Scientific Computing

MATH-GA.2043-001 and CSCI-GA 2112.001

Courant Institute of Mathematical Sciences,
New York University
Fall Semester, 2018
Lectures: Thursday, 5:10 to 7 pm, Room 1302, Warren Weaver Hall

Instructor: Jonathan Goodman, his web page, email:
phone: 212-998-3326, office: 529 Warren Weaver Hall
office hours: 4 to 6 pm Thursday or by appointment
(call or email for a time)

Course content

This is an introduction to scientific computing at the beginning graduate level. You have to be good at a lot of things to be good at scientific computing. There is math involved in designing approximations and understanding how to pose computational problems. There are clever numerical algorithms. There is programming and software engineering and management. This course covers all these areas to some degree so that a student can continue to more a specialized area with an understanding of how it fits into the bigger picture. Specific content will include:

Math: Conditioning of problems and stability of algorithms; Taylor expansions, differences, integration and interpolation; conditioning of some linear algebra problems; basic Monte Carlo.

Mechanics: Floating point arithmetic; outline of processor archecture relating to performance (speed of execution).

Algorithms: FFT; Gaussian elimination; Newton's method for optimization

Software: Performance pitfalls; pitfalls related to inexact arithmetic; using packages; using development tools; modular testing and verification of numerical codes; visualization; using developer tools.