Glenn Hurlbert, Ph.D.
Professor and chair

math.vcu.edu

The Department of Mathematics and Applied Mathematics offers an undergraduate program leading to a Bachelor of Science in Mathematical Sciences with concentrations in applied mathematics, biomathematics, mathematics and secondary mathematics teacher preparation. The department administers the Master of Science in Mathematical Sciences concentrations in applied mathematics or mathematics and is involved in administering the Doctor of Philosophy in Systems Modeling and Analysis. The curricula of these programs are run jointly with additional concentrations offered by the Department of Statistical Sciences and Operations Research.

Students registering for:

CMSC   255Introduction to Programming4
MATH   131Introduction to Contemporary Mathematics3
MATH   141Algebra with Applications3
MATH   151Precalculus Mathematics4
MATH   200Calculus with Analytic Geometry4
MATH   211Mathematical Structures3
MATH   300Introduction to Mathematical Reasoning3
STAT   208Statistical Thinking3
STAT   210Basic Practice of Statistics3

must place into these courses either from receiving VCU credit for stated prerequisite courses (for instance, MATH   151 is a stated prerequisite course for MATH   200) or from a satisfactory score (within a 39-month period immediately preceding the beginning of the course) on the VCU Mathematics Placement Test.

MATH   001. Elementary Algebra. 0 Hours.

Semester course; 3 lecture or 3 laboratory/tutorial hours. No credit. Prerequisite: permission of the department chair. The purpose of this course is to provide laboratory and tutorial instruction for those seeking remediation or review of high school algebra. Topics include basic properties of real numbers, operations with algebraic expressions, solution of equations and inequalities, exponents and radicals, introduction to functions and graphing.

MATH   121. Perspective Geometry. 1 Hour.

Short course (5 weeks); 3 lecture hours. 1 credit. Students will examine ways in which Renaissance artists who developed linear perspective in geometry in order to paint scenes realistically infuenced the development of mathematics and geometry. Topics covered will include the foundations of projective geometry. Pascal's mystic hexagram, Brianchon"s Theorem and duality. A need for higher mathematics will also be introduced and explained. MATH   121-122-123 fulfills the math requirement for art students. The sequence can be taken in any order.

MATH   122. Tessellations. 1 Hour.

Short course (5 weeks); 3 lecture hours. 1 credit. Students will examine ways in which mathematics is rooted in both natural philosophy and art by examining tiling theory. Course topics include Penrose tilings, symmetries and various other tessellations. MATH   121-122-123 fulfills the math requirement for art students. The sequence can be taken in any order.

MATH   123. Visualization. 1 Hour.

Short course (5 weeks); 3 lecture hours. 1 credit. Students will examine ways in which mathematics has been visualized artistically and will develop their own way to express a mathematical idea. Topics covered will include fractals, knots, minimal surfaces, non-Euclidean geometry and the fourth dimension. MATH   121-122-123 fulfills the math requirement for art students. The sequence can be taken in any order.

MATH   131. Introduction to Contemporary Mathematics. 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. An exception to this policy is made in the case where the stated alternative prerequisite course has been completed at VCU. Topics include optimization problems, data handling, growth and symmetry, and mathematics with applications in areas of social choice. Major emphasis is on the process of taking a real-world situation, converting the situation to an abstract modeling problem, solving the problem and applying what is learned to the original situation. Does not serve as a prerequisite for MATH   151 or other advanced mathematical sciences courses.

MATH   141. Algebra with Applications. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: one year of high school algebra and satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course. An exception to this policy is made in the case where the stated alternative prerequisite course has been completed at VCU. Topics include sets, functions, exponents, logarithms, matrix algebra, systems of linear equations, inequalities, binomial theorems, sequences, series, complex numbers and linear programming.

MATH   151. Precalculus Mathematics. 4 Hours.

Semester course; 3 lecture and 1 mathematics laboratory/recitation hours. 4 credits. Prerequisite: MATH   141 or satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course. An exception to this policy is made in the case where the stated alternative prerequisite course has been completed at VCU. Concepts and applications of algebra and trigonometry. Topics include graphics, transformations and inverses of functions; linear, exponential, logarithmic, power, polynomial, rational and trigonometric functions.

MATH   191. Topics in Mathematics. 1-3 Hours.

