APPLIED MATHEMATICS AND STATISTICS

550.111 (E,Q)

STATISTICAL ANALYSIS (4) Maiste 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) Fishkind   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

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Castello   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

550.303 (E,Q)

DIFFERENTIAL EQUATIONS (4) Castello   Course added 06/30/05

Sec.01

MTW 11, Th 2

550.310 (E,Q)

PROBABILITY & STATISTICS FOR THE PHYSICAL SCIENCES AND ENGINEERING (4) Maiste  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  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. Students cannot receive credit for both 550.310 and 550.311.

Sec. 03 added 09/13/05

Lec.

Sec. 01

02

03

MTW 11

Th 1

Th 10:30

Th 12

550.331 (E,Q)

INTRODUCTION TO MATHEMATICAL FINANCE (4) Naiman 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 1

Th 11

550.361 (E,Q)

INTRODUCTION TO OPTIMIZATION (4) Goldman   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.

Sec. 02 added 09/15/05

Lec.

Sec. 01

02

MTW 2

Th 2

Th 10

550.385 (E,Q)

SCIENTIFIC COMPUTING: LINEAR ALGEBRA (4) Fishkind   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 arithmetics, algorithms and convergence, Gaussian elimination, matrix decompositions, iterative methods and approximating eigenvalues.  Theoretical topics are reviewed as needed. Matlab is used to solve all numerical exercises; no previous experience with computer programming is required.

Lec.

Sec. 01

         M 1-2:20, TW 1 MTW 1

W 4 Th  1

550.391 (E,Q)

DYNAMICAL SYSTEMS (4) Castello  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)

              (W)

MATHEMATICAL MODELING AND CONSULTING (4) Torcaso 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    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 demonstrationProbability, 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

MTW 1

Th 1

Th 2

Th 1

Th 12

550.436 (E,Q)

DATA MINING (4) Maiste 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

Th 1

550.437 (E,Q)

INFORMATION, STATISTICS AND PERCEPTION (3) Geman Prereq: 550.310 or 550.311, as well as additional exposure to probability and statistics, eg. 550.420 and/or 550.430; Statistical inference, inductive learning and information theory together provide a cohesive framework for machine perception.  Various problems in image analysis and computational biology will be analyzed in this context in both theory and practice (working algorithms.)  Examples include visual tracking, object recognition, texture modeling, neural decoding and gene expression.

Sec. 01

MTW 2

550.439 (E,Q)

TIME SERIES ANALYSIS (3) Torcaso  Prereq: 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

MTW 10

550.471 (E,Q)

COMBINATORIAL ANALYSIS (4) 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

550.480 (E,Q)

SHAPE AND GEOMETRY (3) Younes     Prereq: Calculus III and Linear Algebra   This class will review the basic definitions and properties of curves and surfaces, and their relation to the description and characterization of 2D and 3D shapes. Intrinsic local and semi-local descriptors, like the curvature of 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 11

550.491 (E,Q)

APPLIED ANALYSIS FOR ENGINEERS AND SCIENTISTS (4) Staff   Prereq: Calculus I, II, and III and either 550.291 and 550.303, 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. Course canceled 08/10/05

Lec.

Sec. 01

MTW 10

Th 10

550.500

UNDERGRADUATE RESEARCH
Course added 09/22/05

Sec. 01

TBA

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

550.503

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.

550.600

DEPARTMENT SEMINAR Fill Wierman
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

550.601

APPLIED MATHEMATICS AND STATISTICS ENTERING GRADUATE STUDENT WORKSHOP  Torcaso
This course is ONLY for new doctoral students in the Department of Applied Mathematics and Statistics to cover fundamental topics necessary for their graduate education

Sec. 01

T 3:30-5pm W 4

550.620

PROBABILITY THEORY I Fill
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.

Sec. 01

M 2:30-4:15,

W 2:30,

 F 2

550.630

STATISTICAL THEORY Priebe 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   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

550.671

COMBINATORIAL ANALYSIS Scheinerman     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 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

550.720

TOPICS IN PROBABILITY Fill  Advanced topics chosen according to the interests of the instructor and graduate students. Possible topics include Markov chains (see 550.723 in the catalog) and the probabilistic analysis of algorithms. Course canceled 04/06/05

Sec. 01

TBA

550.723

MARKOV CHAINS Fill      Recent advances in computer science, physics, and statistics have been made possible by corresponding sharply quantitative developments in the mathematical theory of Markov chains. Possible topics: rates of convergence to stationarity, eigenvalue techniques, Markov chain Monte Carlo, perfect simulation, self-organizing data structures, approximate counting and other applications to computer science, reversible chains, interacting particle systems. Course added 04/06/05

Sec. 01

M 4:30-5:20pm,
W 3:30-5:15pm

550.790

TOPICS IN APPLIED MATH Spall      An introduction to two related areas – neural networks (NNs) and systems based on feedback.  We consider NNs in modern control systems and stochastic (noise) effects in feeback systems.

Sec. 01

T 2-3:20

550.800

DISSERTATION RESEARCH Staff          Reading, research, or project work for advanced graduate students. Arranged individually between students and faculty.

550.810

PROBABILITY AND STATISTICS RESEARCH SEMINAR Staff

Sec. 01

TBA

550.865

DISCRETE MATHEMATICS AND OPTIMIZATION RESEARCH SEMINAR Goldman

Sec. 01

ThF 12