Department of Statistics and Operations Research
VIDYADHAR KULKARNI, Chair
Edward Carlstein, Associate Chair
Douglas G. Kelly, Head, Mathematical Decision Sciences Program
Professors
Amarjit Budhiraja, Edward Carlstein, Alan F. Karr, Douglas G. Kelly, Vidyadhar G. Kulkarni, M. Ross Leadbetter, J. Stephen Marron, Andrew Nobel, J. Scott Provan, Pranab K. Sen, Richard L. Smith, Jayashankar Swaminathan, Jon W. Tolle.
Associate Professors
Jan Hannig, Chuanshu Ji, Gabor Pataki, Vladas Pipiras.
Assistant Professors
Nilay Argon, Yufeng Liu, Shu Lu, Haipeng Shen, Zhengyuan Zhu, Serhan Ziya.
Adjunct Professors
Kenneth A. Bollen, George Christakos, A. Ronald Gallant, Mark E. Hartmann, Harry L. Hurd, Valen Johnson, Karl Petersen, Eric Renault, Robert N. Rodriguez, Randy Tobias, Harvey M. Wagner.
Lecturer
Charles Dunn.
Professors Emeriti
Charles R. Baker, George S. Fishman, Gopinath Kallianpur, Gordon D. Simons, Walter L. Smith, Shaler Stidham Jr., David Rubin.
Introduction
The Department of Statistics (STAT) and the Department of Operations Research (OR) were merged on July 1, 2003, to create the Department of Statistics and Operations Research (STOR). The undergraduate program associated with this merged department leads to a degree in the mathematical decision sciences. This program offers an excellent undergraduate major or minor for students interested in actuarial science, operations research, probability, and statistics, as well as in such fields as business, economics, planning, psychology, and biomedicine where the decision and statistical sciences play an increasingly important role.
Particular areas in which graduates can either obtain employment or go on to graduate school include
Actuarial Science: Actuaries are mathematicians who work primarily in the insurance industry or related businesses or governmental agencies. Students interested in this field take advanced courses in statistics, stochastic processes, and the mathematical theory of risk.
Statistics: Probability and statistics are two of the most important subjects in the mathematical sciences for practical applications. Students in this area study the mathematical theories of probability and statistics and their application to mathematical models that contain an element of uncertainty. Opportunities for employment are manifold, including positions with drug and insurance companies as well as with government agencies.
Operations Research: In this area, students study the mathematics and statistical methodologies related to decision making. This branch of the mathematical sciences is extremely important 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.
Program of Study
The degree offered is bachelor of science in mathematical decision sciences. A minor is also available.
Majoring in Mathematical Decision Sciences: Bachelor of Science
In the first two years of the program, students are required to complete the standard calculus sequence as well as introductory courses in statistics, operations research, and computer science. At the beginning of their third year, students take advanced courses in statistics, probability, and operations research. They have a great deal of flexibility in tailoring their program to meet their individual interests.
First and Second Years
All General Education requirements apply. In addition, a foreign language must be completed through level 4. (Level 4 may be taken Pass/D+/D/Fail if the student does not place into level 4.) The following courses are required:
COMP 116 (110 may be substituted)
MATH 231, 232 Calculus of Functions of One Variable
MATH 233 Calculus of Functions of Several Variables
STOR 155* Introduction to Statistics
STOR 215* Introduction to the Decision Sciences
It is recommended that all mathematical decision sciences majors take ECON 101 as a social and behavioral sciences Approaches course. Students interested in the actuarial profession also should take BUSI 100 as a general elective.
*Prospective mathematical decision sciences majors are encouraged to take STOR 155 and 215 as early as possible in their college careers. Each has a prerequisite of MATH 110 or its equivalent and may be taken before, or concurrently with, MATH 231.
Third and Fourth Years
The following courses must be taken by all majors:
MATH 547 Linear Algebra for Applications
STOR 415 Deterministic Models in Operations Research
STOR 435 Introduction to Probability
STOR 445 Stochastic Models in Operations Research
STOR 455 Statistical Methods I
STOR 456 Statistical Methods II
In addition, all majors must take four courses from the following two groups of courses, including at least two from group A:**
Group A
STOR 305 Decision Making Using Spread Sheet Models
STOR 372 Long Term Actuarial Science I
STOR 465 Simulation Analysis and Design
STOR 472 Short Term Actuarial Science II
STOR 515 Computational Mathematics for Decision Sciences
STOR 555 Mathematical Statistics
Group B
BIOL 526
BIOS 664
BUSI 408
COMP 401, 410
MATH 383, 521, 522, 523, 524, 548, 549, 566
STOR 582
**Students wishing to prepare for an actuarial career should include STOR 372, 472, and 555 from group A in their program and take ECON 410 and 420 and BUSI 408 and 580 as electives. Students who plan to attend graduate school in the mathematical sciences (e.g., in operations research or statistics) should include in their program COMP 401, STOR 555, and either MATH 521 or STOR 515.
