# undergraduate program

# Program descriptions

The Department of Statistical Sciences and Operations Research (in collaboration with the Department of Mathematics and Applied Mathematics) has several degree programs available offering a variety of options. The department offers a Bachelor of Science in Mathematical Sciences with a concentration in either Operations Research or Statistics. In addition, the department offers a Certificate in Statistics, and for students in other programs the department offers a minor in Statistics.

What follows is a brief description of these programs:

- Bachelor of Science in Mathematical Sciences
- Double major within the Mathematical Sciences Department
- The Certificate Program in Statistics
- Minors

## A. Bachelor of Science in Mathematical Sciences

All students majoring in mathematical sciences are required to fulfill certain basic course requirements. There is a great deal of flexibility in choosing courses to fulfill these basic requirements. A student who wishes to emphasize one particular discipline for a concentration will have that indicated on the student's transcript. As an alternative to choosing a concentration, a student, in consultation with the advisor, could design an individual study program combining course work in more than one of the disciplines represented in the mathematical sciences area. The decision to choose a particular concentration does not have to be made until the graduation application is submitted in the senior year, but the student should consult with his or her advisor to determine the timetable necessary to meet the necessary requirements.

### Operations Research

While classical applied mathematics uses mathematical techniques to solve physical science problems, the areas of applications of operations research are diverse, ranging from business and industry to federal and military operations. Operations research is the mathematical discipline devoted to the study of complex systems through the creation and analysis of mathematical models. By developing and exploring the properties of such models, operations research analysts increase our understanding of both the actual behavior of the system of interest under present conditions and how this behavior could change when circumstances are altered. The goal of operations research is more than the academic study of problems in areas like logistics, scheduling, and decision processes -- usually in an industrial or management context. Most users of operations research methodology are instead committed to improving the system they are investigating: making a transportation network more efficient or increasing the profitability of a manufacturing process, for example.

Because of the interdisciplinary character of the problems operations research addresses, people working in operations research come from diverse educational backgrounds. Decision theorists, economists, management scientists, systems analysts, and systems engineers are frequently found in operations research. The focus of operations research is the mathematical model and the mathematical analysis of its properties and solutions. The student in operations research will find that the demands of modeling and analysis are broad. In addition to the mathematical skills and insight necessary to pose a problem and formulate a model, a student in operations research must possess the computational and statistical knowledge required to test and validate the mathematical model and any solutions derived from it. Such techniques include linear and nonlinear mathematical programming, dynamic methods, numerical and statistical simulation, stochastic processes, queuing theory, and statistical inference. Hence, in the operations research concentration in the Department of Statistical Sciences and Operations Research, you will find yourself taking courses in mathematics, computer science, and statistics as well as in operations research. The specific course requirements appear below. Because of this wide exposure to the different mathematical sciences, you will be prepared for a variety of occupations or for graduate work in the many masters and doctoral programs in operations research.

Historically, jobs in operations research have been closely linked to the defense establishment. Operations research had its formal beginnings during World War II in Great Britain with the development and use of radar in the United States and with the location and detection of enemy submarines. After the war, the methods of operations research spread to defense industries and later to corporations, large and small, involved in nonmilitary activities. Today, jobs in operations research can be found in academic, government, commercial, industrial, and management settings.

### Statistics

Statistics is the science of making inferences and drawing conclusions from experimental and sample information. Because such information necessarily represents only partial knowledge of the population or phenomenon under investigation, statistics can also be described as the art of making decisions in the face of uncertainty. Statisticians combine mathematical models, a probability-based logic, and numerical information (data) to address problems that range from the immediate and everyday requirements of industrial production and government regulation to the most esoteric research questions of the social and natural sciences. In the course of their work, statisticians are often involved in the following activities:

- The design of experiments, sampling plans, and surveys.
- The process of gathering information and monitoring its quality.
- The construction of numerical summaries and graphs, both to describe the results of an investigation and to "explore" for anticipated and unanticipated trends and relationships.
- The development and application of appropriate statistical models and methods for assessing the meaning of the observed experimental or sample data and for generalizing from the data actually observed to the broader population or phenomenon of interest.
- The mathematical study of the properties of the various statistical models and methods themselves.

