Linear Algebra:  Schedule of Topics

 

Week 1

Wednesday 9/3:  Introduction to the Course

Friday 9/5:  Introduction to Proofs, Mathematical Induction

 

Week 2

Monday  9/8:  Review of Lines and Planes

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