﻿ Linear Algebra Course Notes

Course Description (from SDSU General Catalog): Math 254. Introduction to Linear Algebra. 3 units. Prerequisite: Mathematics 151*. Matrix algebra, Gaussian elimination, determinants, vector spaces, linear transformations, orthogonality, eigenvalues, and eigenvectors. *At TPHS, students take Math 252/Calculus D before or concurrently with Math 254/Linear Algebra.

## General Information

 Outline: or MCC Calendar:

## Chapters 1, 2, 3Systems of Linear Equations and Matrices, Determinants, Vectors in 2-Space and 3-Space

• Notebook Assignments
• Quizzes
• Additional Notes and Support Materials

## Additional Support

In Spring 2020 I put together this list of video links as additional resources for my students. At the time we focused primarily on Chapters 4 through 8, however these channels should have good support for earlier concepts too.

• Essence of Linear Algebra Video Series: Essence of Linear Algebra on YouTube
I've heard good things about this series for helping to visualize and understand the big ideas. I have not watched all of these and note that the series addresses topics in a different order than we do.

• Professor Dave Explains Video Series: Linear Algebra on YouTube by Professor Dave Explains
I have not watched all of these. What I have seen looks like they would be good support for lessons and review. I wish I had found these earlier instead of while preparing Chapter 7.

• Sheldon Axler Video Series (to Support "Chapter 5 General Vector Spaces")
Of all of the video series I found, this one seems to be most similar to what we do in the first four sections of Chapter 5 and uses essentially the same definitions for Vector Space, Subspace, Span, Linear Independence, Basis, and Dimension. Note: I have not fully watched all of these videos, but skimmed them to check their definitions. The notation is a little different and you do not need to worry about complex numbers. I think these will be good support if you are looking for additional explanations of the key definitions in this part of the chapter.
• This one has some potential...Just posting it for now, but I really haven't looked at it yet.
http://www.math.brown.edu/~sswatson/classes/math0520/index.html

• This is UCSB's list that looks like they gleaned videos from across the internet on different topics. Again, I haven't fully explored it yet.
http://web.math.ucsb.edu/oml/4A.html

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### Additional NotesOriginal links that I'm keeping here for my reference. They all should be already incorporated into the lists above.

The above course notes, assignments, and quizzes are for the Linear Algebra (SDSU Math 254) classes I teach at Torrey Pines High School. I wrote and modified these files over several semesters. Much of the work is my own; however, I borrowed several examples and diagrams from the textbooks* my classes used while I taught the course. These notes, assignments, and quizzes are free for use by my current and former students. If other Linear Algebra students and teachers find these notes useful, I would be happy to know that my work was helpful. - Abby Brown

*Elementary Linear Algebra, 8th edition, Howard Anton, ©2000 John Wiley & Sons, Inc., ISBN 0-471-17055-0. (Chapter, section, page, and formula numbers refer to this text.)

*Elementary Linear Algebra: Student Solutions Manual, 8th edition, Elizabeth M. Grobe and Charles A. Grobe, Jr., ©2000 John Wiley & Sons, Inc., ISBN 0-471-38249-3.

*And a few additional Linear Algebra textbooks that I own or borrowed from friends.

Most of the links are PDF files that can be read with Adobe Reader. If you have trouble downloading the files, try right-clicking and selecting "Save Target As..." If you have trouble printing, try printing five or so pages at a time rather than all at once. For best results, use the most current version of Adobe Reader.