Hi, everyone! I'm proud to present Schoolhouse's first series on Linear Algebra!
In this class we will cover all the standard topics of a first class in Linear Algebra (typically take sometime after Calc 2 for greater mathematical maturity, though it can be taken after Calc 3 or before Calculus in the first place.)
To be clear, here are the pre-requisites:
Algebra (1 and 2, and including Trig) are mandatory.
Calculus 1 and 2 are strongly recommended just for maturity, but not required (if you get straight A's in all of Algebra 2 and Trig you should mostly be fine); Calc 3 helps as well (and when I set up my Calc 3 series we will be employing Linear Algebra so if that interests you this course is recommended.)
I've taken Multivariable Calculus with Linear Algebra (applied) as well as Linear Algebra itself (proof-based) at Stanford OHS and Stanford ULO, getting an average of B+ on both.
Generally, here are the topics we will cover (each week):
1. Basic vector operations in R^n
2. Vector Spaces and Subspaces induction technique.
3. Linear independence and Gram-Schmidt
4. Projections and Fourier's Formula
5. Linear Transformations, Properties, and Kernel
6. Matrix operations, special matrices, and matrix properties.
7. Determinants, Linear Systems, Inverse Matrices, and LU decomposition
8. Row, Column, and Null Space, Rank and Nullity
9. Change of Basis, Eigeneverything, and Diagonalizability
10. TBD: QR Decomposition and more on Transpose, Orthogonal Complements, Markov Chains, or anything else.
The course expectation is at least 5 hours per week apart from class, office hours, and quizzes. (About 3 hours reading and 2 hours doing homework.)
We will meet every Saturday at the same time. In class we will not cover all the content (there is simply enough time), rather we will discuss and go over the proofs the main results, which also appear in the text. We will skip over proofs and results whose proofs we all understand. We will focus on examples and practice in preparation for the assigned exercises and quizzes.
We will use Bronson's "Linear Algebra - Algorithms, Applications, and Techniques" as our main text, ( http://ndl.ethernet.edu.et/bitstream/123456789/24629/1/Richard%20Bronson.pdf ) in addition to Stanford's Math 51 text (fragments taken under fair use law which will be posted gradually).