Although mathematical decision sciences majors are exempt from the supplemental education requirements in the College of Arts and Sciences, they are required to take four elective courses outside of the departments that comprise the mathematical sciences (computer science, mathematics, and statistics and operations research). These courses may not be taken on the pass/fail option.
Mathematical decision sciences majors must complete 123 academic hours. They also must attain at least a grade of C (not C-) in 18 hours of their third and fourth year mathematical science courses.
Minoring in Mathematical Decision Sciences
Students wishing to minor in the mathematical decision sciences are required to take STOR 155 and 215 as well as three courses from among STOR 305, 372, 415, 435, 445, 455, 456, 465, 472, 515, and 555 that are not counted towards their major requirements.
Honors in Mathematical Decision Sciences
The mathematical decision sciences program offers the student the possibility of graduating with honors or highest honors. The requirements for an honors degree can be satisfied in a variety of ways but have a common basis in the minimal standards set by the College of Arts and Sciences. Students interested in graduation with honors should apply to the program director prior to the beginning of their senior year.
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 112 and 215, which are foundation courses in decision models, and the basic statistical courses, STOR 151 and 155. At the intermediate level, STOR 305 provides an introduction to business decision models, while STOR 372 is an introductory course in actuarial science. Substantial coverage of applied statistical methods is provided in STOR 455 and 456. 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 445.
Special Opportunities in Mathematical Decision Sciences
Departmental Involvement
The mathematical decision sciences program sponsors an undergraduate club, CASO, for students interested in a career in the actuarial sciences. CASO organizes study groups for the actuarial exams, sponsors talks by professional actuaries, and maintains contact with alumni in the field.
Undergraduate Awards
Two undergraduate awards for graduating seniors are given each year by the mathematical decision sciences program. One award is given to the outstanding senior major, and the second is the W. Robert Mann Award, given for excellence in actuarial science. Plaques bearing the names of winners are located in the undergraduate study room in Smith 103B.
Undergraduate Research
Undergraduate research under the direction of faculty members from the Department of Statistics and Operations Research is offered through the independent study and research courses (STOR 496 and 497). Students pursuing honors are encouraged to participate in these programs.
Graduate School and Career Opportunities
All tracks in the mathematical decision sciences degree program provide excellent preparation for graduate study. Graduates in operations research often continue work in such fields as statistics, operations research, industrial engineering, biostatistics, and environmental science at the graduate level or enter business school to pursue the masters in business administration (M.B.A.) degree.
A five-year B.S.-M.S. degree program in operations research is also an available option. This program is under the direction of the Department of Statistics and Operations Research. Interested students should consult with the program director.
Graduates in the mathematical decision sciences will find that employment opportunities are numerous for well-paid, challenging jobs.
Contact Information
Mathematical Decision Sciences Office, CB# 3260, 104A Smith, (919) 962-2307, crogers@email.unc.edu. Web site: www.stat-or.unc.edu/programs/MDS.
STOR
052 First-Year Seminar: Decisions, Decisions, Decisions (3). 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.
053 First-Year Seminar: Networks: Degrees of Separation and Other Phenomena Relating to Connected Systems (3). 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.
054 [006D] First-Year Seminar: Statistical Decision-Making Concepts (3). Basic statistical decision-making procedures (for prediction, estimation, and relationships), along with their associated errors and losses; the effects of randomness. Use of computer simulation and physical experimentation.
056 [006E] First-Year Seminar: The Art and Science of Decision Making in War and Peace (3). 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.
060 First-Year Seminar: Statistical Decision-Making Concepts (3). 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.
061 First-Year Seminar: Statistics for Environmental Change (3). A study of parts of the Environmental Protection Agencys Criteria Document, mandated by the Clean Air Act; this document reviews and summarizes current scientific evidence concerning airborne particulate matter. Students will learn about some of the statistical methods used in recent studies to assess the connections between air pollution and mortality, and will review and prepare reports on studies covered in the Criteria Document.
062 First-Year Seminar: Probability and Paradoxes (3). 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. These occurrences are studied using simple chance experiments and spreadsheet calculations.
063 First-Year Seminar: Statistics, Biostatistics, and Bioinformatics: An Introduction to the Ongoing Evolution (3). This course is designed to emphasize the motivation, philosophy, and cultivation of statistical reasoning in the interdisciplinary areas of statistical science and bioinformatics.
064 First-Year Seminar: A Random Walk down Wall Street (3). Introduces basic concepts in finance and economics, useful tools for collecting and summarizing financial data, and simple probability models for quantification of market uncertainty.
066 First-Year Seminar: Visualizing Data (3). 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.
072 First-Year Seminar: Unlocking the Genetic Code (3). Covers the origin and evolution of operations research from the WWII to its modern use in industry and government.
