This is the repository of course materials for the 18.335J/6.7310J course at MIT, taught by Dr. Shi Chen, in Spring 2025.
Lectures: Monday/Wednesday 9:30am–11am in room 2-190
Office Hours: TBD in room 2-239B.
Contact: [email protected]
Topics: Advanced introduction to numerical linear algebra and related numerical methods. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating-point standard, sparse and structured matrices, and linear algebra software. Other topics may include memory hierarchies and the impact of caches on algorithms, nonlinear optimization, numerical integration, FFTs, and sensitivity analysis. Problem sets will involve use of Julia, a Matlab-like environment (little or no prior experience required; you will learn as you go).
Launch a Julia environment in the cloud:
Prerequisites: Understanding of linear algebra (18.06, 18.700, or equivalents). 18.335 is a graduate-level subject, however, so much more mathematical maturity, ability to deal with abstractions and proofs, and general exposure to mathematics is assumed than for 18.06!
Textbook: The primary textbook for the course is Numerical Linear Algebra by Trefethen and Bau. For a classical (and rigorous) treatment, see Nick Higham's Accuracy and Stability of Numerical Algorithms.
Other Reading: Previous terms can be found in branches of the 18335 git repository. The course notes from 18.335 in much earlier terms can be found on OpenCourseWare. For a review of iterative methods, the online books Templates for the Solution of Linear Systems (Barrett et al.) and Templates for the Solution of Algebraic Eigenvalue Problems (Bai et al.) are useful surveys.
Grading: 40% problem sets (three psets due / released every other Friday), 30% take-home mid-term exam (second week of April), 30% final project (one-page proposal due Sunday April 6, project due Thursday May 15).
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Psets will be submitted electronically via Gradescope (sign up for Gradescope with the entry code on Canvas). Submit a good-quality PDF scan of any handwritten solutions and also a PDF printout of a Julia notebook of your computational solutions.
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previous midterms: fall 2008 and solutions, fall 2009 (no solutions), fall 2010 and solutions, fall 2011 and solutions, fall 2012 and solutions, fall 2013 and solutions, spring 2015 and solutions, spring 2019 and solutions, spring 2020 and solutions.
Collaboration policy: Talk to anyone you want to and read anything you want to, with three exceptions: First, you may not refer to homework solutions from the previous terms in which I taught 18.335. Second, make a solid effort to solve a problem on your own before discussing it with classmates or googling. Third, no matter whom you talk to or what you read, write up the solution on your own, without having their answer in front of you.
- You can use psetpartners.mit.edu to help you find classmates to chat with.
Final Projects: The final project will be an 8–15 page paper reviewing some interesting numerical algorithm not covered in the course. See the 18.335 final-projects page for more information, including topics from past semesters.
