Scientific Computing

MATH-GA.2043-001, CSCI-GA.2112

Courant Institute of Mathematical Sciences,
New York University
Fall Semester, 2022
Lecture: in person Thursdays, 5:10-7:00PM, room 1302, WWH

Instructor: Jonathan Goodman, web page, email: goodman@cims.nyu.edu
phone: 212-998-3326, office: 529 Warren Weaver Hall
office hours: 4 am to 6 pm Wednesdays or by appointment
(email for a time)

Course description

An introduction to scientific computing at the MS level for people interested in practical computing. Covers the main theoretical ideas and fundamental algorithms. Attention paid to good programming practice for scientific computing software. Computing assignments (Python) and theoretical exercises.

Specific topics include sources of error, floating point, finite difference, quadrature, and interpolation formulas. order of accuracy and uses of error expansions, dense linear algebra (conditioning of linear algebra problems, factorizations, uses of SVD), FFT and applications, optimization (gradient descent, Newton's method), ODE solution, basic Monte Carlo.

Prerequisites:

Good linear algebra, multi-variate calculus, some programming (Python preferable). Also helpful: basic probability and differential equations.

Assignments, exams, grading:

The final grade will be based on weekly homework assignments (worth 50% of the grade), a final computing assignment (worth 20%) and an in-class written final exam (worth 30%).

Communication:

Please use the Brightspace site for content and homework communications. This way everyone sees and benefits from questions and answers, and there can be class discussion. related comm. Email the instructor for issues that do not involve others such as scheduling appointments, homework extensions, advice, etc.

Academic integrity:

Students are encouraged to explore and collaborate widely to understand the material. This includes looking at print and online sources and interacting with experts and each other. Students may receive some help with assignments, but each student must create (write up, code, run) solutions individually. Students may not share ("borrow" or lend) assignment solutions -- all writing must be done individually. Students may not plagairize solutions from other sources such as books or web sites. Violation of these policies may result in grade lowering or more serious penalties, depending on severity.