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
Chapters 1, 2, 3
Systems of Linear Equations and Matrices, Determinants,
Vectors in 2-Space and 3-Space
- Notebook Assignments
- Quizzes
- Additional Notes and Support Materials
Chapter 4 -- Euclidean Vector Spaces
- Notebook Assignments: Chapters 4 & 5
- Section 4.2 Mathematica:
Matrix
Transformations Mathematica Notebook (.nb file)
- Section 4.3
- Video:
Highlights of 4.3
Properties of Linear Transformations (Abby Brown)
- Note: We will discuss Theorem 4.3.2 in more
detail in class.
- For exercises #8 - 11, you do not need to
fully prove both parts of the theorem for each
transformation. However, think about what would
happen with each property and do at least one
part (a, b, c, etc.) of each of the exercises
fully. Make sure you know why each nonlinear
transformation fails one or fails both
properties.
- Quiz:
Quiz #3
Sections 4.1 - 4.3
- Additional Materials
Chapter 5 -- General Vector Spaces
- Notebook Assignments: Chapters 4 & 5
- Lesson 1: Vector Spaces
- Lesson 2: Spanning, Linear Independence, Basis, and Dimension
- Lesson 3: Row Space, Column Space, and Nullspace
- Quiz #4
Sections 5.1 - 5.6
- Professor Dave Explains Videos for Additional Support
Chapter 6 -- Inner Product Spaces
- Notebook Assignments: Chapters 6, 7 & 8
- Lesson 1: 6.1 & 6.2 Inner Product Spaces
- Lesson 2: 6.3 Orthonormal Bases, Gram-Schmidt, and
QR-Decomposition
- Lesson 3: 6.5 Orthogonal Matrices and Change of Basis
-
Quiz #5
Sections 6.1 - 6.5
Chapter 7 -- Eigenvalues & Eigenvectors
Chapter 8 -- Linear Transformations
- Notebook Assignments: Chapters 6, 7 & 8
(Note: Updated 02/02/2020)
- Lesson: 8.1 & 8.2 General Linear Transformations
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
- Top -
Additional Notes
Original 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.
