APPLIED MATHEMATICS AND STATISTICS

550.111 (E,Q)

STATISTICAL ANALYSIS (4) Maiste Limit 45 35 per section   Prereq: Four years 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, 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. 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

  MTW 12

W 4

 Th 9

Th 10:30

 Th 12

Th 1

Th 2

W 2

550.171 (E,Q)

DISCRETE MATHEMATICS (4) Torcaso   Limit 35 per section   Prereq: Four years 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

03

MTW 11

Th 9

Th 12

Th 1

550.252 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: STOCHASTIC MODELS (4) Castello   Limit 40   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.  Emphasize on model development and case studies, using spreadsheets and other computer software.  The applications studied occur in variety of applications.

Lec.

Sec. 01

MTW 12

Th 12

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

MTW 9

  Th 12

Th 2

550.310 (E,Q)

PROBABILITY & STATISTICS FOR THE PHYSICAL SCIENCES AND ENGINEERING (4) Maiste   Limit 35 per section   Prereq: One year of Calculus; Recommended Coreq: 110.202
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

04

MTW 10

W 3

Th 10:30

Th 12

Th 1

550.311 (E,Q)

PROBABILITY AND STATISTICS FOR BIOLOGICAL SCIENCES AND ENGINEERING (4) Geman   Limit 35 per section    Prereq: One year of Calculus; Recommended  Coreq: 110.202    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

03

MTW 11

Th 1

Th 10:30

Th 12

550.361 (E,Q)

INTRODUCTION TO OPTIMIZATION (4) Castello   Limit 35 per section      Prereq: 550.291 or approved alternative, 110.108-109, computing experience
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

02

MTW 2

Th 2

Th 10

550.385 (E,Q)

SCIENTIFIC COMPUTING: LINEAR ALGEBRA (4) Fishkind    Limit 30     Prereq: Calculus III and 550.291 or approved alternative (ex. 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

MTW 1

W 4

550.391 (E,Q)

DYNAMICAL SYSTEMS (4) Eyink  Limit 25   Prereq: 110.202, 550.291 or 110.201, 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

MTW12

Th 12

550.400 (E,Q)

MATHEMATICAL MODELING AND CONSULTING (4) Torcaso   Limit 15 Prereq: Probability, statistics, and optimization at the 300-level or higher 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.

Sec. 01

MW 2-3:45

550.420 (E,Q)

INTRODUCTION TO PROBABILITY (4) Wierman    Limit 50 35 (Secs. 01 & 02) / 50 (Sec. 03)    Prereq: 110.108-109; Coreq: 110.202   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

MTW 1

Th 1

Th 2

Th 12

550.433 (E,Q)

MONTE CARLO SIMULATION AND RELIABILITY (3) Naiman   Limit 45  Prereq: 550.430; computing experience  Applications of numerical analysis to statistics. Linear least squares; random number generation; Monte Carlo Techniq ues; analysis of variance; time series computations; numerical integration. Emphasis on computational aspects relevant to practical statistical problems.

Sec. 01

MTW 9

550.436 (E,Q)

DATA MINING (4) Maiste   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

MTW 3

F 12 Th 1

550.440 (Q)

STOCHASTIC CALCULUS (3) Torcaso Limit 45   Prereq: 550.420   Stochastic processes recommended, but not required. Introduction to stochastic integration, stochastic differential equations, and the Ito calculus.  Emphasis will be on underlying ideas rather than rigorous development.  Stochastic processes, Brownian motion, conditional expectation, martingales, Ito and Stratonovich integr als and their calculus, stochastic differential equations, some applications to finance, stochastic flow systems, or other areas should be provided.

Sec. 01

MTW 1

550.463 (E,Q)

NETWORK MODELS IN OPERATIONS RESEARCH (4) Fishkind Limit 35   Prereq: 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, maximum volume flow, and minimum-cost flow problems. Emphasis on linear models and flows, with brief discussion of nonlinear models and network design.

