Linear Algebra: Schedule of Topics
Week 1
Wednesday
9/3: Introduction to the Course
Friday 9/5:
Introduction to Proofs, Mathematical Induction
Week 2
Wednesday 9/10: Introduction to Vector Spaces
Friday 9/12:
Introduction to Subspaces
Week 3
Monday 9/15: Solving Systems of Linear Equations
Wednesday
9/17: Linear Dependence and Independence
Friday
9/19: Bases and Dimension
Week 4
Monday 9/22: Review Chapter 1
Wednesday 9/24: Exam 1
Friday 9/26:
Linear Transformations, Ranges,
Nullspaces
Week 5
Monday 9/29: Representing Linear
Transformations by Matrices
Wednesday 10/1: Matrix Algebra
Friday
10/3: Composition of Linear Transformations
Week 6
Monday 10/6: Matrices and Linear Transformations
Wednesday 10/8: Invertibility and Isomorphisms
Friday 10/10: Change of Coordinates
Week 7
Monday 10/13: FALL BREAK
Wednesday 10/15: Elementary Matrices and
Elementary Matrix Operations
Friday 10/17: Matrix Rank and Matrix
Inverses
Week 8
Monday 10/20: Solving Systems of Linear
Equations I
Wednesday 10/22: Solving Systems of Linear Equations II, Review for Exam 2
Friday 10/24: Exam 2
Week 9
Monday 10/27: Determinants:
The 2x2 case
Wednesday 10/29: Determinants:
The General Case
Friday 10/31: Properties of Determinants
Week 10
Monday 11/3: More on Determinants
Wednesday 11/5: Eigenvalues and Eigenvectors
Friday 11/7: The Characteristic Polynomial
Week 11
Monday 11/10: Diagonalizability
Wednesday 11/12: Introduction to Markov Chains
Friday 11/14: Absorbing State Markov
Chains
Week 12
Monday 11/17: Cayley-Hamilton Theorem
Wednesday 11/19: Review for Exam 3
Friday 11/21: EXAM 3
Week 13
Monday 12/1: Review of Abstract Vector Spaces
Wednesday 12/3: Introduction to Inner Products
Friday 12/5: Gram-Schmidt
Orthogonalization
Week 14
Monday 12/8: Introduction to Graph
Theory
Wednesday 12/10: Graph Theory and the
Movies
Friday 12/12: Review for Final Exam