Department of Mathematics and Applied Mathematics 1 DEPARTMENT OF MATHEMATICS Mathematics and applied mathematics MATH 502. Abstract Algebra I. 3 Hours. AND APPLIED MATHEMATICS Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH 401 with a minimum grade of a C, or permission of instructor. A study of Glenn Hurlbert, Ph.D. groups, subgroups, quotient groups and homomorphisms, group actions, Professor and chair sylow theorems, direct and semi-direct products, rings, integrals domains, and polynomial rings. math.vcu.edu (http://www.math.vcu.edu) MATH 505. Modern Geometry. 3 Hours. The Department of Mathematics and Applied Mathematics offers an Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH 300, and undergraduate program leading to a Bachelor of Science in Mathematical MATH 307 or MATH 310, or permission of instructor. Topics in Euclidean, Sciences with concentrations in applied mathematics, biomathematics, projective and non-Euclidean geometries from a modern viewpoint. mathematics and secondary mathematics teacher preparation. The MATH 507. Bridge to Modern Analysis. 3 Hours. department administers the Master of Science in Mathematical Sciences Semester course; 3 lecture hours. 3 credits. Enrollment restricted concentrations in applied mathematics or mathematics and is involved to student with graduate standing. Metric spaces, normed vector in administering the Doctor of Philosophy in Systems Modeling and spaces, inner-product spaces and orthogonality, sequences and series Analysis. The curricula of these programs are run jointly with additional of functions, convergence, compactness, completeness, continuity, concentrations offered by the Department of Statistical Sciences and contraction mapping theorem, and inverse and implicit function Operations Research. theorems. • Mathematical Sciences, Master of Science (M.S.) with a MATH 511. Applied Linear Algebra. 3 Hours. concentration in applied mathematics (http://bulletin.vcu.edu/ Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 310 or graduate/college-humanities-sciences/mathematics-applied- permission of instructor. The algebra of matrices, the theory of finite mathematics/mathematical-sciences-ms-concentration-applied- dimensional vector spaces and the basic results concerning eigenvectors mathematics/) and eigenvalues, with particular attention to applications. • Mathematical Sciences, Master of Science (M.S.) with a MATH 515. Numerical Analysis. 3 Hours. concentration in mathematics (http://bulletin.vcu.edu/graduate/ Semester course; 3 lecture hours. 3 credits. Enrollment restricted to college-humanities-sciences/mathematics-applied-mathematics/ student with graduate standing. Knowledge of a programming language mathematical-sciences-ms-concentration-mathematics/) or mathematical software package recommended. Theoretical derivation • Systems Modeling and Analysis, Doctor of Philosophy (Ph.D.) and implementation of numerical methods. Topics to include direct (http://bulletin.vcu.edu/graduate/college-humanities-sciences/ methods, data fitting, differentiation, integration and solutions to ordinary mathematics-applied-mathematics/systems-modeling-analysis-phd/) differential equations. • Systems Modeling and Analysis, Doctor of Philosophy (Ph.D.) with MATH 535. Introduction to Dynamical Systems. 3 Hours. a concentration in applied mathematics (http://bulletin.vcu.edu/ Semester course; 3 lecture hours. 3 credits. Enrollment restricted graduate/college-humanities-sciences/mathematics-applied- to students with graduate standing. Theoretical and computational mathematics/systems-modeling-analysis-phd-concentration- introduction to continuous and discrete dynamical systems with applied/) applications. Topics include existence and uniqueness of solutions, • Systems Modeling and Analysis, Doctor of Philosophy (Ph.D.) with stability and bifurcations. a concentration in discrete mathematics (http://bulletin.vcu.edu/ MATH 550. Combinatorics. 3 Hours. graduate/college-humanities-sciences/mathematics-applied- Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH 211 mathematics/systems-modeling-analysis-phd-concentration- or MATH 300; and MATH 350, both with a minimum grade of C; or discrete/) permission of instructor. Topics include basic counting, binomial • Systems Modeling and Analysis, Doctor of Philosophy (Ph.D.)with theorems, combinations and permutations, recurrence relations, a concentration in industrial statistics and operations research generating functions, and basic graph theory with emphasis to (http://bulletin.vcu.edu/graduate/college-humanities-sciences/ applications. mathematics-applied-mathematics/systems-modeling-analysis-phd- MATH 553. Linear Optimization. 3 Hours. concentration-industrial/) Semester course; 3 lecture hours. 