APPLIED MATHEMATICS & STATISTICS

550.103 (Q,S)

MATHEMATICS AND POLITICS (4) Scheinerman  Limit 60 Examining interesting problems from the world of politics including apportionment, resource allocation, voting, and conflict, this course is designed for humanities and social science students who enjoy solving logic puzzles.

Lec.

Sec. 01

MWF 10-10:50

Th 10:30-11:20

550.111 (E,Q)

STATISTICAL ANALYSIS I (4) TorcasoLimit 45 per section   Prereq: 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.  First semester of a general survey of statistical methodology.  Topics include descriptive statistics, probability models, random variables, expectation, sampling, and the central limit theorem, classical and robust estimation of location, confidence intervals, hypothesis testing, two-sample problems, introductory analysis of variance, and introductory nonparametric methods. Three lectures and a conference weekly. Some use of computing with the Minitab statistical package, but prior computing experience not required.

Lec.

Sec. 01

02

03

04

05

06

07

MWF 12-12:50

W 3-3:50

W 4:30-5:20

Th 9-9:50

Th 12-12:50

Th 10:30-11:20

Th 1:30-2:20

Th 3-3:50

550.112 (E,Q)

STATISTICAL ANALYSIS II (4) Lee Limit 35 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

05

06

07

MWF 1:30-2:20

W 3-3:50

W 4:30-5:20

Th 9-9:50

Th 10:30-11:20

Th 12-12:50

Th 1:30-2:20

Th 3-3:50

550.171 (Q)

DISCRETE MATHEMATICS (4) Godbole   Limit 35 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

03

MWF 10-10:50

Th 9-9:50

Th 12-12:50

Th 10:30-11:20

550.252 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: STOCHASTIC MODELS (4) Castello   Limit 40   This course is an introduction to management science and the quantitative approach to decision making.  Our focus will be on the formulation and analysis of stochastic models, where some problem data may be uncertain.  The 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.

Lec.

Sec. 01

MWF 1:30-2:20

Th 12-12:50

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Castello   Limit 35 per section   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

MWF 9-9:50

T 1:30-2:20

T 3-3:50

550.310 (E,Q)

PROBABILITY & STATISTICS FOR THE PHYSICAL SCIENCES AND ENGINEERING (4) Jedynak  Limit 35 per section Prereq: One year of calculus. Recommended corequisite: multivariable calculus. Students cannot receive credit for both 550.310 and 550.311 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.

Lec.

Sec. 01

02

03

MWF 11-11:50

T 9-9:50

T 3-3:50

T 4:30-5:20

550.311 (E,Q)

PROBABILITY AND STATISTICS FOR BIOLOGICAL SCIENCES AND ENGINEERING (4) Torcaso Limit 35 per section  Prereq: One year of calculus; Corequisite: 110.202 recommended. Students cannot receive credit for both 550.310 and 550.311 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.

Lec.

Sec. 01

02

MWF 10-10:50

T 9-9:50

T 3-3:50

550.361 (E,Q)

INTRODUCTION TO OPTIMIZATION (4) Castello   Limit 50 35   Prereq: One year of calculus, linear algebra, computing experience.  Appropriate for undergraduate and graduate students without the mathematical background required for 550.661.  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.  Sec. 02 canceled 4/14/08

Lec.

Sec. 01

02

MWF 12-12:50

Th 1:30-2:20

Th 3-3:50

550.385 (E,Q)

SCIENTIFIC COMPUTING: LINEAR ALGEBRA (4) Hur  Limit 30 Prereq: Calculus III, and 550.291 or approved alternative (e.g., 110.201) A first course on computational linear algebra and applications.  Topics include floating-point arithmetic, algorithms and convergence, Gaussian elimination for linear systems, matrix decompositions (LU, Cholesky, QR), iterative methods for systems (Jacobi, Gauss–Seidel), and approximation of eigenvalues (power method, QR-algorithm).  Theoretical topics such as vector spaces, inner products, norms, linear operators, matrix norms, eigenvalues, and canonical forms of matrices (Jordan, Schur) are reviewed 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

T 3-3:50

550.391 (E,Q)

DYNAMICAL SYSTEMS (4) Eyink  Limit 25   Prereq: Multivariable calculus, linear algebra, computing experience.  Mathematical concepts and methods for describing and analyzing linear and nonlinear systems that evolve over time. Topics include boundedness, stability of fixed points and attractors, feedback, optimality, Liapounov functions, bifurcation, chaos, and catastrophes. Examples drawn from population growth, economic behavior, physical and engineering systems. The main mathematical tools are linear algebra and basic differential equations.