Because of the numerical character of their data, statisticians are frequently interested in developing and using computer software for accurate, efficient statistical computations and for flexible data management. In addition, the cross-disciplinary nature of statistical methodology often permits statisticians to become active participants in the search for new scientific knowledge and the extension of existing scientific theory.

Applications of statistical techniques arise naturally in areas like actuarial science, agriculture, bioinformatics, biology, chemistry, economics, engineering, medicine, physics, psychology, and sociology, as well as in less obvious disciplines like history and linguistics. While many statisticians continue their education beyond the baccalaureate level, the widespread adoption of statistical methods by industrial, commercial, and government organizations has dramatically increased the career opportunities for college graduates with an undergraduate major in statistics. In industry and government there are many positions in which experiments, surveys, and investigative studies are conducted or in which building accurate, realistic numerical models is the goal. Government agencies employ statisticians to cope with the tremendous amounts of data collected to plan, organize, and monitor government programs. Graduates of the statistics program can qualify for statistical positions in the federal government. Pharmaceutical companies use statisticians to design and analyze the results of the clinical studies required for the development of new drugs. Industry and business hire statisticians to help solve quantitative problems in product research, marketing, production, and other areas. Insurance companies seek mathematically and statistically trained persons who are interested in actuarial careers. Whenever and wherever numerical information is gathered for decision-making purposes, people knowledgeable in statistical reasoning are involved.

What type of education should a statistician have at the undergraduate level? We believe that a broad training in statistics, mathematics, and science is most desirable. The requirements for this degree are listed below. Within the program at VCU we strongly recommend that students take a minor in an area of application. Obviously, it is necessary to obtain a mathematical foundation as extensive as possible. The ability to use computers as tools in problem-solving has become more important. However, a highly-developed interest in solving real problems remains the central objective of the statisticians' education.

## B. Double major within the Mathematical Sciences Department

A student who meets the requirements for two of the concentrations within the mathematical sciences degree (Applied Mathematics, Mathematics, Operations Research, and Statistics) may receive a double major. The appropriate form for declaring a double major may be obtained from the University Enrollment Services/Records and Registration.

## C. The Certificate Program in Statistics

The Department of Statistical Sciences and Operations Research offers a post-baccalaureate undergraduate Certificate in Statistics that is accessible to persons with undergraduate majors in engineering, natural sciences, economics and other sciences, as well as to traditional mathematical sciences majors. The rationale for the program notes that while students in all these areas get some exposure to statistical concepts and methods, they often find themselves in jobs that require significantly more training in statistics than they received as undergraduates. The certificate program provides the same level of coverage of topics in statistics as the baccalaureate track in statistics, but fewer credits in mathematical sciences than would be required for a second major.

Undergraduate majors in statistics are rare, relative to the number of jobs that utilize statistical knowledge. Liberal arts majors in mathematics and in the social sciences who have had one or two courses in statistical methods as undergraduates often find themselves learning more advanced techniques on the job. The proliferation of short courses, often offered outside university settings, testifies to the need for more advanced skills in the work place. The certificate program offers individuals a more efficient and more effective avenue for receiving such training and getting appropriate credit for it.

For more information about our graduation rates, the median debt of students who completed the program, and other important information, please see the gainful employment website.

Students seeking to enter the certificate program in statistics should contact Dr. D'Arcy P. Mays for information on admission procedures.

## D. Minors

The Department of Statistical Sciences and Operations Research offers a minor in statistics, and in collaboration with the Department of Mathematics and Applied Mathematics, a minor in mathematics. A student may not major and minor in the department.