Department of Statistics and Operations Research

Department of Statistics and Operations Research

http://www.stat-or.unc.edu

318 Hanes Hall, CB# 3260

(919) 843-6024

Serhan Ziya, Director of Undergraduate Studies

ziya@email.unc.edu

Alison Kieber, Administrative Services Assistant

kieber@email.unc.edu

AMARJIT BUDHIRAJA, Chair

Introduction

The major in mathematical decision sciences is an excellent program for students interested in actuarial science, operations research, probability, or statistics, as well as in fields such as business, economics, planning, psychology, and biomedicine where the decision and statistical sciences play an increasingly important role.

Particular areas in which graduates can obtain employment or continue with graduate study include

Statistics

Probability and statistics are two of the most frequently applied areas in the mathematical decision sciences. Students in this area study the mathematical theories of probability and statistics and their application to mathematical models that contain an element of uncertainty or randomness. Opportunities for employment are manifold in businesses and government agencies dealing with many branches of the natural and social sciences, including pharmacology, environmental sciences, and many others.

Operations Research

In this area, students study mathematical and statistical techniques related to decision making. This branch of the mathematical decision sciences is crucial in business, government, and other management areas where difficult problems that depend on large amounts of data are addressed (for example, complex airline route schedules). In addition to their major courses, students interested in this field are encouraged to take courses in business and economics.

Actuarial Science

Actuaries are mathematicians who work primarily in businesses that involve financial risk, including the insurance industry. Students interested in this field take advanced courses in statistics, stochastic processes, and the mathematical theory of risk.

Advising

All majors and minors have a primary academic advisor in Steele Building. Students are strongly encouraged to meet regularly with their advisor and review their Tar Heel Tracker each semester. After contacting the mathematical decision sciences office (see “Contact Information” above), all majors and minors are also assigned an undergraduate advisor in the department. The department’s undergraduate advisors discuss course planning with current majors and, if needed, minors before registration each semester. The director of undergraduate studies works with prospective majors and minors by appointment. Additional information on courses, undergraduate research opportunities, the honors program, careers, and graduate schools may be obtained from the department’s Web site or by contacting the director of undergraduate studies.

Courses for Students from Other Departments

The Department of Statistics and Operations Research offers a variety of courses of potential value to students majoring in other disciplines. Introductory courses include STOR 113 and STOR 215, which are foundation courses in decision models, and the basic statistical courses, STOR 151 and STOR 155. At the intermediate level, STOR 305 provides an introduction to business decision models, while STOR 471 is an introductory course in actuarial science. Substantial coverage of applied statistical methods is provided in STOR 455 and STOR 556. At more advanced mathematical levels, an introduction to probability theory is provided by STOR 435, and the basic theory of statistical inference is given by STOR 555. More advanced deterministic and stochastic models of operations research are provided in STOR 415 and STOR 445.

Graduate School and Career Opportunities

Regardless of the electives chosen, the mathematical decision sciences degree program provides excellent preparation for graduate study. Graduates with concentrations in operations research or statistics often continue work at the graduate level in those fields or related areas such as industrial engineering, biostatistics, and environmental science, or enter business school to pursue the master’s in business administration (M.B.A.) degree.

A five-year B.S.–M.S. degree program in operations research is also an option. This program is under the direction of the Department of Statistics and Operations Research. Interested students should consult the program director.

Graduates in the mathematical decision sciences will find numerous opportunities for well-paid, challenging jobs.

Professors

Amarjit Budhiraja, Edward Carlstein, Jan Hannig, Vidyadhar G. Kulkarni, M. Ross Leadbetter, Yufeng Liu, J. Stephen Marron, Andrew Nobel, Vladas Pipiras, Pranab K. Sen, Richard L. Smith, Serhan Ziya.

Associate Professors

Nilay Argon, Shankar Bhamidi, Chuanshu Ji, Shu Lu, Gabor Pataki.

Assistant Professors

Quoc Tran-Dinh, Yin Xia, Kai Zhang.

Adjunct and Joint Professors

Jason Fine, Joseph Ibrahim, Michael Kosorok, Jayashankar Swaminathan.

Lecturers

Robin Cunningham, Charles Dunn.

Professors Emeriti

Charles R. Baker, George S. Fishman, Douglas G. Kelly, Scott Provan, David Rubin, Gordon D. Simons, Walter L. Smith, Shaler Stidham Jr., Jon W. Tolle.

STOR–Statistics and Operations Research

Undergraduate-level Courses

STOR 52. First-Year Seminar: Decisions, Decisions, Decisions. 3 Credits.

