Link to Content:

edX

Created/Published/Taught by:

UT Austin

Maggie Myers

Robert van de Geijn

Content Found Via:

Lynn Thompson

Free? Yes

Tags: algorithms / eigenvectors / linear algebra / linear independence / linear least-squares / MATLAB / matrix operations / subspaces / vector spaces

Difficulty Rating:

from edX:

“Linear Algebra Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

- It’s visual.
- It connects hand calculations, mathematical abstractions, and computer programming.
- It illustrates the development of mathematical theory.
- It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you’ll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

This summer version of the course will be released at an accelerated pace. Each of the three releases will consist of four ”Weeks” plus an exam . There will be suggested due dates, but only the end of the course is a true deadline.

What you’ll learn

- The connection between linear transformations, matrices, and systems of linear equations
- Partitioning methods and special characteristics of triangular, symmetric, diagonal, and invertible matrices
- A variety of algorithms for matrix and vector operations and for solving systems of equations
- Vector spaces, subspaces, and various characterizations of linear independence
- Orthogonality, linear least-squares, projections, bases, and low rank approximations
- Eigenvalues and eigenvectors
- How to create a small library of basic linear algebra functions

“

Recommended Prerequisites: High School Algebra, Geometry, and Pre-Calculus.

Go to Content: Linear Algebra – Foundations to Frontiers

## By knb May 22, 2017 - 6:36 am

The course start with the very basics of high-school-level vector algebra, siwtches to the basics of matrix algebra and ends with deriving matrix factorization methods, vector spaces and eigenvalues. You can lookup the syllabus yourself.

What distinguishes this course from other linear algebra tutorials? Several things

1) Exercises. There are hundreds of fill-in-the-blank exercises. YOu have to collect a lot of points. This way.

2) Grading. You have as many attempts on solving problems as you want. This holds even for the final exams and midterms. The authors want you to practice, pracice, practice; so they have removed de-motivating course-grading

3) Exams and Exam preparation. There are two midterms and one final. For each there is one practice exam. The practice exams are much tougher than the real exams

4) Teaching methodology. It combines Math and Computer science. Learning the math requires by solving lots of small puzzles, just as in many other classes. But there is also a computer-science aspect that theauthors try to convey: They introduce Big-O notation relatively early, and they also try to explain how the functions in “real” scientific linear algebra libraries work. These libraries (e.g. LAPACK) do so by clever slicing and dicing matrices, and by extensive input validation.

All in all: a nice course that prepares you well for more difficult classes (e.g. Prof. Strang’s courses on Opencourseware). But it requires stamina and persistence, and even then it’s difficult to commit all the methods learned to long-term-memory.

Advanced Beginner- familiar with data science / new to this topic / some prerequisitesIntermediate - had relevant prerequisites / was familiar with this topic

(4) A Lot

Detailed Content Survey:Needed to gain or strengthen general data science knowledge

I regularly select content from this publisher/series

Yes

Most (i.e. read the entire book but didn't complete the exercises)

High school level vector algebra.

matlab (octave works 99%), pencil and paper,

octave 4 can be used instead of matlab, some error messages are more verbose.

http://edx-org-utaustinx.s3.amazonaws.com/UT501x/Spark/index.html

How scientific linear algebra libraries work and how they are designed. Course exercises show the basics; lots of reference papers from the academic literature are linked

the innovative FLAME notation and the associated SPARK code generation tool (has nothing to do with Apache Spark) is a bit weird at first, but the exercises based on it are actually quite simple when you get your head around it.

8-10 hrs per week *without optional content

persistent math geeks who like a baby step approach

Prof. Strang's courses at opencourseware.com (MIT) - there are several - this is a short one https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/introduction/