

Th 9

Th 10

550.310 (E,Q)

(W)

PROBABILITY AND STATISTICS FOR THE PHYSICAL AND INFORMATION SCIENCES AND ENGINEERING (4) Said Prereq: One year of Calculus  Coreq: Multivariable Calculus Recommended     An introduction to probability and statistics at the calculus level, intended for engineering and science students planning to take only one course on the topics. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, goodness-of-fit. Students cannot receive credit for both 550.310 and 550.311

Lec.

Sec. 01

02

03

MTW 11

Th 10:30

Th 12

W 2

550.311 (E,Q)

PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING (4) Jedynak   Prereq: One year of Calculus; Coreq: 110.202 recommended An introduction to probability and statistics at the calculus level, intended for students in the biological sciences planning to take only one course on the topics. The basic scope of this course is similar to 550.310, with an emphasis on examples and problems in the biological sciences. Students are encouraged to consider 550.420-430 instead. Combinatorial probability, independence, conditional probability, random variables, expectation and moments, limit theory, estimation, confidence intervals, hypothesis testing, tests of means and variances, and goodness-of-fit will be covered. Students cannot receive credit for both 550.310 and 550.311

Lec.

Sec. 01

02

MTW 10

Th 10

Th 3

550.371 (E,Q)

CRYPTOLOGY & CODING (4) Fishkind   Prereq: 550.171 (110.204 with permission of instructor), Linear Algebra, computing experience A first course in the mathematical theory of secure and reliable electronic communication. Cryptology is the study of secure communication: How can we ensure the privacy of messages? Coding theory studies how to make communication reliable: How can messages be sent over noisy lines? Topics include finite field arithmetic, error-detecting and error-correcting codes, data compressions, ciphers, one-time pads, the Enigma machine, one-way functions, discrete logarithm, primality testing, secret key exchange, public key cryptosystems, digital signatures, and key escrow.

Lec.

Sec. 01

02

MTW 9

Th 9

Th 1

550.386 (E,Q)

SCIENTIFIC COMPUTING: DIFFERENTIAL EQUATIONS (4) Torcaso   Prereq:  Calculus III & 550.291 or approved alternative
(e.g. 110.201)     A first course on computational differential equations and applications. Topics include floating point arithmetic, algorithms and convergence, root finding (midpoint, Newton and secant methods), numerical differentiation and integration, and numerical solution of initial value problems (Runge-Kutta, multi-step, extrapolation methods, stability, implicit methods and stiffness). Theoretical topics such as existence, uniqueness and stability of solutions to initial-value problems, conversion of higher-order/non-autonomous equations to systems, etc. will be covered as needed. Matlab is used to solve all numerical exercises; no previous experience with computer programming is required.

Lec.

Sec. 01

MTW 1

Th 1

550.413 (E,Q)

APPLIED STATISTICS AND DATA ANALYSIS (4) Maiste Prereq: 550.112 or Perm Req’d    An introduction to basic concepts, techniques, and major computer software packages in applied statistics and data analysis. Topics include numerical descriptive statistics, observations and variables, sampling distributions, statistical inference, linear regression, multiple regression, design of experiments, nonparametric methods, and sample surveys. Real-life data sets are used in lectures and computer assignments. Intensive use of statistical packages such as S+ to analyze data.

Lec.

Sec. 01

MTW 3

Th 2

550.426 (E,Q)

STOCHASTIC PROCESSES I (4) Torcaso   Prereq: 550.420 Mathematical theory of stochastic processes.  Emphasis on deriving the dependence relations, statistical properties, and sample path behavior including random walks, Markov chains (both discrete and continuous time), Poisson processes, martingales, and Brownian motion. Applications that illuminate the theory.

Lec.

Sec. 01

MW 4-5:15pm

Th 1

550.430 (E,Q)

INTRODUCTION TO STATISTICS (4) Maiste    Prereq: 550.420 Section 01 is for Undergraduates; Section 02 is for Graduate Students Introduction to the basic principles of statistical reasoning and data analysis. Emphasis on techniques of application. Classical parametric estimation, hypothesis testing, and multiple decision problems; linear models, analysis of variance, and regression; nonparametric and robust procedures; decision-theoretic setting, Bayesian methods.

