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Course Criteria
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3.00 Credits
Prerequisite: MATH240 and MATH246. Also offered as AMSC452. Credit will be granted for only one of the following: AMSC452, MAPL452 or MATH452. An introduction to mathematical dynamics and chaos. Orbits, bifurcations, Cantor sets and horseshoes, symbolic dynamics, fractal dimension, notions of stability, flows and chaos. Includes motivation and historical perspectives, as well as examples of fundamental maps studied in dynamics and applications of dynamics.
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3.00 Credits
Prerequisites: Any two 400-level MATH courses; or CMSC330 and CMSC351 and permission of department. Also offered as CMSC456. Credit will be granted for only one of the following: MATH456 or CMSC456. Importance in protecting data in communications between computers. The subject lies on the border between mathematics and computer science. Mathematical topics include number theory and probability. Computer science topics include complexity theory.
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3.00 Credits
Prerequisites: MATH141 and one MATH/STAT course for which MATH141 is a prerequisite. This course cannot be used toward the upper level math requirements for MATH/STAT majors. Credit will be granted for only one of the following: MATH240, MATH341, MATH400 or MATH461. Basic concepts of linear algebra. This course is similar to MATH 240, but with more extensive coverage of the topics needed in applied linear algebra: change of basis, complex eigenvalues, diagonalization, the Jordan canonical form.
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3.00 Credits
Prerequisites: MATH241 and MATH246. Linear spaces and operators, orthogonality, Sturm-Liouville problems and eigenfunction expansions for ordinary differential equations. Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation. Boundary value problems, initial value problems and initial-boundary value problems.
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3.00 Credits
Prerequisite: MATH241 or equivalent. The algebra of complex numbers, analytic functions, mapping properties of the elementary functions. Cauchy integral formula. Theory of residues and application to evaluation of integrals. Conformal mapping.
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3.00 Credits
Prerequisite: MATH246. Fourier series, Fourier and Laplace transforms. Evaluation of the complex inversion integral by the theory of residues. Applications to ordinary and partial differential equations of mathematical physics: solutions using transforms and separation of variables. Additional topics such as Bessel functions and calculus of variations.
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3.00 Credits
Prerequisites: MATH 240 and 241. A study of various methods of numerical analysis. Topics include solutions of equations in one variable, interpolation and polynomial approximation, and numerical integration. Discussion also covers direct methods for solving linear systems and applications to finance and actuarial science.
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3.00 Credits
Prerequisite: MATH140, MATH141, and one 400-level Math course. Not open to students who have completed MATH498E. Credit will be granted for only one of the following: MATH470 or MATH498E. Formerly MATH498E. An advanced perspective on some of the core mathematics underlying high school mathematics courses. Topics include number systems, functions of one variable, equations, inequalities, trigonometric functions, curve fitting, and polynomials. The course includes an analysis of alternate approaches to mathematical ideas and problems, and makes connections between ideas that may have been studied separately in different high school and college courses.
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3.00 Credits
Prerequisites: MATH240 and MATH241; and permission of department. Also offered as CMSC475. Credit will be granted for only one of the following: MATH475 or CMSC475. General enumeration methods, difference equations, generating functions. Elements of graph theory, matrix representations of graphs, applications of graph theory to transport networks, matching theory and graphical algorithms.
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1.00 - 3.00 Credits
Prerequisite: one year of college mathematics or permission of department. This course cannot be used toward the upper level math requirements for MATH/STAT majors.
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