MATH-GA.2043 or CSCI-GA.2112

Scientific Computing

Warren Weaver Hall, room 1302, Thursdays, 5:10 - 7 pm
Courant Institute of Mathematical Sciences
New York University
  Fall Semester, 2015

Instructor

Aleksandar Donev, 1016 Warren Weaver Hall
E-mail: donev@courant.nyu.edu ; Phone: (212) 992-7315
Office hours: 3-4 pm Tuesdays, 4-5pm on Thursdays, or by appointment

Graders

Homeworks 1 and 2: Jason Kaye, email kaye at cims.nyu.edu, office hours: Fridays 5-6pm, 506 WWH, on 9/25, 10/2, 10/9 and 10/16
Homeworks 3 and up: Romeo Alexander, email romeo at cims.nyu.edu, office hours: Wednesdays 5-6pm, 930 WWH, starting 10/21

Course description

This course is a graduate-level introduction to practical introduction to computational problem solving, including both mathematical analysis of numerical algorithms (numerical analysis) and practical problem solving. This is not a programming course but programming in homework projects with Matlab (Python, Fortran, C/C++, or other language of your choice) is an important part of the course work.

Take a look at the homepage of the Spring 2012 course as this course will be similar.

3 points per term

Topics covered include:

  • floating point arithmetic, conditioning and stability
  • direct methods for systems of linear equations
  • matrix eigenvalue problems and SVD decomposition
  • numerical interpolation, differentiation and integration
  • nonlinear systems of equations and unconstrained optimization
  • Fourier and wavelet transforms
  • ordinary and partial differential equations
  • Monte Carlo methods.
All materials related to this course, including lecture notes, homeworks, schedule, etc., will be posted here. Homework assignments and the exams will be handled via NYU Classes. Videos of my lectures as well as some example solutions of assignments will also be posted there.

Main Textbook(s) (optional)

I will use my own lecture slides (complemented by the blackboard) that will be posted here, however, you will need to complement the lectures and my slides with additional reading. This will not only give you a broader perspective but it will also give you a different perspective, which is very important. The two textbooks listed below have been placed on 24h reserve in the Courant library.

As a good textbook that I will sometimes point you to for additional reading, I recommend Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greenbaum & Timothy P. Chartier (library call number QA297.G15 2012). Unfortunately, this book is not available in electronic format via NYU. Codes can be found at the author's website.

Very nice case studies demonstrating applications of scientific computing in various disciplines can be found in the book Scientific Computing with Case Studies by Dianne P. O'Leary (library call number QA401.O44 2009 ). Additional case studies can be found here.

Some of the lectures will be more closely based on a draft of an upcoming book Principles of Scientific Computing by my colleagues Jonathan Goodman and David Bindel, to be found here as one PDF or as individual chapters.

Additional Readings

Another textbook you may consult will be Scientific Computing with MATLAB and Octave, by Alfio M. Quarteroni & Fausto Saleri, Springer, now in its fourth edition but older editions will do just as well. The book is available in PDF form through the library subscription to SpringerLink and you can also order a $25 paper-back copy from Springer. The Matlab scripts for the examples in the second edition of the book can be downloaded as a zip archive (use "unzip <filename>" in Linux to extract the files). Erratas as well as the files for the recent third edition of the book can be found on the book website.

There are many free online materials that can be consulted as additional reading, depending on your background and interests. Here are some suggestions (more may be added as the course progresses) that you have special access to through the NYU/Courant library:
  1. Numerical Computing with MATLAB, by Cleve Moler, available for free in PDF form at the MATLAB site.
  2. The Cambridge Engineering guide to MATLAB has lots of useful information.
  3. An Introduction to Programming and Numerical Methods in MATLAB, Stephen R. Otto & James P. Denier, Springer, 2005, available in PDF format through the library. This book provides an elementary introduction to Matlab with less focus on actual scientific computing.
Also see these resources listed by my colleague David Bindell.

Prerequisites

A solid background (undergraduate level) in multivariate calculus and linear algebra. Experience with writing computer programs (in Matlab, Python, Fortran, C, C++, or other language) is strongly recommended as homework assignments will involve programming from the start and you will be expected to catch up on your own (winter break is a good time to learn programming!).

Prior knowledge of Matlab is not required, but it will be used as the main language for the course. If you have experience with other languages (Fortran, C, C++, Python), Matlab will be easy to learn and use, and comes with a great help facility. Please look at some of the "Additional Readings" above for programming guides.

Assignments and grading

There will be regular (biweekly or weekly) challenging assignments and a take-home final. The assignments will be mostly computational. You will be expected to submit a PDF of your solutions, as explained in more detail under Assignments. The grade will be 60% based on assignments and 40% on a take-home final which will be similar to the homework assignments. Assuming the total possible number of points (excluding extra credit) is 100, the grade scale will be based on the weights used in computing your GPA:

  • >92.5       = A
  • 87.5-92.5 = A-
  • 80.0-87.5 = B+
  • 72.5-80.0 = B
  • 65.0-72.5 = B-
  • 57.5-65.0 = C+
  • 50.0-57.5 = C
  • 42.5-50.0 = C-
  • <42.5       = F
Academic integrity policies will be strictly enforced for homework assignments. In particular, group work on assignments is not allowed and will be treated as a violation of academic integrity.

Communication

The NYU Courses webpage will be used for messages related to the assignments and any scheduling changes, as well as material that is for your personal use only such as sample solutions of past assignments. If you register for the class, you automatically have access. All course materials including lecture notes and assignments will be posted on this site as they become available.

You should feel free to email the instructor with any questions, concerns, or special requests such as deadline extensions, meeting outside of office hours, etc.

Computing

Computing on your own will form an essential part of the learning process and your own applied mathematics training. The Courant Institute has computer labs with Linux workstations that have Matlab (matlab), Maple (xmaple), Mathematica (mathematica), the GNU (gcc,g++,gfortran), Intel and Pathscale C/C++/Fortran compiler suites, and other useful software installed.

You can purchase student edition Matlab from the NYU computer store if you want to use it on your own personal computer. If cost is a problem, Octave (octave) provides a free alternative to Matlab that you can download for Linux, Windows or Mac OS X. Note however that the plotting facilities in Octave are not up to par with Matlab's and this may put you at a disadvantage for homework assignments.

You are encouraged to submit reports as PDFs produced using LaTex (latex), as a good practice in learning how to use mathematical typesetting software for future papers and thesis reports. I recommend trying out the LyX word processor as a front-end GUI to LaTex, especially if you are new to LaTex.

Also see these resources listed by my colleague David Bindell. In particular, some coding advice that may be useful in general.