Lec.

Sec. 01

02

MTW 11

Th 11

F 11

550.435 (E,Q)

BIOINFORMATICS & STATISTICAL GENETICS (3) Maiste   Prereq: 550.310 or 550.311 Biological research has evolved to the point where complex quantitative tools are playing an ever increasing role. The aim of this course is to survey various computational and statistical methodologies that have been put into play in the analysis of biological data to better understand biological phenomena. A large spectrum of biological applications used to motivate the choice of topics. Probabilistic methods, as well as algorithmic ideas related to the assembly, alignment, and matching of DNA sequences, will be developed, and statistical inference methods for making genotype to phenotype connections will be presented.

Sec. 01

MTW 9

550.438 (E,Q)

STATISTICAL METHODS FOR COMPUTER INTRUSION DETECTION (3) Marchette Prereq: 550.310, or 550.311 or equiv. This course will give an introduction to the data and methodologiesof computer intrusion detection. The focus will be on statistical and machine learning approaches to detection of attacks on computers. Topics will include Applied Mathematics and Statistics / 355 network monitoring and analysis, including techniques for studying the Internet, and estimating the number and severity of attacks; network-based attacks such as probes and denial of service attacks; host-based attacks such as buffer overflows and race conditions; malicious code such as viruses and worms. Statistical pattern recognition methods will be described for the detection and classification of attacks. Techniques for the visualization of network data will be discussed. The book will be supplemented with readings of various articles.

Cross-listed with Information Security

Sec. 01

W 1-4

550.442 (E,Q)

               (W)

INVESTMENT SCIENCE (4) Tzitzouris      Prereq: One year of Calculus, 550.310, 550.311, or equiv.   Intended for upper-level undergraduate and graduate students, this course offers a rigorous treatment of the subject of investment as a scientific discipline. Mathematics is employed as the main tool to convey the principles of invest-ment science and their use to make investment calculations for good decision-making. Topics covered in the course include the basic theory of interest and its application to fixed-income securities, cash flow analysis and capital budgeting, mean-variance portfolio theory, and the associated capital asset pricing model, utility function theory and risk analysis, derivative securities and basic option theory, portfolio evaluation. The student is expected to be comfortable with the use of mathematics as a method of deduction and problem solving. Some familiarity with optimization is desirable but not necessary.

Lec.

Sec. 01

02

MW 5:30-6:45pm

Th 5 2

Th 12

550.453 (E,Q)

MATHEMATICAL GAME THEORY (4) Goldman Prereq: Multivariable Calculus, probability, linear algebra  Mathematical analysis of cooperative and noncooperative games. Theory and solution methods for matrix game (two players, zero-sum payoffs, finite strategy sets), games with a continuum of strategies, N-player games, games in rule-defined form. The roles of information and memory. Selected applications to economic, recreational, and military situations

Lec.

Sec. 01

MTW 2

Th 2

550.472 (E,Q)

GRAPH THEORY (4) Scheinerman Prereq: 550.171, and 110.201 or 550.291    Study of systems of "vertices" with some pairs joined by "edges." Theory of adjacency, connectivity, traversability, feedback, and other concepts underlying properties important in engineering and the sciences. Topics include paths, cycles, and trees; routing problems associated with Euler and Hamilton; design of graphs realizing specified incidence conditions and other constraints. Attention directed toward problem solving, algorithms, and applications. One or more topics taken up in greater depth.

Lec.

Sec. 01

MTW 10

Th 10 10:30

550.502

UNDERGRADUATE RESEARCH  Reading, research, or project work for undergraduate students. Pre-arranged individually between students and faculty. Recent topics and activities: percolation models, data analysis, course development assistance, and dynamical systems.

550.600

DEPARTMENT SEMINAR Fill
A variety of topics discussed by speakers from within and outside the university. Required of all resident department graduate students.

Sec. 01

Th 3-5

550.621

PROBABILITY THEORY II Fill Prereq: 550.620, 110.405 Probability at the level of measure theory, focusing on limit theory. Modes of convergence, Poisson convergence, three-series theorem, strong law of large numbers, continuity theorem, central limit theory, Berry-Esseen theorem, infinitely divisible and stable laws.