Semester course; 1-3 credits. May be repeated for credit. A study of selected topics in mathematics. For a course to meet the general education requirements it must be stated in the Schedule of Classes. See the Schedule of Classes for specific topics to be offered each semester and prerequisites.

MATH   200. Calculus with Analytic Geometry. 4 Hours.

Continuous courses; 4 lecture hours. 4-4 credits. Prerequisite for MATH   200: MATH   151 or satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course. Prerequisite for MATH   201: completion of MATH   200. Limits, continuity, derivatives, differentials, antiderivatives and definite integrals. Applications of differentiation and integration. Selected topics in analytic geometry. Infinite series.

MATH   201. Calculus with Analytic Geometry. 4 Hours.

Continuous courses; 4 lecture hours. 4-4 credits. Prerequisite for MATH   200: MATH   151 or satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course. Prerequisite for MATH   201: completion of MATH   200. Limits, continuity, derivatives, differentials, antiderivatives and definite integrals. Applications of differentiation and integration. Selected topics in analytic geometry. Infinite series.

MATH   211. Mathematical Structures. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: calculus-level placement on the VCU Mathematics Placement Test within the one-year period immediately preceding enrollment in the course or MATH   151, MATH   200, MATH   201 or MGMT 212. An alternative prerequisite course may be approved at the discretion of the academic adviser. An introduction to mathematical logic and set theory, including applications in Boolean algebras and graph theory.

MATH   230. Mathematics in Civilization. 3 Hours.

Semester course; 3 lecture hours. 3 credits. For Honors College students only. The growth, development and far-reaching applications of trigonometry, navigation, cartography, logarithms and algebra through ancient, medieval, post-Renaissance and modern times are explored. Will include methods to solve mathematical problems using various historical procedures and will involve collaboration through group projects.

MATH   255. Introduction to Computational Mathematics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201. (A core course for mathematics/applied mathematics majors.) An introduction to computer algebra systems (CAS) and their use in mathematical, scientific and engineering investigations/computations. Introductory mathematical computer programming using a CAS, including implementation of problem-specific algorithms.

MATH   291. Topics in Mathematics. 1-3 Hours.

Semester course; 1-3 credits. May be repeated for credit. A study of selected topics in mathematics. See the Schedule of Classes for specific topics to be offered each semester and prerequisites.

MATH   300. Introduction to Mathematical Reasoning. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201. (A core course for mathematics/applied mathematics majors.) An introduction to basic concepts of mathematical reasoning and the writing of proofs in an elementary setting. Direct, indirect and induction proofs. Illustrations of the concepts include basic proofs from mathematical logic, elementary set theory, elementary number theory, number systems, foundations of calculus, relations, equivalence relations, functions and counting with emphasis on combinatorial proofs.

MATH   301. Differential Equations. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201. Solutions of ordinary differential equations of first order. Solutions of higher order linear differential equations with constant coefficients and variable coefficients by the methods of undetermined coefficients and variation of parameters, solutions by Laplace transforms and applications.

MATH   302. Numerical Calculus. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   255 (or knowledge of a programming language/mathematical software package) and MATH   201, or permission of the instructor. An introduction to numerical algorithms for solving systems of linear equations, finding zeroes, numerical differentiation and definite integration, optimization.

MATH   303. Investigations in Geometry. 3 Hours.

Semester course; 2 lecture and 3 laboratory hours. 3 credits. Prerequisite: MATH   361. Restricted to students majoring in the liberal studies for early and elementary education in the Bachelor of Interdisciplinary Studies program. A study of topics in Euclidean geometry to include congruence, similarity, measurement, coordinate geometry, symmetry and transformation in both two and three dimensions. These topics will be investigated using manipulatives and computer software.

MATH   305. Elementary Number Theory. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   300. Divisibility, congruences, Euler phi-function, Fermat's Theorem, primitive roots, Diophantine equations.

MATH   307. Multivariate Calculus. 4 Hours.

Semester course; 4 lecture hours. 4 credits. Prerequisite: MATH   201. The calculus of vector-valued functions and of functions of more than one variable. Partial derivatives, multiple integrals, line integrals, surface integrals and curvilinear coordinates. Lagrange multipliers; theorems of Green, Gauss and Stokes. Applications.

MATH   310. Linear Algebra. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201. Systems of linear equations, vector spaces, linear dependence, bases, dimensions, linear mappings, matrices, determinants, quadratic forms, orthogonal reduction to diagonal form, eigenvalues and geometric applications.

