APPLIED MATHEMATICS AND STATISTICS

550.111 (E,Q)

STATISTICAL ANALYSIS I (4) Fishkind   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

MWF 1:30-2:20
W 3-3:50
Th 9-9:50
Th 10:30-11:20
Th 12-12:50
Th 1:30-2:20

550.112 (E,Q)

STATISTICAL ANALYSIS II(4) Torcaso  Limit 50 per section  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

MWF 12-12:50
Th 9-9:50
Th 10:30-11:20
Th 12-12:50
Th 1:30-2:20

550.171 (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.

Lec.

Sec. 01

02

MWF 10-10:50

Th 1:30-2:20

Th 3-3:50

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

MWF 1:30-2:20

Th 1:30-2:20

Th 3-3:50

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

MWF 9-9:50

T 1:30-2:20

T 3-3:50

550.310 (E,Q)

PROBABILITY AND STATISTICS FOR THE PHYSICAL AND INFORMATION SCIENCES AND ENGINEERING (4) Jedynak  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

MWF 11-11:50
T 1:30-2:20
T 3-3:50
T 4:30-5:20

550.311 (E,Q)

PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING (4) Fishkind  Limit 50 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.  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

MWF 10-10:50

T  1:30-2:20

T 3-3:50

550.362 (E,Q)

INTRODUCTION TO OPTIMIZATION II (4) Castello Limit 50    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

MWF 12-12:50

Th 3-3:50

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

MWF 9-9:50

Th 1:30-2:20

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

MW 4:30-5:45pm

F 1:30-2:20

550.426 (E,Q)

INTRODUCTION TO STOCHASTIC PROCESSES (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 4:30-5:45pm

F 1:30-2:20

550.427 (Q)

STOCHASTIC PROCESSES IN FINANCE (4) Wierman   Limit 50   Prereq: 550.420     A development of stochastic processes with substantial emphasis on the processes, concepts, and methods useful in mathematical finance.   Relevant concepts from probability theory, particularly conditional probability and conditional expection, will be briefly reviewed.  Important concepts in stochastic processes will be introduced in the simpler setting of discrete-time processes, including random walks, Markov chains, and discrete-time martingales, then used to motivate more advanced material.  Most of the course will concentrate on continuous-time stochastic processes, particularly martingales, Brownian motion, diffusions, and basic tools of stochastic calculus. Examples will focus on applications in finance, economics, business, and actuarial science.  

Lec.

Sec. 01

MWF 11-11:50

Th 1:30-2:20

550.430 (E,Q)

INTRODUCTION TO STATISTICS (4) Jedynak    Limit 50 per section
Prereq: 550.420 or approved alternative
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.

Lec.

Sec. 01

02

03

MWF 1:30-2:20

Th 1:30-2:20

Th 3-3:50

Th 4:30-5:20

550.438 (E,Q)
              

STATISTICAL METHODS IN COMPUTER INTRUSION DETECTION (3) Marchette   Limit 25 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. Course added 01/15/08

Sec. 01

T 9:30-11:50

550.439 (E,Q)
              

TIME SERIES ANALYSIS (3) Torcaso  Limit 50
Prereqs: 550.310, 550.311, or equivalent calculus-based probability course, 110.201 or 550.291 and mathematical maturity.  Time series analysis from the frequency and time domain approaches. Descriptive techniques; regression analysis; trends, smoothing, prediction; linear systems; serial correlation; stationary processes; spectral analysis. Sec. 01 canceled 11/06/07

Lec.

Sec. 01

MW 1:30-2:45

F 1:30-2:20

550.442 (E,Q)
           

INVESTMENT SCIENCE (4) Naiman  Limit 60  
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

MWF 9-9:50

Th 3-3:50

550.444 (E,Q)

MODELING AND ANALYSIS OF SECURITIES AND FINANCIAL MARKETS I (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.

Lec.