Lec.

Sec. 01

MWF 10-10:50

Th 12-12:50

550.400 (Q)

MATHEMATICAL MODELING AND CONSULTING (4) Naiman Limit 30 Prereqs: Probability and statistics 310 or 311 or Probability 420. Formulation, analysis, interpretation, and evaluation of mathematical models. Synthesis of ideas, techniques, and models from mathematical sciences, science, and engineering. Case studies to illustrate basic features of the modeling process. Project-oriented practice and guidance in modeling techniques, research techniques, and written and oral communication of mathematical concepts. The focus of this version of the course is on applied statistics, that is, using statistics to solve real world problems. The R statistical package will be introduced. No previous knowledge of computing is necessary. Course added 4/23/08

Lec.

Sec. 01

MWF 11

Th 11

550.420 (Q)

INTRODUCTION TO PROBABILITY (4) Godbole Limit 50 per section Prereq: One year of calculus. Recommended corequisite: multivariable calculus.  Probability and its applications, at the calculus level.  Emphasis on techniques of application rather than on rigorous mathematical demonstration. Probability, combinatorial probability, random variables, distribution functions, important probability distributions, independence, conditional probability, moments, covariance and correlation, limit theorems. Students initiating graduate work in probability or statistics should enroll in 550.620.

Lec.

Sec. 01

02

03

04

MWF 1:30-2:20

Th 10:30-11:20

Th 12-12:50

Th 1:30-2:20

Th 3-3:50

550.427 (Q)

STOCHASTIC PROCESSES IN FINANCE (4) Leung 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 10-10:50

Th 1:30-2:20

550.433 (E,Q)

MONTE CARLO SIMULATION AND RELIABILITY (4) Lee NaimanLimit 45 Prereq: 550.430, computing experience Applications of numerical analysis to statistics. Linear least squares; random number generation; Monte Carlo
techniques; analysis of variance; time series computations; numerical integration. Emphasis on computational aspects relevant to practical statistical problems.

Lec.

Sec. 01

MWF 9-9:50

Th 9-9:50

550.436 (E,Q)

DATA MINING (4) Jedynak Limit 40     Prereq: 550.310 or equivalent. Recommended Prereq: 550.413. Data mining is a relatively new term used in the academic and business world, often associated with the development and quantitative analysis of very large databases. Its definition covers a wide spectrum of analytic and information technology topics, such as machine learning, artificial intelligence, statistical modeling, and efficient database development. This course will review these broad topics, and cover specific analytic and modeling techniques such as advanced data visualization, decision trees, neural networks, nearest neighbor, clustering, logistic regression, and association rules. Although some of the mathematics underlying these techniques will be discussed, our focus will be on the application of the techniques to real data and the interpretation of results. Because use of the computer is extremely important when “mining” large amounts of data, we will make substantial use of data mining software tools to learn the techniques and analyze datasets.

Lec.

Sec. 01

MW 1:30-2:45

Th 10:30-11:20

550.437 (E,Q)

STATISTICAL LEARNING WITH APPLICATIONS (3) Geman   Limit 35   Prereqs: 550.310 or 550.311 as well as some additional exposure to probability and statistics, e.g., 550.420 and/or 550.430 Statistical modeling and inference, inductive learning and information theory together provide a cohesive framework for machine perception, which amounts to building a data-description machine converting physical measurements (images, molecular counts, etc.) to interpretations or descriptions. Recurring themes include quantifying uncertainty, estimating generalization error, Occam’s razor, the bias/variance dilemma and small-sample learning. Various problems in computational vision and computational biology will be analyzed in this context, including visual tracking, object recognition, cancer diagnosis, neural decoding and learning molecular networks.