Lec.

Sec.01

MTW 11

Th 11

550.471 (E,Q)

COMBINATORIAL ANALYSIS (4) Limit 30    Scheinerman     Prereq: One year of Calculus, Linear Algebra   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

MTW 11

Th 11

550.491 (E,Q)

APPLIED ANALYSIS FOR ENGINEERS AND SCIENTISTS (4) Eyink   Limit 45  Prereq: Calculus III and either 550.291 and 500.303 or 110.201 and 110.302  This course will cover techniques and applications of differential and integral analysis that are important for advanced work in engineering and science, including partial differential equations and transform methods.

Lec

Sec. 01.

MTW 10

Th 10

550.493 (E,Q)

MATHEMATICAL IMAGE ANALYSIS (3) Younes   Limit 45    Prereq: Calculus III (110.202 or equivalent) and Linear Algebra (110.201 or equivalent) Elementary Calculus (110.108-109) This course introduces a series of mathematical concepts for low level image processing and the numerical algorithms that are derived from them. These include linear and non-linear Smoothing and enhancement, PDE-based isotropic and anisotropic filters, variational energy-minimization methods, data analysis and decomposition methods allowing low-level image understanding: standard image transforms (Fourier, cosine, wavelets), techniques of principal and independent component analysis.

Sec. 01

MTW 3

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. 

Sec. 01

TBA

550.600

DEPARTMENT SEMINAR Fill     Limit 40   A variety of topics discussed by speakers from within and outside the university. Required of all resident department graduate students. 

Sec. 01

Th 3-5:30

550.620

PROBABILITY THEORY I Fill Limit 45 25    Prereq: 110.405 and 550.420 or equivalent    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

M 2:30-4:15,

W 2:30-3:20, F 2-2:50

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 1-2:15

F 1

550.635

TOPICS IN BIOINFORMATICS Geman Limit 20   Prerequisites: A course in Statistics is required; previous exposure to machine learning or pattern recognition is recommended. Course is recommended for prepared seniors through postdocs and faculty. A “readings” course organized around selected papers (research articles, tutorials, etc.) in bioinformatics and computational biology. The major objective is to prepare students to comfortably read the literature and to understand the nature of research in this field. The common theme is learning from data, for instance inferring phenotype from genotype, or modeling regulatory networks, based on gene or protein expression data. By and large, the students will present the papers. In addition, these expositions will be supplemented by lectures on various aspects of statistical learning, predictive inference and pattern recognition (e.g., class discovery and prediction, feature selection, p-values and permutation analyses, overfitting, the bias/variance dilemma and cross-validation).

Sec. 01

T 4:30-7pm

550.661

FOUNDATIONS OF OPTIMIZATION Han   Limit 40 25   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

MTW 10

F 10

550.664

MODELING, SIMULATION, AND MONTE CARLO Spall    Limit 20  Prereq: Basic Matrix algebra and a grad course in probability and statistics. Familiarity with some programming language.  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 comparisons using  simulations, Markov chain Monte Carlo (MCMC), and input selection using optimal experimental design.

Sec. 01

T 2-3:20

550.671

COMBINATORIAL ANALYSIS Scheinerman   Limit 25   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

MTW 11

F 11

550.692

MATRIX ANALYSIS AND LINEAR ALGEBRA Fishkind  Limit 45 25    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

MTW 9

F 9

550.700

MASTERS RESEARCH Course added 8/01/06

Sec. 01

TBA

550.750

TOPICS IN OPERATIONS RESEARCH Goldman   Limit 20   Applied Matching:    Mathematical models/analyses/solution algorithms for "matching markets" like auctions (buyers & sellers), labor markets (firms & workers), and college admissions.

Sec. 01

MTW 4

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 Naiman   Limit 10

Sec. 01

F 9-10:30

550.865

DISCRETE MATHEMATICS AND OPTIMIZATION RESEARCH SEMINAR Staff    Limit 10

Sec. 01

TBA