Mathematics

Department Information
Math
Department of Mathematics and Computer Science
Joanna Wares, Chair
Professors Caudill, Charlesworth, Davis, Dumbaugh, K. Hoke, Kvam, Nall, Ross
Associate Professors Arnold, Denny, Kerckhove, LeCrone, Russell, Szajda, Wares
Assistant Professors Bhakta, Jiang, Park, Ware
Directors H. Hoke, Torres 
Major
The Math Major
Note: The grade point average of the coursework comprising the major must be no less than 2.00 with no mathematics course grade below C (1.7). Students are strongly advised to consult with faculty in planning their major curriculum.
For either the Bachelor of Arts or Bachelor of Science degree:
Calculus I
Calculus II
Multivariate Calculus
Linear Algebra
Fundamentals of Abstract Mathematics
Abstract Algebra I
Real Analysis I
Introduction to Computing
Four electives in math at the 300level
Only
classes taken for 1 unit will count as electives towards the major.And for the Bachelor of Science degree:
Four other units in computer science with at least two at the 300 level, or two units beyond the introductory level in one of the following fields: physics (200 level or above), chemistry (200 level or above), or biology (numbered higher than 205).
Students are expected to fulfill all prerequisites necessary for courses within the major. Prerequisites do not count toward the major unless otherwise noted.
Notes:
Students are strongly advised to complete either
or prior to the senior year.Any MATH and CMSC doublemajor, or MATH major with CMSC minor, having earned at least an A in
may exempt from but is required to complete an additional CMSC 300level elective to complete the CMSC major or minor. 
Minor
The Math Minor
Note: The grade point average of the coursework comprising the minor must be no less than 2.00 with no mathematics course grade below C (1.7). Students are strongly advised to consult with faculty in planning their minor curriculum.
Six units, including:
Calculus I
Calculus II
Multivariate Calculus
Linear Algebra
Two units at the 300 level

Data Science and Statistics Concentration
The Data Science and Statistics Concentration
The concentration in data science and statistics with a major in mathematics requires six units (where applicable, these may also count for major requirements).
Data Structures with LabIntroduction to Data Science
Probability
Mathematical Statistics
Statistical Learning (may replace with Machine Learning)One unit, chosen from:
Database Systems
Simulation
Selected Topics (with departmental approval)
Introductory Econometrics
Selected Topics in MathematicsNote: Students completing a concentration in data science and statistics may not minor in mathematics or computer science.

Actuarial Sciences
Actuarial Sciences
Students interested in becoming an actuary should consider either majoring in mathematics or mathematical economics. Either of these options will provide the necessary education that can lead to successful entry into the field. A strong background in mathematics is essential for students interested in a career as an actuary. This should include
Three semesters of calculus (, , and ),One semester of linear algebra (), andTwo semesters of calculusbased probability and statistics (and ).In addition, courses in applied statistics, computer science, economics, and finance are also extremely valuable.The best way to ensure that you are attractive from an employment perspective is to pass the beginning actuarial examinations while you are still a student. Actuaries achieve professional status by passing a set of examinations and by satisfying certain educational experiences that are prescribed by the CAS and the SOA. The concepts contained in these assessments can be based on college courses (a B or better is required), or an exam can be taken. For more information about preparing to be an actuary, contact Dr. Kathy Hoke in the Department of Mathematics and Computer Science.

Related
Related Fields

Precalculus
Precalculus
The Math and Computer Science Department at University of Richmond does not offer Precalculus. Students needing this course as a prerequisite to other courses will need to complete it in high school or make their own arrangements to complete it later. The course is not eligible for transfer and will not count toward a B.A., B.S., or B.S.B.A. degree at the University of Richmond.

Honors
Honors Program in Mathematics
Promising, qualified math majors are invited by the faculty to apply to the honors program in mathematics. Successful completion of the program is designated on the student's academic record and diploma.
To qualify, students must have:
 completed 19 or more units of University work;
 earned a cumulative grade point average of at least 3.0;
 completed 3.5 or more units in mathematics courses at the level of or higher;
 submitted a recommendation letter from a member of the mathematics faculty;
 submitted an application to the program, working in conjunction with a faculty member to describe a topic and develop a plan for completing the thesis.
To earn honors in mathematics, students must have successfully completed:
 two 300level courses taken for honors credit;
 one year (2 units) of directed independent study, wherein the student works with one or more faculty members on a selected project;
 the presentation of an honors paper to the mathematics faculty as a culmination of the independent study (the paper must be accepted by the departmental committee.)
Courses

MATH 102 Problem Solving Using Finite Mathematics
Units: 1
Fulfills General Education Requirement (FSSR)
DescriptionTopics to demonstrate power of mathematical reasoning. Course has two components: (1) introduction to the fundamentals of mathematical proof, and (2) the application of these fundamentals to at least one particular area of mathematics. The area is dependent on the instructor. MATH 102 is not open to MATH, CMSC, MTEC, BUAD, or ACCT majors.