MATH   350. Introductory Combinatorics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201 with a minimum grade of C. An introduction to basic combinatorial concepts such as combinations, permutations, binomial coefficients, Fibonacci numbers and Pascal’s triangle; basic theorems such as the pigeonhole principle and Newton’s binomial theorem; algorithms such as bubble sort and quicksort; and discussion of basic applications such as chessboard problems, combinatorial games, magic squares and Latin squares.

MATH   351. Applied Abstract Algebra. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   300. A survey of several areas in applied abstract algebra which have applications in computer science such as groups, codes, matrix algebra, finite fields and advanced graph theory.

MATH   353. Experimental Mathematics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201 with a minimum grade of C. An introduction to a mathematical computing package, computer manipulation of lists and sets, and symbolic computing. Numerical computation will be used to investigate mathematical objects, such as integers, prime numbers, graphs, matrices and to identify properties and patterns among these objects. Random methods will be used to explore properties and patterns in long sequences and large collections.

MATH   356. Graphs and Algorithms. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   201 with a minimum grade of C. An introduction to basic graph theoretic concepts such as trees, colorings and matchings; basic theorems such as the handshaking lemma and the Gallai identities; algorithms such as Dijkstra’s and Kruskal’s; and discussion of famous open problems such as finding shortest tours for a traveling salesman.

MATH   361. Numbers and Operations. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: TEDU   101 and either MATH   131 or satisfactory score on the VCU Mathematics Placement Test within the one-year period immediately preceding the beginning of the course. Ways of representing numbers, relationships between numbers, number systems, the meanings of operations and how they relate to one another, and computation within the number systems as a foundation for algebra. Structured observations and tutoring of elementary-level students. Restricted to students majoring in the liberal studies concentration for early and elementary education in the Bachelor of Interdisciplinary Studies program.

MATH   362. Algebra and Functions. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   361. Topics include algebraic concepts, linear, quadratic, exponential, logarithmic, trigonometric functions including graphical modeling of physical phenomena. Attention will be given to the use of graphing technology, the transition from arithmetic to algebra, working with quantitative change, and the description and prediction of change. Structured observations and tutoring of elementary-level students. Restricted to B.I.S. students in the liberal studies for early and elementary education concentration.

MATH   380. Introduction to Mathematical Biology. 4 Hours.

Semester course; 3 lecture and 2 laboratory hours. 4 credits. Prerequisites: MATH   200 and BIOL   151, or permission of instructor. An introduction to mathematical biology. Various mathematical modeling tools will be covered and implemented in a range of biological areas. Additionally, the collaborative research process will be presented and discussed. Crosslisted as: BNFO   380/BIOL   380.

MATH   391. Topics in Mathematics. 1-3 Hours.

Semester course; 1-3 credits. May be repeated for credit. A study of selected topics in mathematics. See the Schedule of Classes for specific topics to be offered each semester and prerequisites.

MATH   401. Introduction to Abstract Algebra. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300 and MATH   310, each with a minimum grade of C. An introduction to groups, rings and fields from an axiomatic point of view. Coset decomposition and basic morphisms.

MATH   404. Algebraic Structures and Functions. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300 and MATH   310, each with a minimum grade of C; one additional mathematical sciences course; and permission of instructor. Semigroups, groups, rings, integral domains and fields. Exponential, logarithmic and trigonometric functions. Graphing in parametric and polar coordinates. Arithmetic and geometric sequences and series.

MATH   407. Advanced Calculus. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   300. Theoretical aspects of calculus. Topics include properties of real numbers, countable and uncountable sets, sequences and series, limits, continuity, derivatives, and Riemann integration.

MATH   409. General Topology. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH   407 with a minimum grade of C. Foundations and fundamental concepts of point-set topology. Topological spaces, continuity, convergence, connected sets, compactness, product spaces, quotient spaces, function spaces, separation properties.

MATH   415. Numerical Methods. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   255, MATH   301 and MATH   310, each with a minimum grade of C. Numerical methods for interpolation, solving systems of linear equations and initial value problems (ordinary differential equations) and the exploration of computational error.

MATH   427. Excursions in Analysis: Real. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   307, MATH   310 and MATH   407. May be repeated once for credit with a different emphasis and permission of the instructor. Intensive study of ideas and applications from real analysis.

