Here exists a log that I use to remind myself what to cover in class. The main audience is me. It might not be thorough. It might not make sense. It might not be helpful. It might be full of lies. However, I’m already writing it for myself so I might as well share it.

- draw cool diagram explaining change of basis and eigenstuff
- final review

- Eigen-stuff

- midterm

- Review

- Review

- More determinants
- Cofactor -> upper triangular -> REF method

- Talk about 4.4 and determinants

- Left multiplication affects rows
- Row operations yields invertible matrices
- Rank and nullity doesn’t change when multiplied by invertible matrices
- talk a bit about change of basis

- Thursday office hours moved to 4-5
- Basis. How to find. Row and column methods.
- Membership testing.
- http://kevinlui.org/au17m308/log/oct30.pdf
- http://kevinlui.org/au17m308/log/4.2-basis_and_dimension.pdf
- http://kevinlui.org/au17m308/log/4.3-row_and_column_spaces.pdf

- Thursday office hours moved to 4-5
- observe that kernels are given by a span
- Basis. How to find. Row and column methods.
- Membership testing.
- http://kevinlui.org/au17m308/log/oct30.pdf
- http://kevinlui.org/au17m308/log/4.2-basis_and_dimension.pdf
- http://kevinlui.org/au17m308/log/4.3-row_and_column_spaces.pdf

- 3blue1brown 7,8.
- Conceptual problems due in a week.
- More matrix multiplication is function composition.
- Despite what Webassign said to do, inverse to solve system is not that great of an idea. (send to class? https://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/)
- it’s slow
- numerical stability reasons.
- inverse can be dense when if original is not.

- 1b from http://kevinlui.org/m308exams/au17_midterm2.pdf
- Inverses are unique.
- R2 to 3 to 2, one-sided inverse thing
- Subspaces: http://kevinlui.org/au17m308/log/oct27.pdf

- More matrix multiplication
- Matrix multiplication is function composition
- Inverses. Wow you folks already learned this secretly. Nice.

- Conceptual Problems Set 2 posted, due May 10 - use camscanner
- Watch 3blue1brown, 4
- Go over low median problems, 1.3, 2.3, 3.4, 5.2
- Go over matrix multiplication. Do row stuff too.
- http://kevinlui.org/au17m308/log/oct20.pdf
- http://kevinlui.org/au17m308/log/oct23.pdf

- There was a midterm

- Solutions are posted on canvas.
- Midterm on Friday, up to and including 3.1.
- Be sure to understand conceptual problems.
- Do the derivate thing and talk about the kernel…wow integration!
- Relate to the conceptual problem related the derivatives.
- Do more past exam problems, take from Finals.

- Mostly exam review
- Probably do past exam problems.
- Do a cool a problem that involves having to solve a linear system and then stick it into a matrix.

- Convince them that linear transformations are determined by what they do to the standard basis.
- Convince them that every linear transformation comes from a matrix.
- Do this http://kevinlui.org/au17m308/log/oct11.pdf
- If time, Kernel and ranges.

- Make a really big table. LI/Spanning/dims
- Equivalent definitions of spanning, LI
- Unifying theorem
- If time, http://kevinlui.org/au17m308/log/oct09.pdf and http://kevinlui.org/au17m308/log/oct11.pdf

- Introduce Ax=b, as just linear combinations.
- Uniqueness of solutions given by homogeneous solutions
- Mention how LI and spanning relates to existence and uniqueness of solutions
- Do unifying theorem
- Do many many examples in class

- PS 2 is out
- Tell them about Ax=b
- Show them https://cocalc.com/projects/ed9c7f20-1bf8-477b-96e4-2620d084978f/files/Sagemath.ipynb?session=default
- Go through http://kevinlui.org/au17m308/log/oct06.pdf

- reduce echelon forms are unique.
- Chapter 1 Conceptual problems are due with Chapter 2 next Friday.
- Go through: http://kevinlui.org/au17m308/log/oct04.pdf
- In general, talk a lot of about spans.
- Linear combinations of linear combinations are linear combinations of original thing.
- Use this to motivate span of two non-parallel vectors being RR^2.
- Does this work for RR3? No.

- Tell class to watch 3blue1blue video 1
- Tell class that the Chapter 1 of conceptual problems are out
- Do example here: https://en.wikipedia.org/wiki/Gaussian_elimination
- Do Problem 1 here: http://kevinlui.org/m308exams/au17_midterm1.pdf
- Point out what a homogenous solution is
- Tell them what a particular solution is
- Give a math 126 example
- 2.1
- Tell them what a vector is. It has nice properties. See book.
- 2.2
- Go through this: http://kevinlui.org/au17m308/log/oct04.pdf

- Talk about changes to conceptual problems.
- Now have a Canvas.
- There will be a stranger in OH, but it’ll be okay
- Triangular implies echelon
- Go through http://kevinlui.org/au17m308/log/sep29.pdf
- multiply by 2 on the first row

- Basic info
- This is my name, OH, email.
- Syllabus is online
- Here is the grading scale
- Here is the exam schedule
- Please don’t miss exams
- Homework is webassign + conceptual questions
- The conceptual questions are due on the Fridays on week 3,5,7,9
- The week 3 one will be assigned this Friday

- First webassign thing is due Thursday.
- WA office hours are 11-3, 4/4 and 4/8 in the MSC

- Go through http://kevinlui.org/au17m308/log/sep27.pdf