Math 295 Numerical Analysis Syllabus

This is the course syllabus for Fall 2019 Math 295 Numerical Analysis.

Instructor Info

Rob Thompson rthompson@carleton.edu
Anderson 238 x4366
Office hours: see here

Course Description

The name of this class might be misleading. It's not all about numbers, and there will probably be more algebra than analysis. More accurately, it should be called numerical linear algebra and optimization. In 10 short weeks, I would like to give you a tour of some very cool ideas in linear algebra and optimization by looking at theory, application and implementation (in MATLAB). We'll begin with matrix factorizations, linear equations and least squares, then treat linear optimization and the simplex method. With the time remaining, we can study some topics in convex optimization.

Recommended Reading

Because we will jump around to various topics, there is no single suitable textbook for this class. I will try to make lectures self-contained, but I will recommend supplementary reading from a few different books, listed below. I'm not recommending that you buy these books. These books will be available for use 24 hours a day in the Math Skills Center on the bookshelf.

• [TB] Trefethen, Lloyd N., and David Bau III. Numerical linear algebra. Vol. 50. Siam, 1997.
• [BV] Boyd, Stephen, and Lieven Vandenberghe. Introduction to applied linear algebra: vectors, matrices, and least squares. Cambridge university press, 2018.
• [CG] Calafiore, Giuseppe C., and Laurent El Ghaoui. Optimization models. Cambridge university press, 2014.
• [H] Heath, Michael T. Scientific computing: an introductory survey. Vol. 80. SIAM, 2018.
• [GKT] Guenin, Bertrand, Jochen Könemann, and Levent Tuncel. A gentle introduction to optimization. Cambridge University Press, 2014.
• [F] Ferguson, T. S. (2000). Linear programming: A concise introduction. Website. Available at http://www.math.ucla.edu/~tom/LP.pdf.
• more may come as we go

MATLAB

We will write code in MATLAB to implement algorithmic ideas, work with data, and create visualizations. You can install MATLAB on your computer for no cost, use it in the Carleton computer labs, or access it via a web browser using MATLAB online. To install MATLAB:

1. Go to Carleton's MATLAB Portal to download the software.
2. Click “Sign in to get started” under the Get MATLAB and Simulink section.
3. create a MathWorks Account. You will then be able to download and activate MATLAB and/or use MATLAB online from a web browser.

There is a MATLAB tutorial on the MATLAB Portal under “Learn to Use MATLAB and Simulink”. If you have trouble installing MATLAB, try going to the MATLAB Portal and clicking "Need Installation Help".

Assessment

Your grade in this class will be based on weekly problem sets, three exams, and a final project in the proportions below.

Problem Sets	20%
Three Exams	20% each
Final Project	20%

Problem Sets

Every week you will need to submit written homework. This homework will be posted on the course webpage as a pdf, and due the week after they are posted on Thursdays at noon. Please put your completed problem sets in the Math Skills Center box labeled “Rob Thompson Math 295”. I will drop your lowest problem set score from your final grade.

Exams

You will have three take-home exams. These exams will be distributed in the third, sixth, and ninth week of class, and you will have a week to complete them. These exams will be done without collaboration. Exam content and allowed resources will be announced ahead of time.

Final Projects

There will be a final project for this course. This project will be done with a partner, and will include a written paper, MATLAB code, and a final presentation. The topic of the project will be an application of numerical linear algebra or optimization that you choose. More details will discussed in class, and I will give many examples for possible topics.

Note-taking duties

Since we don't have a textbook, class notes will be an important record of what you need to know to succeed on homework and exams. I will ask for two volunteers every class period to be note-takers. On a day that you are a volunteer, you will take extra careful notes, then promptly scan them into a single pdf document and email them to me. I will post them in our Notes directory for everyone to access.