The curriculum in mathematical sciences promotes understanding of the mathematical sciences and their structures, uses and relationships to other disciplines. To this end, the scholarly growth of the faculty and students in the mathematical sciences is nurtured through study, research and a high standard of teaching. The curriculum provides a sound foundation for the student seeking to enter a career with a technological orientation or for the student who wishes to pursue graduate study in applied mathematics, biomathematics, mathematics, operations research, statistics, teaching mathematics in secondary schools or related fields.

A Bachelor of Science is offered jointly by the Department of Mathematics and Applied Mathematics and the Department of Statistical Sciences and Operations Research. In the Department of Statistical Sciences and Operations Research, students pursuing the Bachelor of Science in Mathematical Sciences can choose a concentration of operations research, which focuses on modern mathematical techniques for solving problems arising from other fields, such as engineering, business or economics.

Learning outcomes

Upon completing this program, students will know and know how to do the following:

  • Apply theories of mathematical programming
  • Perform stochastic models and decision analysis
  • Obtain, analyze and interpret data
  • Use commonly used operations research software
  • Identify and apply operations research models
  • Develop understanding of mathematics
  • Communicate technical information orally and in writing

Special requirements

The B.S. in Mathematical Sciences requires a minimum of 120 credits. Along with the general education requirements of the College of Humanities and Sciences and the undergraduate degree requirements, students are required to take core courses and fulfill specific requirements for the degree.

Based on the results of the Mathematics Placement Test, students may be required to take MATH   151. No more than one course in mathematics (MATH) at the 100 level can count for the general requirements toward the degree. Credit for 100-level mathematical sciences courses cannot be applied toward the mathematical sciences courses required for the major in mathematical sciences.

Double major

Students who meet the requirements for two of the concentrations within the mathematical sciences curriculum can receive a double major. To initiate a double major, students must obtain the appropriate form from the Office of Records and Registration.

Second baccalaureate degree

For students possessing a bachelor’s degree and wishing to gain undergraduate preparation in an area of mathematical sciences, second baccalaureate degrees are offered through the department. For detailed information about these programs, refer to the “Academic regulations and general degree requirement” section of this bulletin

Degree requirements for Mathematical Sciences, Bachelor of Science (B.S.) with a concentration in operations research

General Education requirements

University Core Education Curriculum (minimum 21 credits)
UNIV   111 Play VideoPlay course video for Focused Inquiry IFocused Inquiry I3
UNIV   112 Play VideoPlay course video for Focused Inquiry IIFocused Inquiry II3
UNIV   200Inquiry and the Craft of Argument3
Approved humanities/fine arts3
Approved natural/physical sciences3-4
Approved quantitative literacy3-4
Approved social/behavioral sciences3-4
Total Hours21-24
Additional College of Humanities and Sciences requirements (11-23 credits)
HUMS   202Choices in a Consumer Society1
Approved H&S diverse and global communities3
Approved H&S human, social and political behavior (fulfills University Core social/behavioral sciences)
Approved H&S literature and civilization (fulfills University Core humanities/fine arts)
Approved H&S science and technology (fulfills University Core natural/physical sciences)
Approved H&S General Education electives6-8
Experiential fine arts 11-3
Foreign language through the 102 level (by course or placement)0-8
Total Hours11-23
1

Course offered by the School of the Arts

Collateral requirements

Select one of the following natural science sequences:8-10
Sequence 1
Introduction to Biological Sciences I
and Introduction to Biological Science Laboratory I
Introduction to Biological Sciences II
and Introduction to Biological Science Laboratory II
Sequence 2
General Chemistry
and General Chemistry Laboratory I
General Chemistry
and General Chemistry Laboratory II
Sequence 3
General Physics
and General Physics
Sequence 4
University Physics I
and University Physics II
Select another course in the natural sciences that is not from the general education science and technology list. This course must be in a science different from the sequence chosen above.3-5
Total Hours11-15

