Math

Department of Mathematics and Computer Science

B. Lewis Barnett III Chair
Professors Charlesworth, Davis, Fenster, Greenfield, J. Hubbard, Nall, Ross
Associate Professors Barnett, Caudill, K. Hoke, Kerckhove, Lawson, Owen, Szajda
Assistant Professor Shaw
Director of Developmental Mathematics H. Hoke

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:

MATH 211 Calculus I
MATH 212 or 232 Calculus II
MATH 235 Multivariate Calculus
MATH 245 Linear Algebra
MATH 300 Fundamentals of Abstract Mathematics
MATH 306 Abstract Algebra I
MATH 320 Real Analysis I
Four additional units of 300-level mathematics courses
CMSC 150 or 155 Introduction to Computing

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.

Note: Students are strongly advised to complete either MATH 306 or 320 prior to the senior year.

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.

6 units, including

MATH 211 Calculus I
MATH 212 or 232 Calculus II
MATH 235 Multivariate Calculus
MATH 245 Linear Algebra
Two units at the 300 level

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 (MATH 211, 212, and 235), One semester of linear algebra (MATH 245), and Two semesters of calculus-based probability and statistics (MATH 329 and 330). 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. Jason Owen in the Department of Mathematics and Computer Science.

Related Fields

Mathematical Economics

Pre-calculus

The Math and Computer Science Department at University of Richmond does not offer Pre-calculus. Students needing this course as a pre-requisite 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.

Courses

MATH 102 Problem Solving Using Finite Mathematics

Topics to demonstrate power of mathematical reasoning. Course has two components: (1) introduction to sets and symbolic logic (the fundamentals of proving results) and (2) the application of these fundamentals to at least one particular area of mathematics. The area is dependent on the instructor.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 103 An Introduction to Simulation (The Mathematics of Waiting in Line)

Introduction to fundamentals of abstracting practical situations involving waiting lines (e.g., supermarket lines, assembly lines, emergency rooms, computer networks) into mathematical models. Abstracted models will be simulated using computer software to obtain approximate solutions. Introduction to statistical analysis of data is also included.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 104 Symmetry in Tilings and Patterns

Introduction to symmetry and its use in the generation and classification of geometric patterns.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 119 Statistics for Social and Life Sciences

Introduction to statistical methods with some applications in the social and life sciences. Topics include descriptive statistics, graphical methods, estimation, hypothesis testing, regression, correlation, and the analysis of categorical data. The proper use of statistical computing software like SPSS will be emphasized. NOTE: Credit cannot be received for both Mathematics 119 and either Psychology 200 or Business Administration 301.

Unit(s): 1

MATH 190 Integrated Science/Math/Computer Science 2 with Laboratory

One of two courses taught fall semester as part of Integrated Quantitative Science program. Each semester of the course will be organized around a guiding principle that integrates several concepts. Along with co-requisite, will include ten hours for lecture and lab combination.

Prerequisite(s): High school calculus. Co-requisite: Biology 190. Acceptance to Intergrated Quantitative Science course required.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 195 Special Topics

Special topics satisfying neither major nor minor requirements.

Unit(s): .25-1

MATH 211 Calculus I

Limits, continuity, derivatives, and integrals. Derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions; applications to curve sketching; applications to the physical, life, and social sciences; Mean Value Theorem and its applications; Fundamental Theorem of Calculus.

Prerequisite(s): High school precalculus.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 212 Calculus II

Techniques of integration; applications of integration; improper integrals; Taylor's Theorem and applications; infinite series; differential equations. Credit will not be given for both Mathematics 212 and 231.

Prerequisite(s): Mathematics 211 or one year of high school AP calculus.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 219 Introduction to the Design of Experiments

The basic theory and principles related to the design of modern scientific experiments. Topics include: analysis of variance (ANOVA) for experiments with a single factor, multiple comparisons of treatment means, factorial experiments, blocking, randomized block designs, Latin square designs, random effects models, analysis of covariance, nested models, and other topics.

Prerequisite(s): Either Mathematics 119, Psychology 200, Chemistry 300, Business Administration 301, or Mathematics 330.

Unit(s): 1

MATH 232 Scientific Calculus II

Taylor polynomial approximations; discrete and continuous probability; models of dynamical systems via difference equations, differential equations, and systems of linear difference equations, including relevant topics from linear algebra.

Prerequisite(s): Mathematics 211 or one year of high school AP calculus.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 235 Multivariate Calculus

N-dimensional Euclidean space, functions of several variables, partial derivatives, multiple integrals, line and surface integrals, classical integral theorems, applications.

Prerequisite(s): Mathematics 212 or 232.

General Education Requirement: (FSSR)

Unit(s): 1

MATH 245 Linear Algebra

Vector spaces, matrices, systems of linear equations, linear transformations, applications.

Prerequisite(s): Mathematics 212 or 232 or Computer Science 222.

Unit(s): 1

MATH 300 Fundamentals of Abstract Mathematics

Logic, quantifiers, negations of statements with quantifiers, set theory, induction, counting principles, relations and functions, cardinality. Emphasis on methods of proof and proper mathematical expression.

