Numerical Analysis (MATH-UA.0252/MA-UY_4424)

This class will be online on zoom (scheduled via NYU classes) during the Spring of 2021, Mon+Wed 2-3:15pm. Recitation will be Fridays 11am-12:15pm during the first two sessions, and then switch to Tue 9:15am-10:30am to better fit remote students. For some important dates see the Lectures tab.

All materials related to this course, including lecture notes, homeworks, schedule, etc., will be posted here. We will use CampusWire for a communication board for group work and questions (signup link will be sent via NYU Classes), and Gradescope for submitting and grading of homeworks and midterm.

The class content will be very similar to that taught by Profs. Georg Stadler Fall 2018 and Mike O’Neil Spring 2020, so consult those websites for an example of what to expect in terms of content.

Instruction

Instructor

Aleksandar Donev, ad139. Office hours Fridays 12:30pm-1:30pm EST starting 2/19/2021, unless noted otherwise on Campuswire. Feel free to request an appointment by email.

Teaching Assistant

Guanchun Li, gl1705. Office hours Tuesdays 11am-12pm EST starting 2/16.

Grader

Jiasi Yu, jy2792, via Gradescope.

Mode of instruction

The plan for most of the class (except first and exam weeks) is that half of the lectures will be pre-recorded and every student will watch that on their own asynchronously. This would be continued on Mondays in class by a “live” lecture over zoom (recorded on NYU Classes) with some live computing demos. On Wednesdays we will have breakout room group work over zoom, where you will solve problem worksheets (including coding) and maybe also have some Matlab demos in groups. This will be an integral part of the course and every student should participate. For those that cannot make Wednesdays class due to difference in time zone, we will schedule a recitation section at a time suitable for students in China, and the TA will repeat the group work there.

Topics

We will cover classical topics in Numerical Analysis: The solution of linear and nonlinear equations, conditioning, least squares, numerical computation of eigenvalues, interpolation, quadrature, and numerical methods for ODEs. The course will have a focus on the analysis of numerical methods, but also require you to use numerical software (specifically Matlab, but if you have prior experience you are welcome to use Python (numpy), or Julia). If you are not familiar with any of these tools, the recitation will give an introduction to Matlab during the first weeks. Additionally, I strongly recommend to work through the second chapter of the “Practice” textbook listed on the course webpage the course starts or in the first week of the semester.

Textbooks

I will use two textbooks, both of which are freely available to you via the NYU library as ebooks, and I will refer to them as the “theory” and “practice” textbooks in this webpage.

Theory

An Introduction to Numerical Analysis, Endre Suli and David Mayers, Cambridge University Press, 2003. Available electronically via NYU library proxy or from campus network in PDF format. This textbook is mostly theoretical, with no coding in Matlab (though it does present some results from numerical computations), and so it lacks practice which I believe is crucial to this course.

Practice

Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms, Anne Greenbaum & Timothy P. Chartier, Princeton Press, 2012. This book is available to you freely in electronic format via NYU’s library. Codes can be found at the author’s website.

Additional learning materials for programming in Matlab including textbooks and tutorials are available in the Resources tab

Grading

30% Homework, 10% Quizzes, 25% Midterm, 35% Final.