In this course, we will investigate the structure of these decision problems, show how they can be solved (at least in principle), and solve some simple problems.
Gen Ed: QI.
Grading status: Letter grade.

STOR 53. FYS: Networks: Degrees of Separation and Other Phenomena Relating to Connected Systems. 3 Credits.

Networks, mathematical structures that are composed of nodes and a set of lines joining the nodes, are used to model a wide variety of familiar systems.
Gen Ed: QI.
Grading status: Letter grade.

STOR 54. First-Year Seminar: Adventures in Statistics. 3 Credits.

This seminar aims to show that contrary to common belief, statistics can be exciting and fun. The seminar will consist of three modules: statistics in our lives, randomness, and principles of statistical reasoning.
Gen Ed: QI.
Grading status: Letter grade.

STOR 55. First-Year Seminar: Risk and Uncertainty in the Real World. 3 Credits.

The aim of this class is to study the role of uncertainty in our daily lives, to explore the cognitive biases that impair us, and to understand how one uses quantitative models to make decisions under uncertainty in a wide array of fields including medicine, law, finance, and the sciences.
Gen Ed: QI.
Grading status: Letter grade.

STOR 56. First-Year Seminar: The Art and Science of Decision Making in War and Peace. 3 Credits.

This seminar will use recently assembled historical material to tell the exciting story of the origins and development of operations research during and after World War II.
Gen Ed: QI.
Grading status: Letter grade.

STOR 60. First-Year Seminar: Statistical Decision-Making Concepts. 3 Credits.

We will study some basic statistical decision-making procedures and the errors and losses they lead to. We will analyze the effects of randomness on decision making using computer experimentation and physical experiments with real random mechanisms like dice, cards, and so on.
Gen Ed: QI.
Grading status: Letter grade.

STOR 61. First-Year Seminar: Statistics for Environmental Change. 3 Credits.

Studies the Environmental Protection Agency's Criteria Document, mandated by the Clean Air Act; this document reviews current scientific evidence concerning airborne particulate matter. Students learn some of the statistical methods used to assess the connections between air pollution and mortality, and prepare reports on studies covered in the Criteria Document.
Gen Ed: QI.
Grading status: Letter grade.

STOR 62. First-Year Seminar: Probability and Paradoxes. 3 Credits.

The theory of probability, which can be used to model the uncertainty and chance that exist in the real world, often leads to surprising conclusions and seeming paradoxes. We survey and study these, along with other paradoxes and puzzling situations arising in logic, mathematics, and human behavior.
Gen Ed: QI.
Grading status: Letter grade.

STOR 63. FYS: Statistics, Biostatistics, and Bioinformatics: An Introduction to the Ongoing Evolution. 3 Credits.

This course is designed to emphasize the motivation, philosophy, and cultivation of statistical reasoning in the interdisciplinary areas of statistical science and bioinformatics.
Gen Ed: QI.
Grading status: Letter grade.

STOR 64. First-Year Seminar: A Random Walk down Wall Street. 3 Credits.

Introduces basic concepts in finance and economics, useful tools for collecting and summarizing financial data, and simple probability models for quantification of market uncertainty.
Gen Ed: QI.
Grading status: Letter grade.

STOR 66. First-Year Seminar: Visualizing Data. 3 Credits.

This seminar looks at a variety of ways in which modern computational tools allow easy and informative viewing of data. Students will also study the kinds of choices that have to be made in data presentation and viewing.
Gen Ed: QI.
Grading status: Letter grade.

STOR 72. First-Year Seminar: Unlocking the Genetic Code. 3 Credits.

Introduces students to the world of genetics and DNA and to the use of computers to organize and understand the complex systems associated with the structure and dynamics of DNA and heredity.
Gen Ed: QI.
Grading status: Letter grade.

STOR 89. First-Year Seminar: Special Topics. 3 Credits.

Special Topics Course. Contents will vary each semester.
Repeat rules: May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 2 total completions.
Grading status: Letter grade.

STOR 112. Decision Models for Business. 3 Credits.

An introduction to the basic quantitative models of business with linear and nonlinear functions of single and multiple variables. Linear and nonlinear optimization models and decision models under uncertainty will be covered.
Requisites: Prerequisite, MATH 110.
Gen Ed: QR.
Grading status: Letter grade.

STOR 113. Decision Models for Business and Economics. 3 Credits.

An introduction to multivariable quantitative models in economics. Mathematical techniques for formulating and solving optimization and equilibrium problems will be developed, including elementary models under uncertainty.
Requisites: Prerequisite, MATH 110.
Gen Ed: QR.
Grading status: Letter grade.

STOR 151. Introduction to Data Analysis. 3 Credits.