Prerequisite(s): Mathematics 212 or 232.

Unit(s): 1

MATH 304 Mathematical Models in Biology and Medicine

Mathematical 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.

Prerequisite(s): Math 235, 245 or 300.

Unit(s): 1

MATH 306-307 Abstract Algebra I and II

Systematic study of the theory of groups, rings and fields.

Prerequisite(s): Mathematics 245 and 300. Mathematics 306 is prerequisite to 307.

Unit(s): 1-1

MATH 309 Financial Mathematics: The Theory of Interest and Investment

Develops a practical understanding of financial mathematics and interest theory in both finite 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.

Prerequisite(s): Math 235, 245 or 300.

Unit(s): 1

MATH 310 Advanced Multivariable Calculus

Differentiation of vector-valued functions, Jacobians, integration theorems in several variables. Fourier series, partial differential equations.

Prerequisite(s): Mathematics 235.

Unit(s): 1

MATH 312 Differential Equations

Introduction 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; Laplace transforms. Application and modeling of real phenomena included throughout.

Prerequisite(s): Mathematics 212 or 232. Corequisite: Mathematics 245.

Unit(s): 1

MATH 315 Modern Geometry

Geometry of surfaces in 3-dimensional space, including lengths, areas, angles, curvature, and topology. Classification of Euclidean isometries. Classification of compact surfaces having constant Gaussian curvature.

Prerequisite(s): Mathematics 235 or 245.

Unit(s): 1

MATH 320-321 Real Analysis I and II

Topological properties of the real line and Euclidean space. Convergence, continuity, differentiation, integration properties of real-valued functions of real variables.

Prerequisite(s): Mathematics 235 and 300. Mathematics 320 is prerequisite to 321.

Unit(s): 1-1

MATH 323 Discrete Mathematical Models

Applications of discrete mathematics from two viewpoints: how mathematical models are used to solve problems from other fields and how problems from other fields stimulate the development of new mathematics. Probabilistic models are emphasized. Examples of problems include analysis of board games, elections, and DNA.

Prerequisite(s): Mathematics 245.

Unit(s): 1

MATH 324 Continuous Mathematical Models

Continuous models in modern applications. Primary focus on practical understanding of the modeling process, with goals of developing individual modeling skills and ability to critically read modeling reports in scholarly journals. Mathematical topics include ordinary differential and partial differential equations.

Prerequisite(s): Mathematics 312.

Unit(s): 1

MATH 328 Numerical Analysis

Analysis and implementation of algorithms used in applied mathematics, including root finding, interpolation, approximation of functions, integration, solutions to systems of linear equations. (Same as Computer Science 328.)

Prerequisite(s): Mathematics 212 or 232, Mathematics 245, and Computer Science 150, 155, or Physics 191.

Unit(s): 1

MATH 329 Probability

Introduction to the theory, methods, and applications of randomness and random processes. Probability concepts, independence, random variables, expectation, discrete and continuous probability distributions, moment-generating functions, simulation, joint and conditional probability distributions, sampling theory, laws of large numbers, limit theorems.

Prerequisite(s): Mathematics 235. Corequisite: Mathematics 245.

Unit(s): 1

MATH 330 Mathematical Statistics

Introduction 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.

Prerequisite(s): Mathematics 329.

Unit(s): 1

MATH 331 Complex Analysis

Introduction to the calculus of functions of a single complex variable, including series, calculus of residues, and conformal mapping.

Prerequisite(s): Mathematics 310 or Physics 301.

Unit(s): 1

MATH 336 Operations Research

Linear and Integer Programming: algorithms, complexity, sensitivity, and duality. Applications such as assignments, networks, scheduling.

Prerequisite(s): Mathematics 323.

Unit(s): 1

MATH 340 Directed Independent Study

For well-qualified students who wish to work independently in areas not included in curriculum. Proposal must be approved by departmental committee.

Prerequisite(s): Permission of department chair and instructor.

Unit(s): .25-1

MATH 350 Coding Theory

Error-correcting codes are used to ensure reliable electronic communication in everything from compact disc players to deep-space transmission. Topics include linear codes, design theory, cyclic codes, counting arguments for nonexistence, decoding algorithms.

Prerequisite(s): Mathematics 245 or permission of instructor.

Unit(s): 1

MATH 355 Cryptography

History and development of "secret codes" with applications to electronic commerce, diplomatic and military communication and computer security. Emphasis on mathematical structures underlying classical, arithmetic, algebraic, mechanical, electronic, and public-key cryptosystems.

Prerequisite(s): Mathematics 245 and either Mathematics 300 or Computer Science 222 or permission of instructor.

Unit(s): 1

MATH 395 Special Topics

Selected topics in mathematics.

Prerequisite(s): Varies with topic.

Unit(s): .5-1

MATH 406 Summer Undergraduate Research

Documentation 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 full-time (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.

Prerequisite(s): Approval for summer Arts and Sciences fellowship by faculty mentor

Unit(s): 0