3 credits. Enrollment is restricted • Systems Modeling and Analysis, Doctor of Philosophy (Ph.D.) with a to graduate students in mathematical sciences or systems modeling concentration in statistics and data science (http://bulletin.vcu.edu/ and analysis programs or by permission of the instructor. Introduction graduate/college-humanities-sciences/mathematics-applied- to linear optimization and mathematical programming. Course mathematics/systems-modeling-analysis-phd-concentration-stats- addresses the simplex algorithm, duality, the primal-dual relationship, data/) complementary slackness and optimality certificates. Other topics may include integer linear programming, relaxations, cutting planes • Mathematics and applied mathematics (MATH) (p. 1) and related applications, including matching theory and other classical • Systems modeling and analysis (SYSM) (p. 3) combinatorial problems. MATH 555. Dynamics and Multivariable Control I. 3 Hours. Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 301 and 310 or the equivalent. Systems of differential equations with controls, linear control systems, controllability, observability, introduction to feedback control and stabilization. Crosslisted as: EGRE 555. 2 Department of Mathematics and Applied Mathematics MATH 556. Graph Theory. 3 Hours. MATH 632. Ordinary Differential Equations I. 3 Hours. Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH 211 Semester course; 3 lecture hours. 3 credits. Prerequisites: MATH 507 or MATH 300; MATH 310; and MATH 356, each with a minimum grade and MATH 535. Linear systems theory; existence, uniqueness and of C; or permission of instructor. Introduction to graph classes, graph continuous dependence for nonlinear systems; invariant manifolds; invariants, graph algorithms, graph theoretic proof techniques and stable manifold theorem; Hartman-Grobman theorem; Lyapunov stability applications. theory; Hamiltonian and gradient systems. MATH 585. Biomathematics Seminar:____. 1 Hour. MATH 633. Partial Differential Equations. 3 Hours. Semester course; 2 lecture hours. 1 credit. Prerequisite: MATH 301 Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 507. or permission of instructor. May be repeated with different thematic Classification of partial differential equations, initial and boundary content. Opportunity for students to develop their understanding of value problems, well-posedness; first-order equations and methods the connection between mathematics and the areas of biology and of characteristics; wave equation; heat equation, transform methods, medicine. Activities include reading of classical and contemporary maximum principle, energy methods; Laplace's equation. Other topics research literature, attending seminar talks and class discussions. may vary depending on the interest of the students and the instructor. MATH 591. Topics in Mathematics. 1-3 Hours. MATH 640. Mathematical Biology I. 3 Hours. Semester course; 1-3 credits. May be repeated for credit with different Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 535. topics. Prerequisite: permission of the instructor. Open to qualified Mathematical modeling in the biological and medical sciences. Topics undergraduates. A study of selected topics in mathematical sciences. will include continuous and discrete dynamical systems describing See the Schedule of Classes for specific topics to be offered each interacting and structured populations, resource management, biological semester and prerequisites. control, reaction kinetics, biological oscillators and switches, and the MATH 592. Teaching and Communicating Mathematics. 1 Hour. dynamics of infectious diseases. Semester course; 1 lecture hour. 1 credit. Enrollment is restricted to MATH 650. Advanced Combinatorics. 3 Hours. graduate or professional students. This course focuses on the art and Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 550. science of teaching and communicating mathematics in both higher Topics include advanced applications of the pigeonhole principle and education and nonacademic settings. Throughout the course students inclusion-exclusion principle, recurrence relations, generating functions, will explore and critically examine research on evidence-based teaching special counting sequences, Ramsey theory, and combinatorial designs practices. In addition, the course will focus on how the skills students are and codes. developing as teaching assistants can transfer to nonacademic careers. MATH 656. Advanced Graph Theory. 3 Hours. This course will not count toward degree requirements for any program. Semester course; 3 lecture hours. 3 credits. Prerequisite: MATH 556. This Graded as S/U/F. course lays a rigorous theoretical