DEPARTMENT OF STATISTICAL SCIENCES
AND OPERATIONS RESEARCH HANDBOOK
TABLE OF CONTENTS
I. INTRODUCTION top
The mathematical sciences program in the
College of Humanities and Sciences at Virginia Commonwealth
University offers a variety of options and opportunities for
students. As new discoveries have been made and new applications
of the mathematical sciences have become important, separate
degree programs have been developed. The Department of Mathematics
and Applied Mathematics offers mathematical sciences degree
programs in the following areas:
- APPLIED MATHEMATICS
- MATHEMATICS
- MATHEMATICS EDUCATION
The mathematics education program is offered
in conjunction with the School of Education. Additionally, the
Department of Statistical Sciences and Operations Research offers
mathematical sciences degree programs in the following areas:
- OPERATIONS RESEARCH
- STATISTICS
Virginia Commonwealth University offers complete
programs in each of these disciplines at both the undergraduate
and master's level. The collaboration between the two departments
to manage the mathematical sciences degree allows students interested
in any one of these areas to see the interrelationships between
this area and the others. This is particularly important since
each of the disciplines uses skills and techniques from the
others. For example, statisticians make use of mathematics and
computer science; individuals employed in the area of operations
research make use of mathematics, computer science and statistics;
and teachers of mathematics should be aware of the application
of mathematics in all of these areas. This arrangement makes
it possible for students with interest and ability in quantitative
areas to sample a variety of courses and then make a decision
concerning their particular program.
Department Location top
The Department of Statistical Sciences and
Operations Research is located on the second floor of Oliver
Hall PH (Kapp wing), phone (804) 828-1301, ext. 103. The Department
Chair located in room 2054 and the Administrative Assistant
in room 2052 can answer many of your questions and direct you
to an appropriate person for answers to other questions.
Computing Facilities top
The Department of Statistical Sciences and
Operations Research and the Department of Mathematics share
computing resources. Currently, they operate an undergraduate
lab (24 machines) and a graduate lab (7 machines) equipped
with high end Windows based PCs. They also operate two teaching
labs equipped with computers for each student (16 computers
in one and 24 in another) and a computer with projection and
audio/visual equipment for the instructor. Several other classrooms
are also equipped with computer projection and audio/visual
equipment. All computers are connected to the College and University
networks as well as have Internet access. Standard desktop
software is installed on all machines as well as specialized
software for mathematical computation, statistical analysis,
decision analysis, computer simulation, and optimization.
II. ADVISING top
Mathematics Placement Test
All incoming students who wish to enroll
in mathematical sciences courses must take the Mathematics Placement
Test to determine their appropriate starting level. On the basis
of the results of this test, students may be required to take
one or more preparatory courses before enrolling in the courses
required for a mathematical sciences degree. For this reason
it is important that you take this test before developing your
plan of study.
The test covers basic algebra and trigonometry
and is generally taken during summer testing, advising and registration
(STAR). If you are unable to attend STAR or begin your studies
in other than the fall semester, it would be advisable to arrange
to take the test before you register. This can be done by going
to room 3013 in Oliver Hall on campus or by calling (804) 828-1320.
Advisors
Upon admission to the university each student
is assigned an advisor. The initial contact with this advisor
should be made near the beginning of the first semester. Students
who are transferring to VCU from another university should have
their transfer credit evaluated by the dean's office, Room 205
Hibbs, prior to meeting with their advisor. The faculty advisor
is an important personal link with the university organization.
The advisor helps the student establish a relationship between
the student's special needs and the university services, assists
the student in career selection, and helps the student understand
administrative procedures. Faculty advisors also assist students
in the selection of courses and the preparation of the graduation
application.
Graduation Worksheet
Each student, together with their advisor,
should continually update a graduation worksheet that allows
the student to plan a course of study that will meet all of
the degree requirements. A worksheet can picked up from the
Administrative Assistant in room 2052 Oliver Hall.
A completed graduation worksheet containing
your intended plan of study should be submitted to the department
Undergraduate Credentials Committee for approval some time in
the junior year. THIS IS AN IMPORTANT STEP IN THE GRADUATION
PROCESS. It is designed to inform you of any possible deficiencies
in your plan while you still have time to correct them.
University Career Center
The University Career Center located in the
University Student Commons at 907 Floyd Avenue provides services
both to help you clarify career goals and to assist you in locating
employment as you near graduation. Career counseling and special
career planning groups are available for those students who
desire assistance in selecting a career path. In addition, the
University Career Center maintains a sizable collection of career
literature.
A variety of placement services are also
offered to seniors nearing graduation. Students who register
with the Placement Office will receive weekly notices regarding
employment opportunities and may participate in on-campus interviews
with prospective employers. In order to participate in the interview
program, you must have a resume on file with the placement office.
They have sample resumes and offer short courses to help you
write your resume.
For more information, visit the VCU Career
Center at http://www.students.vcu.edu/careers/.