MATH 195 Special Topics
Units: .251
DescriptionSpecial topics satisfying neither major nor minor requirements.

MATH 209 Introduction to Statistical Modeling
Units: 1
DescriptionTopics will include exploratory data analysis, correlation, linear and multiple regression, design of experiments, basic probability, the normal distribution, sampling distributions, estimation, hypothesis testing and randomization approach to inference. Exploratory graphical statistics, model building and model checking techniques will be emphasized with extensive use of statistical software for data analysis.
PrerequisitesPrecalculus.

MATH 211 Calculus I
Units: 1
Fulfills General Education Requirement (FSSR)
DescriptionLimits, continuity, derivatives, and integrals. Derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions; the derivative as a rateofchange; linear approximations; Fundamental Theorem of Calculus; applications to the sciences, social sciences, and economics.
PrerequisitesHigh school precalculus.

MATH 212 Calculus II
Units: 1
Fulfills General Education Requirement (FSSR)
DescriptionTechniques of integration; applications of integration; improper integrals; Taylor's Theorem and applications; infinite series; differential equations; applications to the sciences, social sciences, and economics.

MATH 235 Multivariate Calculus
Units: 1
Fulfills General Education Requirement (FSSR)
DescriptionNdimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, line and surface integrals, classical integral theorems, applications.
PrerequisitesMATH 212.

MATH 245 Linear Algebra
Units: 1
DescriptionVector spaces, matrices, systems of linear equations, linear transformations, applications.
PrerequisitesMATH 212 or CMSC 222.

MATH 288 Mathematics Apprenticeship
Units: .25.5
DescriptionParticipation in practical application of mathematics skills, such as statistics, data science, or mathematical modeling, with supervision of mathematics or statistics faculty. Does not count for mathematics major or minor or for mathematical economics major. No more than a total of 1.5 units of MATH 288 may count toward the total number of units required for a degree.

MATH 289 Introduction to Data Science
Units: 1
DescriptionMultiple linear regression, logistic regression, ANOVA and other modeling based topics. Exploratory graphical methods, model selection and model checking techniques will be emphasized with extensive use a statistical programming language (R) for data analysis.
PrerequisitesMath 209 OR CMSC150 OR Bio 320 OR Econ 270.

MATH 300 Fundamentals of Abstract Mathematics
Units: 1
DescriptionLogic, quantifiers, negations of statements with quantifiers, set theory, induction, counting principles, relations and functions, cardinality. Includes introductory topics from real analysis and abstract algebra. Emphasis on methods of proof and proper mathematical expression.
PrerequisitesMATH 212.

MATH 304 Mathematical Models in Biology and Medicine
Units: 1
DescriptionMathematical models in modern biological and medical applications. Primary focus on practical understanding of the modeling process, and development of requisite modeling skills. Topics include discrete and continuous dynamical systems, including parameter estimation.
PrerequisitesMATH 235, 245 or 300.

MATH 306 Abstract Algebra I
Units: 1
DescriptionAn introduction to the theory of groups. Topics include subgroups, cyclic groups, permutation groups, homomorphisms, isomorphisms, cosets, Lagrange's Theorem, normal subgroups, and the Fundamental Theorem of Finite Abelian Groups.
PrerequisitesMATH 245 and MATH 300.

MATH 307 Abstract Algebra II
Units: 1
DescriptionAn introduction to the theory of rings and fields. Topics include rings, integral domains, ideals, factor rings, polynomial rings, ring homomorphisms, fields, and extension fields.
PrerequisitesMATH 306.

MATH 309 Financial Mathematics: The Theory of Interest and Investment
Units: 1
DescriptionDevelops a practical understanding of financial mathematics and interest theory in both discrete and continuous time. This theory includes the fundamentals of how annuity functions are applied to the concepts of present and accumulated value for various cash flow streams and how this is used for future planning in valuation, pricing, duration, immunization, and investment. Topics include: rates of interest and discount, the force of interest, level and varying annuities, evaluation of financial instruments (e.g. bonds, stocks, leveraged strategies), measures of interest rate sensitivity, and the term structure of interest rates.
PrerequisitesMATH 235 or 245 or 300.

MATH 310 Advanced Multivariable Calculus
Units: 1
DescriptionDifferentiation of vectorvalued functions, Jacobians, integration theorems in several variables. Fourier series, partial differential equations.
PrerequisitesMATH 235.

MATH 312 Differential Equations
Units: 1
DescriptionIntroduction to ordinary differential equations and their use as models of physical systems. Linear and nonlinear equations and systems of equations, including existence and uniqueness theorems, analytical solution techniques, numerical methods, and qualitative analysis. Includes studies of global behavior and local stability analysis of solutions of nonlinear autonomous systems; bifurcation analysis. Application and modeling of real phenomena included throughout.
PrerequisitesMATH 212 and MATH 245.

