### AMSC 661: Scientific Computing II (graduate, UMD)

Boundary value problems for ODEs, Elliptic PDEs, The elliptic eigenvalue problem, Sparse matrix methods, Initial value problems for ODEs, Parabolic PDEs, Hyperbolic PDEs, Fourier and wavelet methods

### AMSC 667: Numerical Analysis II (graduate, UMD)

Nonlinear systems of equations: fixed point iterations, Newton & quasi-Newton methods, solving equations in Banach spaces. Ordinary differential equations: one-step methods, Runge-Kutta methods, multistep methods, stability and convergence, multivalue methods. Boundary value problems: the finite difference method, variational formulation, the finite element method

### Math 130: Calculus for Life Sciences (UMD)

Functions, exponential growth, discrete-time dynamical systems, biological applications, derivatives, applications of derivatives, integration

### Math 51: Linear Algebra and Calculus of Several Variables (Stanford)

Linear Algebra, differential calculus of functions of several variables

### Math 90Q: The Mathematics of Fractals (sophomore seminar, Stanford)

Classical fractals, self similarity, fractal dimensions, discrete maps, the Mandelbrot set, the Julia set, chaotic dynamics and fractals, fractal interpolation.

### Math 103: Linear Algebra (Stanford)

Solution of linear systems, subspaces and dimension, orthogonal projections, orthogonal matrices, least squares, the Gram-Schmidt process, determinants, eigenvectors and eigenvalues, diagonalisation, symmetric matrices, singular values.

### Math 106: Complex Analysis (Stanford)

Complex numbers, functions, limits and continuity, differentiation, analytic functions, elementary functions, integration, series, residues, conformal mapping.

### Math 118: Numerical Analysis (Stanford)

Interpolation theory, splines, approximation of functions, numerical differentiation and integration, solving nonlinear equations.

### Math 131: Partial Differential Equations (Stanford)

First-order equations, second-order equations, wave equations, diffusion equations, reflections and sources, boundary problems, Fourier series.

### Math 135: Nonlinear Dynamics and Chaos (Stanford)

One- and two-dimensional flows, bifurcations, phase plane analysis, limit cycles and their bifurcations, Lorenz equations, fractals and strange attractors.

### Math 205A: Real Analysis (graduate, Stanford)

Lebesgue's theorem on Riemann integration, sigma-algebras, Borel sets, abstract measure spaces, outer measures, Caratheodory's theorem on measurability, measurable functions and the Lebesgue integral, Fatou's lemma, convergence theorems, product outer measures, Fubini theorem, Tonelli's theorem, covering theorem, differentiation theory, functions of bounded variation and absolutely continuous functions, Borel outer measures in topological spaces, Hahn decomposition, Radon-Nikodym theorem, Lebesgue decomposition theorem, Riesz representation theorem.

### Math 220B: Partial Differential Equations II (graduate, Stanford)

Parabolic and elliptic partial differential equations, Green's functions, potential theory, eigenvalue problems.

### Math 222: Computational Methods for Fronts, Waves, and Interfaces (graduate, Stanford)

Numerical methods for linear hyperbolic and parabolic equations, spectral methods for time-dependent problems, Godunov-type schemes for conservation laws, high-order methods for multi-dimensional conservation laws, monotone and high-order methods for Hamilton-Jacobi equations, discontinuous Galerkin methods.

### Math 224: Math Biology (graduate, Stanford)

Single-species population models, models for interacting populations, dynamics of infectious diseases, reaction-diffusion equations, biological waves, discrete time Markov chains, biological applications of DTMS, stochastic epidemic models.

### Math 266: Computational Signal Processing and Wavelets (graduate, Stanford)

Fourier analysis, sampling theorems, discrete signal analysis, time-frequency and wavelet transforms, frame theory, regularity measurements and multiscale analysis, wavelet bases and multiresolution approximations, linear and nonlinear approximations.