III. DESCRIPTION OF PROGRAMS top
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.
A. Bachelor of Science in Mathematical Sciences top
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
top
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 top
The Department of Statistical Sciences and
Operations Research offers a post-baccalaureate 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.
D. Cooperative Education top
Co-op or "cooperative education"
allows students to combine classroom learning with PAID, supervised
work experiences related to their majors. Virginia Commonwealth
University's co-op program places students in Richmond and throughout
the United States with governmental agencies, private industries,
small businesses and non-profit organizations. Upon graduation,
co-op students have both a degree and practical work experience
that will help them succeed in the work place. Co-op students
have valuable opportunities to earn partial funds to support
a college education, to make professional contacts, to develop
professional work habits, and to test career interests.
Co-op is open to all degree-seeking VCU
students. Undergraduates must have completed at least 23 semester
credits. Transfer students must complete one full semester at
VCU before becoming eligible for the program. An overall grade
point average of 2.5 is required for sophomores; juniors and
seniors must have a 2.0 grade point average. Graduate and certificate
students must be in good academic standing with the university.
Employers may set their own eligibility requirements, and they
have the final decision in the hiring process.
Co-op offers two types of work schedules.
The parallel schedule enables students to work 15 to 20 hours
per week while attending classes. Parallel students must carry
a minimum of six credits per semester (summer semester excluded).
The alternating schedule allows students to rotate between semesters
of full-time study and full-time work. In order to maximize
the co-op experience, most students will work two or more semesters
with co-op employers. Once placed, co-op students register for
the appropriate non-credit co-op course each semester they work
(including summer semesters) and pay the co-op fee of $35 for
part-time placements and $70 for full-time placements.
For additional information, contact:
Cheryl Melton
University Career Center
Division of Student Affairs
Virginia Commonwealth University
907 Floyd Ave., Student Commons Room 130
PO Box 842508
Richmond VA 23284-2508
Telephone: 804-828-1645
Fax: 804-828-2060
For more information on VCU Co-Op programs, visit http://www.pubinfo.vcu.edu/dsa/coop/index.html.
E. Minors top
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. The requirements for the minors appear below.
IV. Program Requirements
Basic Requirements for the Bachelor of Science Degree in Mathematical
Sciences top
To qualify for any mathematical sciences
degree the student must satisfy the general education requirements
of the College of Humanities and Sciences and the University
for a Bachelor of Science degree. The College and University
requirements are described in the undergraduate bulletin and
on the graduation worksheet. What follows are the mathematical
sciences program requirements.
Science Requirement
Mathematical sciences majors must satisfy
the following natural science requirements:
- A. Complete one of the following sequences:
- 1. BIOL 151-152, BIOZ 151L-152L
- 2. CHEM 101-102, CHEZ 101L-102L
- 3. PHYS 207-208 or PHYS 201-202
- B. Complete another course, including laboratory, in the
natural sciences from List D in the Undergraduate Bulletin.
This course must be in the biological sciences if the CHEM
or PHYS sequence was selected in (A) above; it must be in
the physical sciences if the BIOL sequence was selected in
(A).
- C. Complete one other course in the natural sciences OR
complete a minor or second major offered outside the mathematical
sciences program.
The student may use these courses in fulfillment
of the appropriate College of Humanities and Sciences general
education requirements.
Writing Requirement
The general education requirements for the
Bachelor of Science degree include the provision that each student
must take ENGL 101 and ENGL 200, passing each with a grade of
C or better, and complete two writing intensive (WI) courses,
at least one of which must be in the student’s major.
Students in operations research and statistics
should take OPER/STAT 490 – Communications in Statistics
and Operations Research – to satisfy the in-major writing
intensive requirement. This 2-credit course counts toward the
minimum of 41 credits in mathematical sciences courses.
Mathematical Sciences Core
All students majoring in mathematical sciences
are required to take at least 41 credits in courses labeled
CMSC, MATH, OPER, or STAT. These must include at least 24 credits
in upper-level (300-500 level) courses and the following core
courses:
- MATH 200-201 - Calculus with Analytic Geometry I, II
- STAT 212 - Concepts of Statistics
- MATH 307 - Multivariate Calculus
- MATH 310 - Linear Algebra
Each student should discuss with his or her
advisor the recommended courses for the freshman year. Since
most upper-level mathematical science courses have one or more
core courses as a prerequisite, these courses should be taken
as early as possible. The mathematics placement test is a requirement
to help determine this selection. Credit for 100-level mathematical
sciences courses may not be applied toward the mathematical
sciences credits required for the mathematical sciences major.