Major requirements

MATH   200
MATH   201
Calculus with Analytic Geometry
and Calculus with Analytic Geometry 1
8
MATH   300Introduction to Mathematical Reasoning 13
MATH   307Multivariate Calculus4
MATH/STAT 309 13
MATH   310Linear Algebra3
MATH/OPER 327 13
OPER   427Deterministic Operations Research 13
OPER   428Stochastic Operations Research 13
SSOR   490Developing Professional Skills in Operations Research and Statistics (capstone) 13
STAT   212Concepts of Statistics (fulfills University Core quantitative literacy)3
STAT   403Introduction to Stochastic Processes 13
Select one of the following advanced mathematical science electives:3
Advanced Calculus 1
Introduction to Abstract Algebra 1
General Topology I-II 1
Select one of the following computing sequences:6-7
Introduction to Programming Using C++
and Advanced Programming Using C++
Introduction to Programming
and Data Structures and Object Oriented Programming
Engineering Programming Using C
and Advanced Engineering Programming Using C++
Select three courses from the operations research concentration electives below9-12
Total Hours54-58
1

A minimum grade of C is required in these courses/credits.

Open electives

Select two to 23 open elective credits2-23

Total minimum requirement 120 credits

Electives

For the operations research concentration, three electives must be chosen from the following list:

CMSC   302Introduction to Discrete Structures3
CMSC   303Introduction to the Theory of Computation3
CMSC   391Topics in Computer Science 23
CMSC   401Algorithm Analysis with Advanced Data Structures3
INFO   364Database Systems3
MATH   301Differential Equations3
MATH   305Elementary Number Theory3
MATH/BNFO/BIOL 380Introduction to Mathematical Biology4
MATH   391Topics in Mathematics 21-3
MATH   407Advanced Calculus3
MATH   501Introduction to Abstract Algebra3
MATH   507Bridge to Modern Analysis3
MATH   508Analysis II3
MATH   509General Topology I-II3
MATH   510General Topology I-II3
MATH   511Applied Linear Algebra3
MATH   512Complex Analysis for Applications3
MATH   515Numerical Analysis3
MATH   517Methods of Applied Mathematics3
MATH   518Methods of Applied Mathematics3
MATH/OPER 520Game Theory and Linear Programming3
MATH   525Introduction to Combinatorial Mathematics3
MATH   532Ordinary Differential Equations I3
MATH   533Partial Differential Equations I3
MATH   534Applied Discrete Dynamical Systems3
OPER   591Topics in Operations Research 21-3
SSOR   492Independent Study 22-4
STAT   310Introduction to Statistical Inference3
STAT   314Applications of Statistics 34
STAT   321Introduction to Statistical Computing3
STAT   391Topics in Statistics 23
STAT   421Applied Statistical Computing Using R3
STAT   422Structured Problem Solving Using Statistics3
STAT   435Industrial Statistics3
STAT   441Applied Statistics for Engineers and Scientists3
STAT/BIOS 513Mathematical Statistics I3
STAT/BIOS 514Mathematical Statistics II3
STAT/BIOS 544Statistical Methods II3
STAT   546Linear Models3
STAT   591Topics in Statistics 23
2

Special topics and independent study courses require prior approval from the department chair or the student’s adviser.

3

Students may not choose both STAT   314 and STAT   441.

What follows is a sample plan that meets the prescribed requirements within a four-year course of study at VCU. Please contact your adviser before beginning course work toward a degree.