Lec.

Sec. 01

MW 1:30-2:45

F 1

550.631

STATISTICAL THEORY II Priebe Prereq: 550.630   Advanced concepts and tools fundamental to research in mathematical statistics and statistical inference: asymptotic theory; optimality; various mathematical foundations.

Sec. 01

TTh 10:15-12:15

550.640

MACHINE LEARNING Younes Prereq 550.430 This course will focus on theoretical and practical aspects of statistical learning. We will review a collection of learning algorithms for classification and regression estimation, including linear methods, kernel methods, tree-based and boosting methods; we will also discuss unsupervised methods for linear and nonlinear data reduction and clustering. We will introduce fundamental concepts of the theory of model selection and validation: bias/variance dilemma, penalty methods, and some measures of complexity; the course will also include standard validation algorithms, like cross-validation and bootstrap.

Sec. 01

MW 3-4:15 MTW 3

550.662

OPTIMIZATION ALGORITHMS Han   Prereq: 550.661   Design and analysis of algorithms for linear and nonlinear optimization. The revised simplex method, the primal-dual algorithm, algorithms for network problems, first- and second-order methods for nonlinear problems, quadratic programming techniques, and methods for constrained nonlinear problems.

Lec.

Sec. 01

MTW 11

F 11

550.663

STOCHASTIC SEARCH AND OPTIMIZATION Spall   Prereq: Graduate course in probability and statistics and knowledge of basic matrix algebra    An introduction to stochastic search and optimization, including discrete and continuous optimization problems.  Topics will include the “no free lunch” theorems, beneficial effects of injected Monte Carlo randomness, algorithms for global and local optimization problems, random search, recursive least squares, stochastic approximation, simulated annealing, evolutionary and genetic algorithms, machine (reinforcement) learning, and statistical multiple comparisons.

Sec. 01

T 2-3:30

550.672

GRAPH THEORY Scheinerman        Prereq: 550.171 and 110.201 or 550.291    An introduction to graph theory at the graduate level. Meets concurrently with 550.472. See 550.472 for course description.

Lec.

Sec. 01

MTW 10

Th F 10:30-11:30

550.681

NUMERICAL ANALYSIS Han Prereq: Multivariable Calculus and Linear Algebra, Computing experience; Coreq: 110.405     Mathematical formulation and analysis of numerical algorithms. Brief review of topics in elementary numerical analysis such as floating-point arithmetic, Gaussian elimination for linear equations, inter-polation and approximation. Core topics to be covered: numerical linear algebra including eigenvalue and linear least-squares problems, iterative algorithms for nonlinear equations and least squares problems, and convergence theory of numerical methods. Other possible topics: sparse matrix computations, numerical solution of partial differential equations, finite element methods, and parallel algorithms.

Lec.

Sec. 01

MTW 12

F 12

550.770

TOPICS IN DISCRETE MATHEMATICS – GRAPH CLASSES AND REPRESENTATIONS OF GRAPHS Scheinerman   Prereq: 550.672 (Req’d.), 550.671 (Recommended) An overview of important classes of graphs and their  properties. Hereditary classes (closed under induced subgraph or other such orders) including  perfect graphs, interval graphs, chordal graphs, etc. Will consider graph classes as objects of study unto themselves and  (depending on student interests) algorithms for recognition (and related computational complexity results). Students will be expected to be active participants in the course and will be responsible for lecturing on specific topics.

Sec. 01

TTh 12:30-1:45

550.800

DISSERTATION RESEARCH
01 - Eyink
02 - Fill
03 - Fishkind
04 - Geman
05 - Goldman
06 - Han
07 - Naiman
08 - Priebe
09 - Scheinerman
10 - Wierman
11 - Younes

Sec. 01-11

TBA

550.810

PROBABILITY & STATISTICS SEMINAR Staff

Sec. 01

F 2-5

550.865

OPTIMIZATION & DISCRETE MATH SEMINAR Staff

Sec. 01

TBA