550.111 (E,Q)

STATISTICAL ANALYSIS I (4) Torcaso   Limit 50 per section 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 computing with 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) Aksakalli    Limit 50 per section  Prereq: 550.111 Second semester of a general survey ofstatistical 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. Prerequisite: 550.111. 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 Limit 50   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.  There is no prerequisite beyond high school mathematics.  Not open to students who have taken two semesters of Calculus

Sec. 01

MTW 12

550.171 (E,Q)

DISCRETE MATHEMATICS (4) Torcaso   Limit 50 per section Prereq: Four years of high school mathematics 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. Co-listed with 650.471

Lec.
Sec. 01
02

MTW 10
Th 10:30-11:20
Th 2

550.251 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: DETERMINISTIC MODELS (4) Castello   Limit 35 per section Prereq: One semester of calculus   This course is an introduction to management science and the quantitative approach to decision making.  Our focus will be on deterministic models, in which we assume that all problem parameters are known with certainty.  The 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 1
Th 11
Th   3

550.281 (E,Q)

COMPUTING IN APPLIED MATHEMATICS (4) Naiman  Limit 50   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 10

Th 11

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Castello   Limit 40 per section   Prereqs: 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)

PROBABILITY AND STATISTICS FOR THE PHYSICAL AND INFORMATION SCIENCES AND ENGINEERING (4) Fishkind  Limit 50 per section   Prerequisite: One year of Calculus Recommended Coreq: Multivariable
Calculus    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. This course will be at the same technical level as 550.311.  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) Fishkind  Limit 75 per section Prerequisite: One year of calculus; Corequisite: 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. This course will be at the same technical level as 550.310.  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

550.362 (E,Q)

INTRODUCTION TO OPTIMIZATION II (4) Castello Limit 60    Prerequisites: 550.361 and multivariable calculus An introductory survey of optimization methods, supporting mathematical theory and concepts, and application to problems of planning, design, prediction, estimation, and control in engineering, management, and science.  Study of varied optimization techniques including linear programming, network-problem methods, dynamic programming, integer programming, and nonlinear programming.  Appropriate for undergraduate and graduate students without the mathematical background required for 550.661.

Lec.
Sec. 01

MTW 2
Th 2

550.371 (E,Q)

CRYPTOLOGY & CODING (4)
Scheinerman   Limit 30 per section Prerequisites: 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) Eyink  Limit 40  Prerequisites: Calculus III, and 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, multistep, 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) Aksakalli   Limit 60
Prerequisite: 550.112 or equivalent 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) Fill   Limit 50   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) Jedynak    Limit 75 per section
Prereq: 550.420
Sec. 01 – Meant for undergraduates
Sec. 02 – Meant for graduates 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.

Sec. 03 added 01/25/07

Lec.

Sec. 01

02

03

MTW 11

Th 11

F 11

Th 1

550.435 (Q,N)

BIOINFORMATICS & STATISTICAL GENETICS (3) Naiman Limit 50   Prereqs: 550.310, 550.311 or equivalent  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  Limit 40 Prereqs: 550.310 or 550.311, or equivalent This course will give an introduction to the data and methodologies of computer intrusion detection. The focus will be on statistical and machine learning approaches to detection of attacks on computers. Topics will include 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 JHUISI

Sec. 01

W 1-4

550.442 (E,Q)
(W)

INVESTMENT SCIENCE (4) Tzitzouris  Limit 60 per section  Prereqs:  One year of calculus, an introductory course in probability and statistics (such as 550.310, 550.311 or its equivalent), some familiarity with optimization is desirable but not necessary. 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 investment 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.

Lec.

Sec. 01

02

MW 5:30-6:45pm

Th 5

Th 10 12

550.444 (E,Q)

MODELING AND ANALYSIS OF SECURITIES AND FINANCIAL MARKETS (4) Audley   Limit 60 Prereqs: 110.302, 550.420
This course will develop the mathematical concepts and techniques for modeling cash instruments and their hybrids and derivatives.

Sec. 01

T 1-3
F 1

550.457 (E,Q)

TOPICS IN OPERATIONS RESEARCH APPLICATIONS TO SPORTS (3) Goldman  Limit 40 Sports provide interesting topics for a variety of mathematical analyses (optimization, statistical, etc.)  The course will discuss a number of these applications.

Sec. 01

MTW 4

550.472 (E,Q)

GRAPH THEORY (4) Scheinerman  Limit 40   Prereq: Linear Algebra 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

550.486 (E,Q)

ASYMPTOTIC METHODS (4) Torcaso   Limit 50  Prereqs: Calculus I & II and an introductory course in differential equations (550.291 or 550.303) Methods for obtaining approximate analytical solutions to ordinary differential equations and difference equations. Topics vary depending on the instructor, but the course is likely to cover local analysis, asymptotic approximation, expansion of integrals, Laplace's method, Watson's Lemma, perterbation theory, summation of series, multiple scale analysis. 

Lec.
Sec. 01

MTW 11
Th 11

550.500

UNDERGRADUATE RESEARCH  Staff  Reading, research, or project work for undergraduate students. Pre-arranged individually between students and faculty.

550.510

READINGS IN ACTUARIAL MATHEMATICS Fill Perm Req'd . Course added 01/26/07

550.600

DEPARTMENT SEMINAR Fill  Limit 50 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 Limit 45  Prereqs: 550.620, 110.405, or equivalents 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 PriebeLimit 45 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 Limit 40 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 2:30-3:45

550.662

OPTIMIZATION ALGORITHMS Han   Limit 45   Prereqs: 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

550.672

GRAPH THEORY Scheinerman  Limit 45   Prereq: Linear Algebra 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

F 10:30

550.681

NUMERICAL ANALYSIS Han  Limit 45 Prereqs: Multivariable calculus, 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, interpolation and approximation. Core topics to be covered: numerical linear algebra including eigenvalue and linear least-squares problems, iterative algorithms for nonlinear equations and leastsquares 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

550.700

MASTER’S RESEARCH
Reading, research, or project work for Master’s level students.  Arranged individually between students and faculty.

550.730

TOPICS IN STATISTICS Spall Limit 45 Prereq: Matrix Theory and graduate course in probability (should have prior exposure to maximum likelihood & Bayes’ Rules) Roundtable course covers maximum likelihood (ML) and Markov chain Monte Carlo (MCMC), including EM (expectation-maximization) and variants, Fisher information, standard MCMC and popular extensions, and Monte Carlo algorithms for ML.

Sec. 01

T 2-3:30

550.735

STATISTICAL PATTERN RECOGNITION Priebe Limit 45 This course will cover topics in classifier design and dimensionality reduction from a statistical perspective.

Sec. 01

TBA

550.800

DISSERTATION RESEARCH Staff Limit 20 per section
Sec. 01 - Eyink
Sec. 02 - Fill
Sec. 03 - Fishkind
Sec. 04 - Geman
Sec. 05 - Goldman
Sec. 06 - Han
Sec. 07 - Naiman
Sec. 08 - Priebe
Sec. 09 - Scheinerman
Sec. 10 - Wierman
Sec. 11 – Younes

Sec. 01

TBA

550.810

PROBABILITY & STATISTICS SEMINAR Staff  Limit 20

Sec. 01

TBA

550.865

OPTIMIZATION & DISCRETE MATH SEMINAR Staff  Limit 20

Sec. 01

TBA