Freshman year
Fall semesterHours
MATH   200 Calculus with Analytic Geometry 4
UNIV   101 Introduction to the University 1
UNIV   111 Play VideoPlay course video for Focused Inquiry I Focused Inquiry I 3
Approved H&S diverse and global communities 3
Approved H&S general education elective 3-4
 Term Hours: 14-15
Spring semester
HUMS   202 Choices in a Consumer Society 1
MATH   201 Calculus with Analytic Geometry 4
STAT   212 Concepts of Statistics 3
UNIV   112 Play VideoPlay course video for Focused Inquiry II Focused Inquiry II 3
Approved H&S human, social and political behavior 3-4
 Term Hours: 14-15
Sophomore year
Fall semester
MATH   300 Introduction to Mathematical Reasoning 3
MATH   327
3
UNIV   200 Inquiry and the Craft of Argument 3
Foreign language 101 4
Computing sequence: Select one of the following:  
CMSC   245
Introduction to Programming Using C++
or Introduction to Programming
or Engineering Programming Using C
3-4
 Term Hours: 16-17
Spring semester
MATH   307 Multivariate Calculus 4
MATH   310 Linear Algebra 3
Approved H&S science and technology 3-4
Foreign language 102 4
Computing sequence: Select one of the following with appropriate matching course from previous semester:  
CMSC   246
Advanced Programming Using C++
or Data Structures and Object Oriented Programming
or Advanced Engineering Programming Using C++
3
 Term Hours: 17-18
Junior year
Fall semester
MATH   309
3
Approved H&S general education elective 3-4
Experiential fine arts 1-3
Operations research concentration elective (listed below) 3-4
Natural sciences sequence: Select one of the following: 4-5
BIOL   151
BIOZ   151
Introduction to Biological Sciences I
and Introduction to Biological Science Laboratory I
4
CHEM   101
CHEZ   101
General Chemistry
and General Chemistry Laboratory I
4
PHYS   201 General Physics 4
PHYS   207 University Physics I 5
 Term Hours: 14-19
Spring semester
STAT   403 Introduction to Stochastic Processes 3
Approved H&S literature and civilization 3
Natural sciences elective (not from general education science and technology list and different science than chosen for sequence) 3-5
Operations research concentration elective (listed below) 3-4
Natural sciences sequence: Select one of the following with appropriate matching course from previous semester: 4-5
BIOL   152
BIOZ   152
Introduction to Biological Sciences II
and Introduction to Biological Science Laboratory II
4
CHEM   102
CHEZ   102
General Chemistry
and General Chemistry Laboratory II
4
PHYS   202 General Physics 4
PHYS   208 University Physics II 5
 Term Hours: 16-20
Senior year
Fall semester
MATH   501
Introduction to Abstract Algebra
or Advanced Calculus
or General Topology I-II
3
OPER   427 Deterministic Operations Research 3
OPER   428 Stochastic Operations Research 3
Open electives 6
 Term Hours: 15
Spring semester
SSOR   490 Developing Professional Skills in Operations Research and Statistics 3
Operations research concentration elective (listed below) 3-4
Open electives 8-9
 Term Hours: 14-16
 Total Hours: 120-135

Statistical Science and Operations Research

SSOR   490. Developing Professional Skills in Operations Research and Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: UNIV   200 or HONR   200; either OPER   427 and OPER   428, or STAT   321 and either STAT   305 or STAT   314. Capstone course designed to help students apply analysis techniques and attain proficiency in professional and academic communication in the context of statistics and operations research. Focuses on the discipline-specific skills necessary to excel in careers or graduate studies in these disciplines.

SSOR   492. Independent Study. 2-4 Hours.

Semester course; variable hours. 2-4 credits. Maximum 4 credits per semester; maximum total of 6 credits. Generally open only to students of junior or senior standing who have acquired at least 12 credits in the departmental discipline. Determination of the amount of credit and permission of instructor and department chair must be procured prior to registration in the course. The student must submit a proposal for investigating some area or problem not contained in the regular curriculum. The results of the student's study will be presented in a report.

SSOR   493. Internship. 3 Hours.

Semester course; the equivalent of at least 15 work hours per week for a 15-week semester. 3 credits. Enrollment restricted to mathematical sciences/statistics and mathematical sciences/operations research majors only with junior or senior standing. Admission by permission from the department chair. Through placement in a position in business, industry, government or the university, the student will serve as an intern in order to obtain a broader knowledge of statistics or operations research techniques and their applications.

Statistics

STAT   206. Data Analysis and Statistics for Elementary Education. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: Passing score on the PRAXIS I exam. Restricted to students majoring in liberal studies for early and elementary education. Understanding probability, describing data both graphically and numerically, regression/correlation, common distributions and interpretation, item analysis for tests, interpreting test scores and educational studies, experimental design and limitations, comparing results using t-tests. This course relies heavily on using a graphing calculator as a data-analysis tool. Students may receive credit toward graduation for only one of STAT   206, STAT   208, STAT   210, STAT   212 or SCMA   301.

STAT   208. Statistical Thinking. 3 Hours.

Semester course; 2 lecture and 1.5 laboratory hours. 3 credits. Prerequisite: satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course, or a minimum grade of C in MATH   131, MATH   141, MATH   151, MATH   200 or MATH   201. An exploration of the use of statistics in the world around us through in-depth case studies. Emphasis is on understanding statistical studies, charts, tables and graphs frequently seen in various media sources. Laboratories involve learning activities centered on case studies. Students may receive credit toward graduation for only one of STAT   206, STAT   208, STAT   210, STAT   212, STAT 312 or SCMA   301.

