There is no official textbook. All lecture notes will be posted here. Homework is based on lectures. Exams are based on lectures and homework solutions. For extra reading I recommend any book written by Gilbert Strang.
Office Hours: TBA
Here is the syllabus.

Item 
Date 
Lecture Notes 
Homework 1
Solutions

Fri Sept 9

Introduction, Euclidean Space
Euclidean Space, Inner Product Space
Concept of a Basis
More About Bases
Fourier Series
Complex Fourier Series
Fourier Transform

Typed Notes for HW1 
Homework 2
Solutions

Fri Sept 23

Matrices, Linear Functions
Matrix Arithmetic, Matrix Norms
Matrix Inverses
Rotation, Reflection, Projection
HW2 Discussion
Review for Exam 1

Typed Notes for HW2 
Exam 1: Fri, Sept 30
Solutions

Homework 3
Solutions

Mon, Oct 17

Fundamental Theorem, Part I
Fundamental Theorem, Part II
Existence of Inverse Matrices
Systems of Linear Equations
Big Example
Least Squares Approximation
HW3 Help Session
HW3 Discussion

Typed Notes for HW3 
Homework 4

Mon, Oct 31

Linear and Bilinear Forms
Multivariable Taylor Expansion
Multilinear Forms
Alternating Forms, Determinants
Determinants, Volume
Volume, Application to Calculus
Review for Exam 2

Typed Notes for HW4 
Exam 2: Fri, Nov 4
Review
Solutions

Homework 5
Solutions in the typed notes

Mon, Nov 21

Intro to Eigenvalues/vectors
Characteristic Polynomial, Diagonalization
Eigenvalues of Special Matrices
Schur's Theorem, Spectral Theorem
GramSchmidt, QR Factorization

Typed Notes for HW5 and HW6 
Homework 6

Tues, Dec 13

Principal Axes Theorem, Pos Def Matrices
HW5 Discussion, Complex Eigenvalues of Real Matrices
Dynamical Systems, Jordan Form
Dynamical Systems, Markov Chains
Companion Matrices, Markov Chains
Page Rank, Total Least Squares
SVD, Image Compression