Sec. 01

MW 12-1:15

550.442 (E,Q)

INVESTMENT SCIENCE (4) TzitzourisLimit 50   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

MW 6-7:15

Th 3-3:50

550.444 (E,Q)

MODELING AND ANALYSIS OF SECURITIES AND FINANCIAL MARKETS (4) Audley   Limit 30 Prereqs: 110.302 and 550.420 This course will develop the mathematical concepts and techniques for modeling cash instruments and their hybrids and derivatives.

Lec.

Sec. 01

MW 3-4:15

F 3-3:50

550.446 (E,Q)

RISK MANAGEMENT ANALYSIS AND HEDGING (4) Audley   Limit 35   Prereq: 550.444 This course applies advanced mathematical techniques to the measurement, analysis, and management of risk.  The focus is on financial risk.  Sources of risk for financial instruments (e.g., market risk, interest rate risk, credit risk) are analyzed; models for these risk factors are studied and the limitation, shortcomings and compensatory techniques are addressed.

Lec.

Sec. 01

MW 12:1:15

F 1:30-2:20

550.457 (E,Q)

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

Sec. 01

MW 3-4:15

550.463 (E,Q)

NETWORK MODELS IN OPERATIONS RESEARCH (4) FishkindLimit 35   Prereqs: 550.361 or 550.661  In-depth mathematical study of network flow models in operations research, with emphasis on combinatorial approaches for solving them. Introduction to techniques for constructing efficient algorithms, and to some related data structures, used in solving shortest path, maximumvolume flow, and minimum-cost flow problems. Emphasis on linear models and flows, with brief discussion of nonlinear models and network design.

Lec.

Sec. 01

MW 12-1:15

F 1:30-2:20

550.471 (Q)

COMBINATORIAL ANALYSIS (4) Fishkind    Limit 30   Prereq: Linear Algebra, one year of Calculus.  Counting techniques: generating functions, recurrence relations, Polya’s theorem. Combinatorial designs: Latin squares, finite geometries, balanced incomplete block designs. Emphasis on problem solving.

Lec.

Sec. 01

MWF 11-11:50

T 3-3:50

550.493 (E,Q)

MATHEMATICAL IMAGE ANALYSIS (3) Younes  Limit 35  Prereq: Calculus III (110.202) and Linear Algebra (110.201 or equivalent)     The course introduces a few of the basic concepts of functional analysis and of the calculus of variations, and describes how they apply to low level image processing (denoising, deblurring, contour extraction, image transforms). We will define Hilbert and Banach spaces, orthogonal bases, the notion of duality, and discuss the choice of an appropriate space for images. This will induce linear and nonlinear image smoothing methods, and the Chan-Vese’s segmentation algorithm. We will also discuss the extraction of local information from images, including the SIFT and other feature extractors, windowed Fourier and continuous wavelet transforms, and an introduction to orthogonal wavelet transforms.

Sec. 01

MW 4:30-5:45

550.500

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.

550.501

SENIOR THESIS
Preparation of a substantial thesis based upon independent student research, under the pre-arranged supervision of at least one faculty member in Applied Mathematics and Statistics. 

550.551

INTERNSHIP

550.600

DEPARTMENT SEMINAR Staff       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 3-5:20

550.620

PROBABILITY THEORY I Fill
Limit 45 Prereq: 110.405 and 550.420 or equivalents    Probability as a mathematical discipline, including introductory measure theory. Axiomatic probability, combinatorial probability, random variables, conditional probability, independence, distribution theory, expectation, Lebesgue-Stieltjes integration, variance and moments, probability inequalities, characteristic functions, conditional expectation.

Lec.