STAT   210. Basic Practice of Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course, or a minimum grade of C in MATH   131, MATH   141, MATH   151, MATH   200 or MATH   201. An exception to this policy is made in the case where the stated alternative prerequisite course has been completed at VCU. Designed for students who will likely take another quantitative reasoning course for which statistics may be a prerequisite. Not open to mathematical sciences or computer science majors. Topics include examining distributions, examining relationships, producing data, sampling distributions and probability, introduction to inference. Students may receive credit toward graduation for only one of STAT   206, STAT   208, STAT   210, STAT   212, STAT 312 or SCMA   301.

STAT   212. Concepts of Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course, or MATH   151, MATH   200 or MATH   201. Introductory statistics course with an emphasis on descriptive statistics, correlation and regression, probability, normal distributions, t distributions, and statistical inference. Graphing calculators will be used extensively. A core course for mathematical sciences. Students may receive credit toward graduation for only one of STAT   206, STAT   208, STAT   210, STAT   212, STAT 312 or SCMA   301.

STAT   291. Topics in Statistics. 1-3 Hours.

Semester course; 1-3 lecture hours. 1-3 credits. A study of selected topics in statistics. Specific topics may fulfill general education requirements. See the Schedule of Classes for specific topics and prerequisites.

STAT   305. Intermediate Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   200 and STAT   212, or their equivalents. A study of intermediate-level statistical inference procedures, including categorical data analysis, analysis of variance, multiple regression and nonparametric procedures. Students may receive credit toward graduation for only one of STAT   305 or STAT   314.

STAT   309. Introduction to Probability Theory. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   307 and either MATH   211 or MATH   300. A study of the mathematical theory of probability, including finite and infinite sample spaces, random variables, discrete and continuous distributions, mathematical expectation, functions of random variables and sampling distributions.

STAT   310. Introduction to Statistical Inference. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   212 and STAT/MATH 309, or permission of instructor. Framework for statistical inference. Point and interval estimation of population parameters. Hypothesis testing concepts, power functions, Neyman-Pearson lemma and likelihood ratio tests. Elementary decision theory concepts.

STAT   314. Applications of Statistics. 4 Hours.

Semester course; 4 lecture hours. 4 credits. Prerequisite: STAT   210 or 212. A study of the concepts and application of statistical methods including: estimation and hypothesis testing for two sample problems; one factor analysis of variance and multiple comparisons; randomized block designs and analysis; inferences on categorical data, including chi-square test for independence for contingency tables; simple linear regression and correlation; multiple linear regression. Special topics include distribution-free (nonparametric) methods in various statistical problems, two factor analysis of variance and the use of a statistical software package for data analysis. Students may receive credit toward graduation for only one of STAT   305 or STAT   314.

STAT   321. Introduction to Statistical Computing. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   212 and MATH   200 or their equivalents. The application of computers and computing software to statistical concepts using R, SAS and other quantitative software. Topics include data storage and retrieval, data modification and file handling, standard statistical analyses, graphical representations, practical presentation of results.

STAT   391. Topics in Statistics. 1-3 Hours.

Semester course; 1-3 lecture hours. 1-3 credits. Prerequisite: because of the changing subject matter to be treated in this course, permission of the instructor is required. A study of selected topics in statistics. See the Schedule of Classes for specific topics to be offered each semester and prerequisites.

STAT   403. Introduction to Stochastic Processes. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   307 and STAT/MATH 309. Introduction to the theory of stochastic processes and their applications. In-depth studies of random variables, conditional probability and conditional expectation. Topics include Markov chains, random walks, Poisson processes, birth and death processes and applications to classical problems (e.g., gambler's ruin, physics, etc.).

STAT   415. Statistical Consulting. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   305 and STAT   321, or their equivalents. An introduction to the techniques of statistical consulting. Topics include applying statistical concepts to real-world scenarios, dealing with messy data and communicating results.

