550.100 (E,Q)

INTRODUCTION TO APPLIED MATHEMATICS AND STATISTICS (1) Naiman  Prereq: One semester of Calculus   A seminar-style series of lectures and assignments to acquaint the student with a range of intellectual and professional activities performed by applied mathematicians and statisticians.  Department faculty and outside speakers present problems arising in applied mathematics and statistics.

Sec. 01

Th 2

550.111 (E,Q)

STATISTICAL ANALYSIS I (4) Fishkind   Prereq: Four years of 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, introductory nonparametric methods. Three lectures and a conference weekly. Some use of computer terminals and 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

MTW 1

W 2

Th 9

Th 10:30

Th 12

Th 1

550.112 (E,Q)

STATISTICAL ANALYSIS II (4) Maiste   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

MTW 12

Th 9

Th 10:30

Th 12

Th 1

550.122 (Q)

CHANCE AND RISK (3) Wierman Students will develop an appreciation and understanding of probability, randomness, chance, and risk.  Applications, controversies, and paradoxes involving risk in business and economics, health and medicine, law, politics, sports, and gambling will illustrate probabilistic concepts. Not open to students who have taken 2 semesters of Calculus

Sec. 01

MTW 10

550.171 (E,Q)

DISCRETE MATHEMATICS (4) Torcaso   Prereq: Four years of 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

MTW 10

Th 10:30

Th 2

550.251 (E,Q)

MATHEMATICAL MODELS FOR DECISION MAKING (4) Torcaso Prereq: One semester of Calculus.As society's enterprises and technologies grow more and more complex, their operation and planning rely increasingly on mathematics-based analyses. This course is an introduction to management science and the quantitative approach to decision making. Emphasis on model development and case studies, using spreadsheets or other computer software, applied to a variety of problems in manufacturing, transportation, finance, and general management.

Lec.

Sec. 01

           02

MTW 12

Th 12

Th 1

550.291 (E,Q)

LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS (4) Castello Torcaso  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 9

Th 10

550.303 (E,Q)

DIFFERENTIAL EQUATIONS (4) Torcaso  Prereq: Calculus II The aim of this course is to present the formulation, solution, and qualitative understanding of differential equations of various types that are used to model real world phenomena. Topics include first order, second order and higher order differential equations, series solutions, Laplace transforms, systems of equations, numerical methods, and nonlinear equations. Course added 12/02/04

Sec.02 added 02/03/05

Lec.

Sec. 01

02

MTW 9

Th 9

F 9

550.310 (E,Q)

PROBABILITY AND STATISTICS FOR THE PHYSICAL AND INFORMATION SCIENCES AND ENGINEERING (4) Jedynak Prereq: One year of Calculus  Coreq: Multivariable Calculus Recommended:  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

MTW 11

Th 10:30

Th 12

W 2

550.311 (E,Q)

PROBABILITY AND STATISTICS FOR THE BIOLOGICAL SCIENCES AND ENGINEERING (4) Younes   Prereq: One year of Calculus;  Coreq: 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. 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.

Lec.

Sec. 01

02

MTW 10

Th 10

Th 3

550.362 (E,Q)

INTRODUCTION TO OPTIMIZATION II (4)  Goldman Prereq:  550.361, multivariable calculus An introductory survey of optimization methods, supporting mathematical theory and concepts, and application to problems of planning, design, pre-diction, estimation, and control in engineering, management, and science. Study of varied optimization techniques including linear programming, network-problem methods, dynamic program-ming, integer programming, and non-linear programming. Appropriate for undergraduate and graduate students without the math-ematical background required for 550.661.

Course canceled 02/03/05

Lec.

Sec. 01

MTW 2

Th 2

550.371 (E,Q)

CRYPTOLOGY & CODING (4) Fishkind   Prereq: 550.171 (110.204 with permission of instructor), Linear Algebra, computing experience
A first course in the mathematical theory of secure and reliable electronic communication. Cryptology is the study of secure communication: How can we ensure the privacy of messages? Coding theory studies how to make communication reliable: How can messages be sent over noisy lines? Topics include finite field arithmetic, error-detecting and error-correcting codes, data compressions, ciphers, one-time pads, the Enigma machine, one-way functions, discrete logarithm, primality testing, secret key exchange, public key cryptosystems, digital signatures, and key escrow.
Co-listed as 650.471 (reopened: 02/14/05)

Sec. 02 added 02/14/05

Lec.