Elementary introduction to statistical reasoning, including sampling, elementary probability, statistical inference, and data analysis. STOR 151 may not be taken for credit by students who have credit for ECON 400 or PSYC 210.
Requisites: Prerequisite, MATH 110.
Gen Ed: QR.
Grading status: Letter grade.

STOR 155. Introduction to Data Models and Inference. 3 Credits.

Data analysis; correlation and regression; sampling and experimental design; basic probability (random variables, expected values, normal and binomial distributions); hypothesis testing and confidence intervals for means, proportions, and regression parameters; use of spreadsheet software.
Requisites: Prerequisite, MATH 110.
Gen Ed: QR.
Grading status: Letter grade.

STOR 215. Foundations of Decision Sciences. 3 Credits.

Introduction to basic concepts and techniques of discrete mathematics with applications to business and social and physical sciences. Topics include logic, sets, functions, combinatorics, discrete probability, graphs, and networks.
Requisites: Prerequisite, MATH 110.
Gen Ed: QR.
Grading status: Letter grade.

STOR 305. Decision Making Using Spreadsheet Models. 3 Credits.

The use of mathematics to describe and analyze large-scale decision problems. Situations involving the allocation of resources, making decisions in a competitive environment, and dealing with uncertainty are modeled and solved using suitable software packages.
Requisites: Prerequisite, MATH 152 or STOR 155.
Gen Ed: QI.
Grading status: Letter grade.

STOR 358. Sample Survey Methodology. 4 Credits.

Fundamental principles and methods of sampling populations, with emphasis on simple, random, stratified, and cluster sampling. Sample weights, nonsampling error, and analysis of data from complex designs are covered. Practical experience through participation in the design, execution, and analysis of a sampling project.
Requisites: Prerequisite, BIOS 550; permission of the instructor for students lacking the prerequisite.
Gen Ed: EE-Field Work.
Grading status: Letter grade
Same as: BIOS 664.

Advanced Undergraduate and Graduate-level Courses

STOR 415. Introduction to Optimization. 3 Credits.

Linear, integer, nonlinear, and dynamic programming, classical optimization problems, network theory.
Requisites: Prerequisite, MATH 547.
Grading status: Letter grade.

STOR 435. Introduction to Probability. 3 Credits.

Introduction to mathematical theory of probability covering random variables; moments; binomial, Poisson, normal and related distributions; generating functions; sums and sequences of random variables; and statistical applications.
Requisites: Prerequisite, MATH 233.
Gen Ed: QI.
Grading status: Letter grade
Same as: MATH 535.

STOR 445. Stochastic Modeling. 3 Credits.

Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems, inventory, and reliability, with emphasis on systems modeling, design, and control.
Requisites: Prerequisite, BIOS 660 or STOR 435.
Grading status: Letter grade.

STOR 455. Statistical Methods I. 3 Credits.

Review of basic inference; two-sample comparisons; correlation; introduction to matrices; simple and multiple regression (including significance tests, diagnostics, variable selection); analysis of variance; use of statistical software.
Requisites: Prerequisite, STOR 155.
Grading status: Letter grade.

STOR 465. Simulation for Analytics. 3 Credits.

Introduces concepts of random number generation, random variate generation, and discrete event simulation of stochastic systems. Students perform simulation experiments using standard simulation software.
Requisites: Prerequisite, STOR 445.
Grading status: Letter grade.

STOR 471. Long-Term Actuarial Models. 3 Credits.

Probability models for long-term insurance and pension systems that involve future contingent payments and failure-time random variables. Introduction to survival distributions and measures of interest and annuities-certain.
Requisites: Prerequisite, STOR 435.
Gen Ed: QI.
Grading status: Letter grade.

STOR 472. Short Term Actuarial Models. 3 Credits.

Short term probability models for potential losses and their applications to both traditional insurance systems and conventional business decisions. Introduction to stochastic process models of solvency requirements.
Requisites: Prerequisite, STOR 435.
Grading status: Letter grade.

STOR 493. Internship in Statistics and Operations Research. 3 Credits.

Requires permission of the department. Mathematical decision sciences majors only. An opportunity to obtain credit for an internship related to statistics, operations research, or actuarial science. Pass/Fail only. Does not count toward the mathematical decision sciences major or minor.
Gen Ed: EE-Academic Internship.
Repeat rules: May be repeated for credit. 6 total credits. 2 total completions.
Grading status: Pass/Fail.

STOR 496. Undergraduate Reading and Research in Statistics and Operations Research. 1-3 Credits.

Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. May be repeated for credit.
Gen Ed: EE-Mentored Research.
Repeat rules: May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 6 total completions.
Grading status: Letter grade.

