550.103 (Q, S)

MATHEMATICS AND POLITICS (4) Scheinerman  Limit 60   Limit 30 - Secs. 02-03 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. Secs. 02 & 03 added 9/11/07

Lec.

Sec. 01

02

03

MTW 10

Th 10

Th 11

Th 12

 550.111 (E,Q)

STATISTICAL ANALYSIS (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

MTW 12
W 4
 Th 9
Th 10:30
 Th 12
Th 1
Th 2
W 2

550.171 (Q)

DISCRETE MATHEMATICS (4) Abrams   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

MTW 11
Th 9
Th 12
Th 1

550.252 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING: STOCHASTIC MODELS (4) Castello   Limit 40  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 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

MTW 12
Th 12

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Torcaso   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) 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
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) Fishkind   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
03

MTW 11
Th 1
Th 10:30
Th 12

550.331 (E,Q)

INTRODUCTION TO MATHEMATICAL FINANCE (4) Naiman   Limit 50   Prereq: Calculus I, II and III.  The principal aim of this course is to provide the mathematical ideas leading up to the now famous Black-Scholes formula for options pricing. Topics to be covered will include: basic probability, normal random variables, Brownian motion, interest rates, the arbitrage theorem, pricing of various types of options.

Lec.

Sec. 01

MTW 9

Th 9

550.361 (E,Q)

INTRODUCTION TO OPTIMIZATION (4) Castello   Limit 35 per section     
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. 

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 (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

MTW 1
W 4

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

MTW 10 12
Th 12

550.400 (E,Q)

MATHEMATICAL MODELING AND CONSULTING (4) Castello 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. 

Lec.
Sec. 01

MTW10
Th 10

550.420 (Q)

INTRODUCTION TO PROBABILITY (4) Wierman 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.
Sec. 04 canceled 3/21/07

Lec.
Sec. 01
02
03
04
         

MTW 1
Th 1
Th 2
Th 12
Th 12

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

MTW 3
F 12

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 integrals and their calculus, stochastic differential equations, some applications to finance, stochastic flow systems, or other areas should be provided.

Sec. 01

MTW 1

550.445 (E,Q)

MODELING AND ANALYSIS OF SECURITIES AND FINANCIAL MARKETS II (4) Audley  Limit 60   Advances in corporate finance, investment practice and the capital  markets have been driven by the development of a mathematically rigorous theory for financial instruments and the markets in which they trade.  This course builds on the concepts, techniques, instruments and markets introduced in 550.444.  In addition to new topics in credit enhancement and structured securities, the focus is expanded to include applications in portfolio theory and risk management, and covers some numerical and computational approaches.

Sec. 01

T 1-3
F 1

550.457 (E,Q)

TOPICS IN OPERATIONS RESEARCH: APPLICATIONS TO TRANSPORTATION (3) Goldman    Limit 40   Prereq: Linear programming, general mathematical maturity
The course will examine some of the challenging operational and planning problems presented for modeling/analysis by air transportation: flight scheduling/routing, personnel assignment, revenue management, and effective response to exceptional situations (e.g., weather).

Sec. 01

MTW 4

550.471 (Q)

COMBINATORIAL ANALYSIS (4) Abrams 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

MTW 2
Th 2

550.480 (E,Q)

SHAPE AND DIFFERENTIAL GEOMETRY (3) Younes  Limit 40  Prereq: Linear Algebra and Calculus III   The purpose of this class is to provide an elementary knowledge of the differential geometry of curves and surfaces, and to place this in relation with the description and characterization of 2D and 3D shapes. Intrinsic local and semi-local descriptors, like the curvature or the second fundamental form will be introduced, with an emphasis on the invariance of these features with respect to rotations, translations, etc. Extension of this point of view to other class of linear transformations will be given, as well as other types of shape descriptors, like moments or medial axes.

Sec. 01

MTW 12

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

UNDERGRADUATE INTERNSHIP
Added 10/05/07

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 3-5:30

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

M 2:30-4:15,
W 2:30-3:20,

F 2

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

550.661

FOUNDATIONS OF OPTIMIZATION Han   Limit 40   Prereq: 110.202 or 110.211 and 110.201 or 110.212 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

550.671

COMBINATORIAL ANALYSIS Abrams  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

MTW 2
F 2

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

MTW 9
F 9

Sec. 01

M 11, T 11-12:30

550.700

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

550.740

TOPICS IN FINANCIAL MATHEMATICS    Audley Limit: 25  Prereq: 550.442 or 550.444 and courses in Probability, Statistics, and Optimization at the 400-level or above. Advanced topics chosen according to the interests of the instructor and graduate students. The couse will focus on recent research articles in the financial mathematics literature. Course added 08/13/07

MW 11-12:30

550.790

TOPICS IN APPLIED MATHEMATICS: NEURAL NETWORKS AND FEEDBACK CONTROL SYSTEMS Spall  Limit 25  Prereq: Matrix theory, differential equations, and a graduate course in probability and statistics   Course is introduction to two related areas: neural networks (NNs) and feedback systems.  Course considers important theory and applications for NNs and considers modern control systems, especially with stochastic effects.

Sec. 01

T 2-3:30

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  Han Staff    Limit 10

Sec. 01

T 11
Th 9:15-10:30
F 1-2:30