Bachelor of Science in Mathematical Sciences/Operations Research
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In addition to the core courses required
for all B.S. degree programs in mathematical sciences, the following
courses are required for the operations research concentration:
- MATH 211 - Mathematical Structures
- STAT 309 - Introduction to Probability Theory
- OPER 527-528 - Mathematical Foundations of Operations Research
I, II
- OPER 327 - Mathematical Modeling or
STAT 503 - Introduction to Stochastic Processes
- CMSC 255 - Structured Programming
- OPER 490 - Communications in Statistics and Operations
Research
- four additional upper-level credits in the mathematical
sciences
Students considering the program in operations research should
take MATH 211 and STAT 309 as soon as possible. The four additional
upper-level credits should be chosen to match one's interests.
Bachelor of Science in Mathematical Sciences/Statistics top
In addition to the core courses required
for all B.S. degree programs in mathematical sciences, the following
courses are required for the statistics concentration:
- STAT 309 - Introduction to Probability Theory
- STAT 314 - Applications of Statistics
- STAT 404 - Introduction to Statistical Inference
- STAT 544 - Statistical Methods II
- CMSC 255 - Structured Programming
- STAT 490 - Communications in Statistics and Operations
Research
- Six additional upper-level credits in mathematical sciences,
of which at least three must be in statistics
Certificate in Statistics top
The Department of Statistical Sciences and
Operations Research offers a certificate program in statistics
for students who have received a bachelor's degree in other
areas. The primary goal of the program is to allow students
with undergraduate majors in science, engineering and the social
sciences an opportunity to acquire the formal training in statistics
that is currently in demand in industry and government. Some
students may also find this program a useful way to prepare
for graduate study in statistics.
The certificate program in statistics requires
completion of a minimum of 32 approved credits at the 200 level
or higher in mathematical sciences or related areas. A maximum
of 14 credits toward certification may be transferred from course
work completed before or after receiving a bachelor’s
degree. At least 18 approved credits must be from courses in
statistics and probability at the 300 level or higher and must
be taken at VCU. No more than six of these 18 credits can be
from courses taken before admission to the certificate program.
The student must achieve a GPA (on courses taken at VCU) of
2.5 or better with no grade below “C.” All requirements
for the certificate must be completed within five years of admission
to the program.
The following courses are required:
- MATH 200-201 Calculus with Analytical
Geometry (or equivalent)
- CMSC 201 Introduction to Computing Using
FORTRAN or
CMSC 245 Introduction to Programming Using C++ or
CMSC 255 Structured Programming (or equivalent)
- STAT 210 Basic Practice of Statistics
(or equivalent)
- STAT 309 Introduction to Probability Theory
- STAT 314 Applications of Statistics
- STAT 404 Introduction to Statistical Inference
- STAT/BIOS 544 Statistical Methods II
Students will work closely with the program
coordinator in selecting appropriate elective courses. While
some students may have the background necessary for a 600-level
graduate course, it is expected that most elective courses will
be drawn from the 300- to 500-level statistics course offerings
of the department. Statistics courses taught in other units
of the university may be credited toward the certificate with
the permission of the program coordinator.
Students seeking to enter the certificate
program in statistics should contact Dr.
James Davenport for information on admission procedures.
Minors in Mathematical Sciences/Statistics top
A minor in mathematical sciences/statistics
shall consist of at least 18 credits in courses labeled CMSC,
MATH, OPER, or STAT, including a minimum of one semester of
calculus and nine upper-level (300-500 level) credits in statistics
courses. Neither STAT 208 or STAT 210, nor any 100-level mathematics
can be used to fulfill the required 18 credits. It is strongly
recommended, but not required, that students seeking a minor
in statistics take STAT 212 Concepts of Statistics. A minimum
grade-point average of 2.0 must be achieved in the minor.
Course Selections (Special Cases) top
1. Students in the Department of Statistical
Sciences and Operations Research who entered the program as
transfers from other schools, or changed their majors to Mathematical
Sciences, may petition the Undergraduate Credentials Committee,
through their advisors, for waiver of the STAT 212 requirement
provided they have taken STAT 208 or STAT 210 (or equivalent)
and have successfully completed an upper-level statistics course.
2. The material covered in certain courses
outside the department overlaps with that of some mathematical
sciences courses. This may prevent applying one of these courses
to a degree in mathematical sciences. If you have any questions
about a particular course be sure to check with your advisor.
The Major Grade Point Average top
In order to receive a Bachelor of Science
degree in the department a student must have a grade point average
of 2.0 or better in his or her major. At the time of the filing
of the graduation application the student will select those
CMSC, MATH, OPER, and STAT courses to be used to fulfill the
major requirements (see "major GPA"). The list of
courses selected must include at least enough courses to fulfill
the minimum major requirements for the degree and for the concentration,
if one is chosen. Additional mathematical sciences courses may
be included in the list with the following exceptions:
- 100-level courses (or their equivalent)
and 200-level computer-programming courses cannot be included.
- Any other course that is not applicable
toward the major according to the Undergraduate Bulletin cannot
be included.
A mathematical sciences course that has been
omitted from this list of major courses (and from the major
GPA computation) can still be applied toward the 120 credits
required by the College by listing it as an elective on the
graduation worksheet.
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