Sec. 01

Sec. 02

MTW 9

Th 9

Th 1

550.386 (E,Q)

SCIENTIFIC COMPUTING: DIFFERENTIAL EQUATIONS (4) Eyink  Prereq:  Calculus III & 550.291 or approved alternative (ex. 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, multi-step, 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

MTW 1

Th 1

550.413 (E,Q)

APPLIED STATISTICS AND DATA ANALYSIS (4) Maiste Prereq: 550.112 or Perm Req’d
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

MTW 3

Th 2

550.426 (E,Q)

STOCHASTIC PROCESSES I (4) Fill  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 4-5:15pm

Th 1

550.430 (E,Q)

INTRODUCTION TO STATISTICS (4) Naiman    Prereq: 550.420 Section 01 is for Undergraduates; Section 02 is for Graduates Students 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

MTW 11

   Th 11

F 11

550.435 (Q,N)

BIOINFORMATICS & STATISTICAL GENETICS (3)  Maiste  Prereq: one year of calculus Biological research has evolved to the point where complex quantitative tools are playing an ever increasing role. The aim of this course is to survey various computational and statistical methodologies that have been put into play in the analysis of biological data to better understand biological phenomena. A large spectrum of biological applications used to motivate the choice of topics. Probabilistic methods, as well as algorithmic ideas related to the assembly, alignment, and matching of DNA sequences, will be developed, and statistical inference methods for making genotype to phenotype connections will be presented.

Sec. 01

MTW 9

550.438 (E,Q)

STATISTICAL METHODS FOR COMPUTER IONTRUSION DETECTION (3) Marchette Prereq: 550.310, or 550.311 or equiv.
Cross-listed with Information Security

Sec. 01

W 1-4

550.442 (E,Q)

               (W)

INVESTMENT SCIENCE (4) Tzitzouris      Prereq: One year of Calculus, 550.310, or 550.311   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 invest-ment 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. Some familiarity with optimization is desirable but not necessary.

Lec.


Sec. 01

02

MW 5:30-6:45pm

Th 2

Th 12

550.472 (E,Q)

GRAPH THEORY (4) Fishkind Prereq: 110.201, 550.291, 550.171 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

MTW 10

Th 10:30

550.502

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.

Sec. 01

550.510

READINGS IN ACTUARIAL MATHEMATICS Fill Course added 02/23/05

Sec. 01

TBA

550.600

DEPARTMENT SEMINAR 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

550.621

PROBABILITY THEORY II Fill Prereq: 550.620, 110.605   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 1:30-2:45

F 1

550.631

STATISTICAL INFERENCE Younes Prereq: 550.630   Advanced concepts and tools fundamental to research in mathematical statistics and statistical inference: asymptotic theory;optimality; various mathematical foundations.

Sec. 01

MW 2:45-4
3-4:15

550.662

OPTIMIZATION ALGORITHMS Han   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

MTW 11

F 11

550.672

GRAPH THEORY Fishkind  Prereq: 550.171 and Linear Algebra    An introduction to graph theory at the graduate level. Meets concurrently with 550.472. See 550.472 for course description.

Lec.

Sec. 01

MTW 10

Th 10:30-11:30

550.681

NUMERICAL ANALYSIS Han Prereq: Multivariable Calculus and 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, inter-polation and approximation. Core topics to be covered: numerical linear algebra including eigenvalue and linear least-squares problems, iterative algorithms for nonlinear equations and least squares 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

MTW 12

F 12

550.790

TOPICS IN APPLIED MATHEMATICS Spall   
Prereq: Graduate course in Probability and Statistics and knowledge of basic Matrix Algebra.  Roundtable in Stochastic Methods for Modeling, Optimization, and Simulation. This roundtable-format course considers stochastic optimization and Monte Carlo methods in simulation and computation Each class session will cover a paper from the literature or a research project.

Sec. 01

T 2-3:30
F 6pm

550.800

DISSERTATION RESEARCH Staff

Sec. 01

TBA

550.810

PROBABILITY & STATISTICS SEMINAR Staff

Sec. 01

TBA

550.865

OPTIMIZATION & DISCRETE MATH SEMINAR Goldman

Sec. 01

M 12-2