MATH 315 Modern Geometry
Units: 1
DescriptionGeometry of surfaces in 3dimensional space. Arc length, Frenet frame, parallel translation and geodesics. Gaussian curvature, constant curvature surfaces, GaussBonnet theorem. Topological classification of compact surfaces.
PrerequisitesMATH 235 or 245.

MATH 319 Game Theory
Units: 1
DescriptionMathematical introduction to game theory. Foundational material on rationality and the expected utility theorem; problems for single decisionmakers who maximize utility in uncertain circumstances; classical twoperson matrix games and Nash equilibria; dynamic games, behavioral strategies, and repeated games; population games and evolutionarily stable strategies in biology; evolutionary dynamics.
PrerequisitesMATH 245.

MATH 320 Real Analysis I
Units: 1
DescriptionTopological properties of the real line and Euclidean space. Convergence, continuity, differentiation, integration properties of realvalued functions of real variables.
PrerequisitesMATH 235 and 300.

MATH 328 Numerical Analysis
Units: 1
DescriptionAnalysis and implementation of algorithms used in applied mathematics, including root finding, interpolation, approximation of functions, integration, solutions to systems of linear equations. Computer error. (Same as Computer Science 328.)
PrerequisitesMATH 245 and CMSC 150.

MATH 329 Probability
Units: 1
DescriptionIntroduction to the theory, methods, and applications of randomness and random processes. Probability concepts, independence, random variables, expectation, discrete and continuous probability distributions, momentgenerating functions, simulation, joint and conditional probability distributions, sampling theory, laws of large numbers, limit theorems.
PrerequisitesMATH 235 and MATH 245, which can be taken concurrently.

MATH 330 Mathematical Statistics
Units: 1
DescriptionIntroduction to basic principles and procedures for statistical estimation and model fitting. Parameter estimation, likelihood methods, unbiasedness, sufficiency, confidence regions, Bayesian inference, significance testing, likelihood ratio tests, linear models, methods for categorical data, resampling methods.
PrerequisitesMATH 329.

MATH 331 Complex Analysis
Units: 1
DescriptionIntroduction to the calculus of functions of a single complex variable, including series, calculus of residues, and conformal mapping.
PrerequisitesMATH 235 OR PHYS 301.

MATH 336 Operations Research
Units: 1
DescriptionLinear and Integer Programming: algorithms, complexity, sensitivity, and duality. Applications such as assignments, networks, scheduling.
PrerequisitesMATH 245 and either MATH 300 or CMSC 222, which can be taken concurrently.

MATH 340 Directed Independent Study
Units: .251
DescriptionFor wellqualified students who wish to work independently in areas not included in curriculum. Proposal must be approved by departmental committee.
PrerequisitesPermission of department chair and instructor.

MATH 350 Coding Theory and Cryptography: The Mathematics of Communication
Units: 1
DescriptionErrorcorrecting codes are used to ensure reliable electronic communication in everything from Blue Ray players to deepspace transmission. Cryptographic systems are developed to keep communication secret in everything from ecommerce to military communication. This course develops the mathematics underlying the transmission of messages. In coding theory, we will develop theoretical constraints on codes, construction methods for good codes, and algorithms for encoding and decoding efficiently. In cryptography, we will explore historically important systems as well as modern publickey cryptosystems.
PrerequisitesMATH 245 and either MATH 300 or CMSC 222 or permission of instructor.

MATH 388 Individual Internship
Units: .251
DescriptionNo more than 1.5 units of internship in any one department and 3.5 units of internship overall may be counted toward required degree units.
PrerequisitesPermission of department chair.

MATH 389 Statistical Learning
Units: 1
DescriptionComputational statistics and statistical algorithms for building predictive models from large data sets. Topics include model complexity, hyperparameter tuning, over and underfitting, and the evaluation of predictive performance. Models covered include linear regression, penalized regression, additive models, gradientboosted trees, and neural networks. Applications are drawn from many areas, with a particular focus on processing unstructured text and image corpora.
PrerequisitesMath 289 or Math 329.

MATH 395 Special Topics
Units: 1
DescriptionSelected topics in mathematics.
PrerequisitesVaries with topic.

MATH 396 Selected Topics in Mathematics
Units: 1
DescriptionSelected topics in mathematics for mathematical economics.

MATH 406 Summer Undergraduate Research
Units: 0
DescriptionDocumentation of the work of students who receive summer fellowships to conduct research [or produce a creative arts project] in the summer. The work must take place over a minimum of 8 weeks, the student must engage in the project fulltime (at least 40 hours per week) during this period, and the student must be the recipient of a fellowship through the university. Graded S/U.
PrerequisitesApproval for summer Arts and Sciences fellowship by faculty mentor