Sec. 01

MW 1:30-2:45

F 1:30-2:20

550.630

STATISTICAL THEORY Priebe Limit 25   Prereq: 550.420 or 550.620 The fundamentals of mathematical statistics. Distribution theory for statistics of normal samples; exponential statistical models; sufficiency principle; least squares, maximum likelihood, and UMVU estimation; hypothesis testing, the Neyman-Pearson lemma, likelihood ratio procedures; the general linear model, the Gauss-Markov theorem, multiple comparisons; contingency tables, chi-square methods, goodness-of-fit; nonparametric and robust methods; decision theory, Bayes and minimax procedures.

Lec.

Sec. 01

MW 3-4:15

F 3-3:50

550.635

TOPICS IN BIOINFORMATICS Geman
Limit 20   Prereq: A course in statistics is required; previous exposure to machine learning or pattern recognition is recommended     A "readings" course organized around research articles in the recent bioinformatics and computational biology literatures. In this term, the choice of papers will favor work on inferring phenotype from genotype, and modeling signaling networks, based on gene microarrays bearing the expression levels of thousands of transcripts, and on properties of proteins, such as predicting active sites and detecting harmful mutations. One major objective is to prepare students to comfortably read articles which involve extensive mathematical and statistical modeling as well as techniques from pattern recognition and machine learning. Most papers will be presented by the students.  In addition, student expositions will be preceded by “tutorials” by the instructor on various aspects of statistical learning, modeling and prediction, such as properly estimating generalization error in cancer classification and avoiding over-fitting in learning networks of molecular interactions.

Sec. 01

MW 4:30-5:45pm 3-4:15

550.661

FOUNDATIONS OF OPTIMIZATION Han   Limit 40   Prereq: Multivariable Calculus, Linear Algebra; Coreq: 110.405   Study of the fundamental theory underlying linear and nonlinear optimization. Unconstrained optimization, constrained optimization, saddlepoint conditions, Kuhn-Tucker conditions, linear programming, the simplex algorithm, post-optimality, duality, convexity, quadratic programming.

Lec.

Sec. 01

MWF 11-11:50

T 9-9:50

550.664

MODELING, SIMULATION AND MONTE CARLO Spall   Limit 20   Prereq: Basic matrix algebra and a grad course in probability and statistics. Concepts and statistical techniques critical to constructing and analyzing effective simulations; emphasis on generic principles rather than specific applications. Topics include model building (bias-variance tradeoff, model selection, Fisher information), benefits and drawbacks of simulation modeling, random number generation, simulation-based optimization, discrete multiple comparisions using simulations, Markov change Monte Carlo (MCMC), and input selection using optimal experimental design. Course added 4/14/08

Sec. 01

T 1:30-3:20

550.671

COMBINATORIAL ANALYSIS Fishkind   Limit 30   Prereq: One year of Calculus and Linear Algebra  An introduction to combinatorial analysis at the graduate level. Meets concurrently with 550.471 (see 550.471 for course description)

Lec.

Sec. 01

MWF 11-11:50

T 4:30-5:20

550.692

MATRIX ANALYSIS AND LINEAR ALGEBRA   Fishkind   Limit 45 Prereq: 110.405, Linear Algebra, multi-variable calculus A second course in linear algebra with emphasis on topics useful in analysis, economics, statistics, control theory, and numerical analysis. Review of linear algebra, decomposition and factorization theorems, positive definite matrices, norms and convergence, eigenvalue location theorems, variational methods, positive and nonnegative matrices, generalized inverses.

Lec.

Sec. 01

MWF 9-9:50

T 10:30-11:20

550.700

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

550.747

TOPICS IN FINANCIAL MATH Audley
Course added 6/23/08

MTWThF 8-8:50

550.800

DISSERTATION RESEARCH Staff  Reading, research, or project work for advanced graduate students. Arranged individually between students and faculty.
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 – Scheirerman
Sec. 10 – Wierman
Sec. 11 - Younes

550.810

PROBABILITY AND STATISTICS SEMINAR  Staff   Limit 10

Sec. 01

TBA

550.865

DISCRETE MATHEMATICS AND OPTIMIZATION RESEARCH SEMINAR  Staff    Limit 10

Sec. 01

TBA