STAT   421. Applied Statistical Computing Using R. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   310 and either STAT   305 or STAT   314, or their equivalents. Completion of STAT   321 is strongly recommended. Introduction to object-oriented programming in the R environment for use with statistical analyses. Topics include basic algorithms in R and applications involving random number generation, parametric and non-parametric data analysis and inference, linear models, simulation, and advanced data manipulation.

STAT   422. Structured Problem Solving Using Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: STAT   314, PSYC   214 or MGMT 302, or permission of instructor. Focuses on using analytic frameworks and applying statistics to solve problems in a real-world environment. Topics include discussion of analytical frameworks, problem restatement, divergent/convergent thinking, causal flow diagramming, the matrix method, decision tree analysis, review of sampling, confidence intervals, regression, ANOVA, chi squared tests, as well as applications of these concepts to solve case studies.

STAT   423. Nonparametric Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   305 and STAT   321. Introduction to statistical estimation and inference methods that require relatively mild assumptions about the underlying population distribution. Topics include classical nonparametric hypothesis testing methods, permutation tests, bootstrap methods and density estimation.

STAT   425. Multivariate Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   307, MATH   310, STAT/MATH 309, and either STAT   305 or STAT   314. Completion of STAT   421 is strongly recommended. Introduction to multivariate statistical analysis methods. Topics include multivariate probability distributions and their properties, conditional and marginal distributions, multivariate normal distribution, Hotelling’s T2 distribution, multivariate analysis of variance, repeated measures, multivariate regression, principle component analysis, exploratory factor analysis, linear discriminant analysis, cluster analysis, and regression trees. Students will use modern statistical software to perform these analyses.

STAT   435. Industrial Statistics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   309/MATH 309 and either STAT   305 or STAT   314. Introduction to statistical methods for quality control and process improvement. Topics include special versus common causes of variation, statistical thinking in industrial settings, Shewhart control charts, capability analysis, components of variation, design of experiments and response surface methods. Incorporates use of statistical software.

STAT   441. Applied Statistics for Engineers and Scientists. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   201 or equivalent, and a working knowledge of computers. An introduction to applied statistics intended primarily for students in engineering. The fundamental ideas about the collection and display of information, descriptive statistics and exploratory data analysis, elementary probability theory, frequency distributions, and sampling are covered. Other topics include tests of hypotheses and confidence intervals for one and two sample problems; ANOVA; principles of one-factor experimental designs including randomized complete black designs, fixed and random effects and multiple comparisons; correlation and linear regression analysis; control charts; contingency tables and goodness-of-fit. Students may receive degree credit for only one of STAT   441, STAT   543/BIOS   543 or STAT   641.

STAT   443. Regression. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   305 and STAT   321, or permission of instructor. Completion of MATH   310 is strongly recommended. Introduction to the concepts and methods of linear regression, logistic regression, and other nonlinear regression models. Topics include model development and assumptions, estimation of model parameters, statistical inferences about the regression model, selection of an appropriate model, and diagnostics regarding multicollinearity and influence points. Applications involve the use of a statistical software package.

STAT   475. Time Series. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: STAT   321 and either STAT   305 or STAT   314. Completion of STAT   421 is strongly recommended. Introduction to the modeling of univariate time series data. Topics include simple and exponential moving averages, Brown's double exponential smoothing, Holt-Winters model, autocorrelation, partial autocorrelation, autoregressive integrated moving average models, seasonal autoregressive moving average models, harmonic analysis and time series regression. Students will use modern statistical software to perform these analyses.

Operations Research

OPER   327. Mathematical Modeling. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   200. Fundamental concepts of mathematical modeling. Topics may include differential equation models, optimization models and probabilistic models. Practical problems will be discussed throughout.

OPER   427. Deterministic Operations Research. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC   245 or 255, MATH/OPER   327 and MATH   310. Introduction to topics in optimization including linear programming, network models and integer programming. Focuses on constructing sound models and on solving them using appropriate software. Algorithms and model properties are also discussed. Students may not receive degree credit for both OPER   427 and OPER   527.

OPER   428. Stochastic Operations Research. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: CMSC   245 or 255, MATH/STAT   309 and MATH   310. Introduction to topics in discrete-event and Monte Carlo simulation including the application of probabilistic models in real-world situations, random number generation, random variate generation and Monte Carlo integration. Students may not receive degree credit for both OPER   428 and OPER   528.