Undergraduate Courses Algebra I Algebra II Calculus Calculus With Applications Calculus With Theory I Calculus With Theory II Linear Algebra Linear Algebra Multivariable Calculus Multivariable Calculus ...All Graduate Courses Advanced Analytic Methods in Science and Engineering Advanced Calculus for Engineers Advanced Complexity Theory Advanced Partial Differential Equations with Applications Algebraic Geometry Combinatorial Theory: Hyperplane Arrangements Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics Computational Science and Engineering I Differential Analysis Differential Analysis ...All Web Links Master's Degree Programs Mathematics Departments	Graduate Courses Advanced Analytic Methods in Science and Engineering Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Advanced Calculus for Engineers Differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory. Advanced Complexity Theory The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved. Advanced Partial Differential Equations with Applications The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc. Algebraic Geometry This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field. It also analyzes the relations between complex algebraic varieties and complex analytic varieties. Combinatorial Theory: Hyperplane Arrangements This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids. Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields. Computational Science and Engineering I Differential equations of equilibrium; Laplaces equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Differential Analysis Fundamental solutions for elliptic, hyperbolic and parabolic differential operators, method of characteristics, review of Lebesgue integration, distributions, fourier transform, homogeneous distributions, asymptotic methods. Differential Analysis The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis. Geometric Combinatorics This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems. Infinite Random Matrix Theory In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices. Integral Equations Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications. Introduction to Numerical Methods Linear systems of equations, least square problems, eigenvalue problems, and singular value problems. Introduction to Numerical Methods Direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Mathematical Methods for Engineers II Numerical methods, initial-value problems, network flows and optimization. Mathematical Methods in Nanophotonics Computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Blochs theorem and conservation laws, perturbation methods, and coupled-mode theories, to understand surprising optical phenomena from band gaps to slow light to nonlinear filters. Measure and Integration This graduate-level course covers Lebesgues integration theory with applications to analysis, including an introduction to convolution and the Fourier transform. Nonlinear Dynamics and Chaos This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software. Nonlinear Dynamics and Waves This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. Numerical Methods for Partial Differential Equations This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Random Walks and Diffusion This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion. Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities. Teaching College-Level Science Topics include: using current research in student learning to improve teaching, developing courses, lecturing, promoting students ability to think critically and solve problems; communicating with a diverse student body, using educational technology, creating effective assignments and tests; and utilizing feedback to improve instruction. Teaching College-Level Science and Engineering Teaching equations for understanding, designing exam and homework questions, incorporating histories of science, creating absorbing lectures, teaching for transfer, the evils of PowerPoint, and planning a course. Theory of Computation Automata and Language Theory, Computability Theory, and Complexity Theory. Theory of Probability This course covers the laws of large numbers and central limit theorems for sums of independent random variables. It also analyzes topics such as the conditioning and martingales, the Brownian motion and the elements of diffusion theory. Topics in Algebraic Combinatorics The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings. Topics in Several Complex Variables This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem and Vanishing theorems. Topics in Theoretical Computer Science: An Algorithmists Toolkit This course covers a collection of geometric techniques that apply broadly in modern algorithm design. Wave Propagation Basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media. Wavelets, Filter Banks and Applications Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallats pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.