STOR 555. Mathematical Statistics. 3 Credits.

Functions of random samples and their probability distributions, introductory theory of point and interval estimation and hypothesis testing, elementary decision theory.
Requisites: Prerequisite, STOR 435.
Grading status: Letter grade.

STOR 556. Advanced Methods of Data Analysis. 3 Credits.

Topics selected from: design of experiments, sample surveys, nonparametrics, time-series, multivariate analysis, contingency tables, logistic regression, and simulation. Use of statistical software packages.
Requisites: Prerequisites, STOR 435 and 455.
Grading status: Letter grade.

STOR 565. Machine Learning. 3 Credits.

Introduction to theory and methods of machine learning including classification; Bayes risk/rule, linear discriminant analysis, logistic regression, nearest neighbors, and support vector machines; clustering algorithms; overfitting, estimation error, cross validation.
Requisites: Prerequisites, STOR 215 or MATH 381, and STOR 435.
Grading status: Letter grade.

STOR 612. Models in Operations Research. 3 Credits.

Required preparation, calculus of several variables, linear or matrix algebra. Formulation, solution techniques, and sensitivity analysis for optimization problems which can be modeled as linear, integer, network flow, and dynamic programs. Use of software packages to solve linear, integer, and network problems.
Grading status: Letter grade.

STOR 614. Linear Programming. 3 Credits.

Required preparation, calculus of several variables, linear or matrix algebra. The theory of linear programming, computational methods for solving linear programs, and an introduction to nonlinear and integer programming. Basic optimality conditions, convexity, duality, sensitivity analysis, cutting planes, and Karush-Kuhn-Tucker conditions.
Grading status: Letter grade.

STOR 634. Measure and Integration. 3 Credits.

Required preparation, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces.
Grading status: Letter grade.

STOR 635. Probability. 3 Credits.

Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.
Requisites: Prerequisite, STOR 634; permission of the instructor for students lacking the prerequisite.
Grading status: Letter grade
Same as: MATH 635.

STOR 641. Stochastic Models in Operations Research I. 3 Credits.

Review of probability, conditional probability, expectations, transforms, generating functions, special distributions, and functions of random variables. Introduction to stochastic processes. Discrete-time Markov chains. Transient and limiting behavior. First passage times.
Requisites: Prerequisite, STOR 435.
Grading status: Letter grade.

STOR 642. Stochastic Models in Operations Research II. 3 Credits.

Exponential distribution and Poisson process. Birth-death processes, continuous-time Markov chains. Transient and limiting behavior. Applications to elementary queueing theory. Renewal processes and regenerative processes.
Requisites: Prerequisite, STOR 641.
Grading status: Letter grade.

STOR 654. Statistical Theory I. 3 Credits.

Required preparation, two semesters of advanced calculus. Probability spaces. Random variables, distributions, expectation. Conditioning. Generating functions. Limit theorems: LLN, CLT, Slutsky, delta-method, big-O in probability. Inequalities. Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions. Distribution theory for linear models.
Grading status: Letter grade.

STOR 655. Statistical Theory II. 3 Credits.

Point estimation. Hypothesis testing and confidence sets. Contingency tables, nonparametric goodness-of-fit. Linear model optimality theory: BLUE, MVU, MLE. Multivariate tests. Introduction to decision theory and Bayesian inference.
Requisites: Prerequisite, STOR 654.
Grading status: Letter grade.

STOR 664. Applied Statistics I. 3 Credits.

Permission of the instructor. Basics of linear models: matrix formulation, least squares, tests. Computing environments: SAS, MATLAB, S+. Visualization: histograms, scatterplots, smoothing, QQ plots. Transformations: log, Box-Cox, etc. Diagnostics and model selection.
Grading status: Letter grade.

STOR 665. Applied Statistics II. 3 Credits.

ANOVA (including nested and crossed models, multiple comparisons). GLM basics: exponential families, link functions, likelihood, quasi-likelihood, conditional likelihood. Numerical analysis: numerical linear algebra, optimization; GLM diagnostics. Simulation: transformation, rejection, Gibbs sampler.
Requisites: Prerequisite, STOR 664; permission of the instructor for students lacking the prerequisite.
Grading status: Letter grade.

STOR 691H. Honors in Mathematical Decision Sciences. 3 Credits.

Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.
Gen Ed: EE-Mentored Research.
Grading status: Letter grade.

STOR 692H. Honors in Mathematical Decision Sciences. 3 Credits.

Permission of the department. Majors only. Individual reading, study, or project supervised by a faculty member.
Gen Ed: EE-Mentored Research.
Grading status: Letter grade.