Sec. 01

TTh 9-10:15

T 3-3:50

550.448 (E,Q)

FINANCIAL ENGINEERING (4) Audley   Limit 50   Prereqs: 550.442 or 550.444 or Perm. Req’d.
This course focuses on structured securities and the structuring of aggregates of financial instruments into engineered solutions of problems in capital finance. Topics include the fundamentals of creating asset-backed and structured securities – including mortgage-backed securities (MBS), stripped securities, collateralized mortgage obligations (CMOs), and other asset-backed collateralized debt obligations (CDOs) – structuring and allocating cash-flows as well as enhancing credit; equity hybrids and convertible instruments; asset swaps, credit derivatives and total return swaps; assessment of structure-risk interest rate-risk and credit-risk as well as strategies for hedging these exposures; managing portfolios of structured securities; and relative value analysis (including OAS and scenario analysis).

Lec.

Sec. 01

TTh 1:30-2:45

F 1:30-2:20

550.453 (E,Q)

MATHEMATICAL GAME THEORY (4) Goldman  Limit 40 Prereqs: multivariable calculus, probability, linear algebra. Mathematical analysis of cooperative and noncooperative games. Theory and solution methods for matrix games (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

MW 3-4:15

F 1:30-2:20

550.472 (Q)

GRAPH THEORY (4) Fishkind 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

MWF 9-9:50

Th 3-3:50

550.506

SPRING INDEPENDENT STUDY Staff
Course added 11/30/07

Sec. 01

TBA

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 3-4:50

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 3-4:15

F 3-3:50

550.631

STATISTICAL THEORY II Priebe Limit 45   Prereq: 550.630   Advanced concepts and tools fundamental to research in mathematical statistics and statistical inference: asymptotic theory; optimality; various mathematical foundations.

Lec.

Sec. 01

TTh 9-10:15

F 10-10:50

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 3-4:15

550.643

GRAPHICAL MODELS Younes  Limit 50 Prereq:  550.420 or equivalent, 550.430 or equivalent This course describes how models based on networks encoding the conditional dependency structure between random variables, also called graphical models, can be used to design multivariate probability distributions. A special focus will be made on important particular cases, like Markov Chains, Bayesian networks or Markov Random Fields. We will also discuss parametric estimation and inference problems, and issues arising when some of the variables cannot be observed.

Sec. 01

MW 4:30-5:45pm

550.662

OPTIMIZATION ALGORITHMS Han   Limit 45  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

MWF 11-11:50

F 1:30-2:20

550.663

STOCHASTIC SEARCH AND OPTIMIZATION Spall   Limit 30   Prerequisites: 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 1:30-3:20

550.672

GRAPH THEORY Fishkind Limit 45   Prereq: Linear Algebra An introduction to graph theory at the graduate level.  See 550.472 for course description.   Meets with 550.472

Lec.

Sec. 01

MWF 9-9:50

F 10-10:50

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

MWF 12-12:50

F 3-3:50

550.694

TURBULENCE THEORY II  Eyink Limit 25 Prereq: 550.693 This course will continue the theoretical investigation of fluid turbulence, directly following on from 550.693. Topics to be considered are turbulent vortex dynamics, Lagrangian dynamics, and special topics such as wall-bounded turbulence, free shear flows, two-dimensional and quasigeostrophic turbulence, MHD turbulence, etc.
Cross-listed with Physics & Astronomy Course added 12/21/07

Sec. 01

MW 12-1:15

550.700

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

550.735

TOPICS IN STATISTICAL PATTERN RECOGNITION Priebe  Limit 25   Prereq: 550.630 or equivalent The Dissimilarity Representation for Pattern Recognition.  This course will investigate aspects of statistical inference and statistical pattern recognition associated with observing only dissimilarites between entities rather than observing feature vectors associated with the individual entities themselves.

Sec. 01

T 3-5:50pm

550.790

TOPICS IN APPLIED MATHEMATICS Abrams   Limit 25   Prereq: Linear Algebra
A survey of theory and techniques from the cutting-edge field Computational Topology, which emphasizes discrete versions of ideas from algebraic topology and differential topology, including relevant computational algorithms.

Sec. 01

TTh 1:30-2:45

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