112 Decision Models for Business (3). Prerequisite, MATH 110. 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.
113 Decision Models for Economics (3). Prerequisite, MATH 110. 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.
151 Basic Concepts of Statistics and Data Analysis I (3). Prerequisite, MATH 110 (or exemption). 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.
155 Introduction to Statistics (3). Prerequisite, MATH 110 (or exemption). 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.
215 Introduction to the Decision Sciences (3). Prerequisite, MATH 110 (or exemption). Introduction to basic concepts and techniques of decision making and information management in business, economics, and the social and physical sciences. Topics include discrete optimization, discrete probability, networks, decision trees, games, Markov chains.
305 Decision Making Using Spreadsheet Models (3). Prerequisite, MATH 152 or STOR 155. 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.
358 Sample Survey Methodology (BIOS 664) (4). Prerequisite, STOR 455 or equivalent. Fundamental principles and methods of sampling populations, with primary attention given to simple random sampling, stratified sampling, and cluster sampling. Also, the calculation of sample weights, dealing with sources of nonsampling error, and analysis of data from complex sample designs are covered. Practical experience in sampling is provided by student participation in the design, execution, and analysis of a sampling project.
372 Long Term Actuarial Models (3). Prerequisites, MATH 232, STOR 155, and 215. 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.
415 Deterministic Models in Operations Research (3). Prerequisite, MATH 547. Linear, integer, nonlinear, and dynamic programming, classical optimization problems, network theory.
435 Introduction to Probability (MATH 535) (3). Prerequisite, MATH 233. 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.
445 Stochastic Models in Operations Research (3). Prerequisite, BIOS 660 or STOR 435. 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.
455 Statistical Methods I (3). Prerequisite, STOR 155. 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.
456 Statistical Methods II (3). Prerequisite, STOR 455. Topics selected from design of experiments, sample surveys, nonparametrics, time-series, multivariate analysis, contingency tables, logistic regression, simulation. Use of statistical software packages.
465 Simulation Analysis and Design (3). Prerequisite, STOR 435. Introduces concepts of random number generation, random variate generation, and discrete event simulation of stochastic systems. Students perform simulation experiments using standard simulation software.
472 Short Term Actuarial Models (3). Prerequisite, STOR 435. 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.
496 [090] Undergraduate Reading and Research in Statistics (121). Permission of the director of undergraduate studies. This course is intended primarily for students working on honors projects. No student may receive more than three credit hours for this course.
497 Undergraduate Reading and Research in Operations Research (3). Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. No one may receive more than three semester hours credit for this course.
515 Computational Mathematics for Decision Sciences (3). Permission of the instructor. Reviews basic mathematical and computational theory required for analyzing models that arise in operations research, management science, and other policy sciences. Solution techniques that integrate existing software into student-written computer programs will be emphasized.
555 Mathematical Statistics (3). Prerequisite, STOR 435 or equivalent. Functions of random samples and their probability distributions, introductory theory of point and interval estimation and hypothesis testing, elementary decision theory.
582 Neural Network Models for the Decision and Cognitive Sciences (3). Prerequisite, one of MATH 231, PHIL 155, PSYC 210, STOR 155 or 215. The interactions between cognitive science and the decision sciences are explored via neural networks. The history of these networks in neuroscience is reviewed and their adaptation to other fields such as psychology, linguistics, and operations research is presented.
612 [210] Models in Operations Research (3). Prerequisite, 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.
614 [211] Linear Programming (3). Prerequisites, 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.
634 [154] Measure and Integration (3). Prerequisite, advanced calculus. Lebesgue and abstract measure and integration, convergence theorems, differentiation. Radon-Nikodym theorem, product measures. Fubini theorems. Lp spaces.
635 [155] Probability (MATH 635) (3). Prerequisite, STOR 634 or permission of the instructor. Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.
641 [220] Stochastic Models in Operations Research I (3). Prerequisite, STOR 435 or equivalent. Review of probability, conditional probability, expectations, transforms, generating functions, special distributions, functions of random variables. Introduction to stochastic processes. Discrete-time Markov chains. Transient and limiting behavior. First passage times.
642 [221] Stochastic Models in Operations Research II (3). Prerequisite, STOR 641 or equivalent. 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.
654 [164] Statistical Theory I (3). Prerequisite, two semesters of advanced calculus. Probability spaces. Random variables, distributions, expectation. Conditioning. Generating functions. Limit theorems: LLN, CLT, Slutzky, delta-method, big-O in probability. Inequalities. Distribution theory: normal, chi-squared, beta, gamma, Cauchy, other multivariate distributions. Distribution theory for linear models.
655 [165] Statistical Theory II (3). Prerequisite, STOR 654 or equivalent. 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.
664 [174] Applied Statistics I (3). 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.
665 [175] Applied Statistics II (3). Prerequisite, STOR 664 or permission of the instructor. 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.