courses.md

Course Selection

Here are some courses that could be useful for you all to take, separated by category.

Applied Math (Math)

Definitely Useful

• 221: Advanced Matrix Computations
  Direct solution of linear systems, including large sparse systems: error bounds, iteration methods, least square approximation, eigenvalues and eigenvectors of matrices, nonlinear equations, and minimization of functions.

• 228A: Numerical Solution of Differential Equations
  Linear multistep methods; Runga-Kutta methods; Stability theory; Stiff equations; Boundary value problem; Eigenvalue problem; Discretization

• 228B: Numerical Solution of Differential Equations
  Theory and practical methods for numerical solution of partial differential equations. Finite difference methods for parabolic and hyperbolic problems, finite volume methods for hyperbolic conservation laws, finite element methods for elliptic equations, discontinuous Galerkin methods for first and second order systems of conservation laws.

Note: When Professor Per Persson teaches 228A/B in Fall/Spring the structure is slightly different. He teaches numerical methods for both ODE/PDE in 228A, including FD methods for parabolic and hyperbolic. 228B is entirely FEM, FVM, and DG.

Probably Useful

• 128A: Numerical Analysis
  Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.

• 128B: Numerical Analysis
  Iterative solution of systems of nonlinear equations, evaluation of eigenvalues and eigenvectors of matrices, applications to simple partial differential equations. Practice on the computer.

• 222A: Partial Differential Equations
  The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Laplace's equation, heat equation, wave equation, nonlinear first-order equations, conservation laws, Hamilton-Jacobi equations, Fourier transform, Sobolev spaces. (theoretical)

• 222B: Partial Differential Equations
  Second-order elliptic equations, parabolic and hyperbolic equations, calculus of variations methods, Hamilton-Jacobi equations and conservation laws (theoretical)

Possibly Useful

• 104: Introduction to Analysis
  The real number system. Sequences, limits, and continuous functions in R; the concept of a metric space; uniform convergence, interchange of limit operations; infinite series; mean value theorem and applications; the Riemann integral.

• 110: Linear Algebra
  Matrices, vector spaces, linear transformations, inner products, determinants; eigenvectors; QR factorization; quadratic forms and Rayleigh's principle; Jordan canonical form, applications; linear functionals.

• 121A: Mathematical Tools for the Physical Sciences
  Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Rapid review of series and partial differentiation, complex variables and analytic functions, integral transforms, calculus of variations.

• 121B: Mathematical Tools for the Physical Sciences
  Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Special functions, series solutions of ordinary differential equations, partial differential equations arising in mathematical physics, probability theory.

• 123: Ordinary Differential Equations
  (1) Introduction: examples and tricks (2) Existence and uniqueness of solutions (3) Linear ODE and systems (4) Stability (5) Boundary value problems: Sturm-Liouville theory (6) Additional topics

• 224A: Mathematical Methods for the Physical Sciences
  Introduction to the theory of distributions. Fourier and Laplace transforms; partial differential equations; Green's function; operator theory, with applications to eigenfunction expansions, perturbation theory and linear and non-linear waves.

• 224B: Mathematical Methods for the Physical Sciences
  The course will survey basic theory and practical methods for solving the fundamental problems of mathematical physics. It is intended for graduate students in applied mathematics, physics, engineering or other mathematical sciences. The overall purpose of the course will be to develop non-numerical tools for understanding and approximating solutions of differential equations.

• E 231: Mathematical Methods in Engineering
  This course offers an integrated treatment of three topics essential to modern engineering: linear algebra, random processes, and optimization. These topics will be covered more rapidly than in separate undergraduate courses covering the same material, and will draw on engineering examples for motivation. The stress will be on proofs and computational aspects will also be highlighted. It is intended for engineering students whose research focus has a significant mathematical component, but who have not previously had a thorough exposure to these topics.*

*Note: Good class for graduate student who hasn't had exposure to linear algebra, statistics, and optimization in the past. This is probably not very useful for people who have already taken lots of linear algebra, statistics, or optimization courses.

• 273: Advanced Topics in Nuclear Methods

• 275: Topics in Applied Mathematics
  Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Actual Computer Science (CS)

• 152: Computer Architecture and Engineering
  Instruction set architecture, microcoding, pipelining (simple and complex). Memory hierarchies and virtual memory. Processor parallelism: VLIW, vectors, multithreading. Multiprocessors. (F,SP)

• 169: Software Engineering
  Ideas and techniques for designing, developing, and modifying large software systems. Function-oriented and object-oriented modular design techniques, designing for re-use and maintainability. Specification and documentation. Verification and validation. Cost and quality metrics and estimation. Project team organization and management. Students will work in teams on a substantial programming project. (F,SP)

• 252: Graduate Computer Architecture
  Graduate survey of contemporary computer organizations covering: early systems, CPU design, instruction sets, control, processors, busses, ALU, memory, I/O interfaces, connection networks, virtual memory, pipelined computers, multiprocessors, and case studies. Term paper or project is required. (F,SP)

• 262A: Advanced Topics in Computer Systems
  Graduate survey of systems for managing computation and information, covering a breadth of topics: early systems; volatile memory management, including virtual memory and buffer management; persistent memory systems, including both file systems and transactional storage managers; storage metadata, physical vs. logical naming, schemas, process scheduling, threading and concurrency control; system support for networking, including remote procedure calls, transactional RPC, TCP, and active messages; security infrastructure; extensible systems and APIs; performance analysis and engineering of large software systems. Homework assignments, exam, and term paper or project required. (F,SP)

• 267: Applications of Parallel Computers
  Models for parallel programming. Fundamental algorithms for linear algebra, sorting, FFT, etc. Survey of parallel machines and machine structures. Existing parallel programming languages, vectorizing compilers, environments, libraries and toolboxes. Data partitioning techniques. Techniques for synchronization and load balancing. Detailed study and algorithm/program development of medium sized applications. Also listed as Engineering C233. (SP)

• ME 280A: Introduction to the Finite Element Method
  Weighted-residual and variational methods of approximation. Canonical construction of finite element spaces. Formulation of element and global state equations. Applications to linear partial differential equations of interest in engineering and applied science.

Note: Do not take both the undergraduate (ME 180) and graduate versions of this course, since there is a fair amount of overlap, with the graduate course focusing more on understanding the method and the undergraduate course more on using FEM software (COMSOL) for a larger variety of applications.

Writing

• GSPDP 320