MATH   428. Excursions in Analysis: Complex. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   307, MATH   310 and MATH   407. May be repeated once for credit with a different emphasis and permission of the instructor. Intensive study of ideas and applications from complex analysis.

MATH   429. Excursions in Analysis: Applied. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   301, MATH   307, MATH   310 and MATH   407. May be repeated once for credit with a different emphasis and permission of the instructor. Intensive study of ideas and applications from applied analysis.

MATH   430. The History of Mathematics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300, MATH   307, MATH   310, and either MATH   301 or OPER   327, all with a minimum grade of C. Surveys major trends in the development of mathematics from ancient times through the 19th century and considers the cultural and social contexts of mathematical activity.

MATH   431. Expositions in Modern Mathematics. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300, MATH   307, MATH   310, and either MATH   301 or OPER   327, all with a minimum grade of C. Descriptively studies several major ideas relevant to present-day mathematics, such as the advent of pure abstraction, difficulties in the logical foundations of mathematics, the impact of mathematics and statistics in the 20th century and the computer revolution.

MATH   432. Ordinary Differential Equations. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300, MATH   301, MATH   307 and MATH   310, each with a minimum grade of C. Existence and uniqueness of solutions, linearization and stability analysis, Lyapunov stability theory, periodic solutions, and bifurcations. Applications and simulations are emphasized.

MATH   433. Partial Differential Equations. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300, MATH   301, MATH   307 and MATH   310, each with a minimum grade of C. Parabolic (heat), hyperbolic (wave) and elliptic (steady-state) partial differential equations are studied. Solution techniques such as separation of variables, reflection methods, integral transform methods and numerical methods are demonstrated. Practical problems and applications are emphasized.

MATH   434. Discrete Dynamical Systems. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   300, MATH   301, MATH   307 and MATH   310, each with a minimum grade of C. Theory and applications of difference equations including existence and uniqueness of solutions, linearization and stability, periodic solutions, and bifurcations.

MATH   454. Using Technology in the Teaching of Mathematics. 3 Hours.

Semester course; 2 lecture and 2 laboratory hours. 3 credits. Prerequisites: MATH   200 and STAT   212, each with a minimum grade of C; six additional credits in the mathematical sciences; and permission of the instructor. Using graphing calculators, calculator-based labs and computer software packages in teaching topics in algebra, geometry, trigonometry, statistics, finance and calculus.

MATH   480. Methods of Applied Mathematics for the Life Sciences: Discrete. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   301, MATH   307, MATH   310 and MATH   380, each with a minimum grade of C. Focuses on the use of discrete dynamical system models to describe phenomena in biology and medicine. Students will explore the theoretical mathematics necessary to analyze these models. Computational solutions to these models will be developed and implemented to validate the models and to further explore the biological phenomena.

MATH   481. Methods of Applied Mathematics for the Life Sciences: ODE. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   301, MATH   307, MATH   310 and MATH   380, each with a minimum grade of C. Focuses on the use of ordinary differential equation models to describe phenomena in biology and medicine. Students will explore the theoretical mathematics necessary to analyze these models. Computational solutions to these models will be developed and implemented to validate the models and to further explore the biological phenomena.

MATH   482. Methods of Applied Mathematics for the Life Sciences: PDE. 3 Hours.

Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH   301, MATH   307, MATH   310 and MATH   380, each with a minimum grade of C. Focuses on the use of partial differential equation models to describe phenomena in biology and medicine. Students will explore the theoretical mathematics necessary to analyze these models. Computational solutions to these models will be developed and implemented to validate the model and to further explore the biological phenomena.

MATH   490. Mathematical Expositions. 3 Hours.

Semester course; 2 lecture hours. 2 credits. Prerequisites: UNIV   200 or HONR   200. Restricted to seniors in mathematical sciences with at least 85 credit hours taken toward the degree. Required for all majors in the Department of Mathematics and Applied Mathematics. A senior capstone course in the major designed to help students attain proficiency in expository mathematical writing and oral presentation, which require the efficient and effective use of mathematics and the English language. Students will learn a variety of topics in mathematics, write reviews of selected award-winning mathematics papers and write a senior paper.

MATH   492. Independent Study. 1-4 Hours.

Semester course; variable hours. 1-4 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 for 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.

MATH   493. Mathematical Sciences Internship. 3 Hours.

Semester course; the equivalent of at least 15 work hours per week for a 15-week semester. 3 credits. Mathematical sciences 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 the mathematical sciences and their applications.