A rough outline of the material we intend to cover will appear here.

Week 1 Jan. 6 - 9, vector spaces as general algebraic structures - this will roughly follow parts of Lang's first chapter supplemented by lecture notes; practice problems: Chapter 1, section 1: 1 - 5, 14; section 2, 7 - 10

Week 2 Jan. 13 - 16, introduction to vectors spaces, linear equations and matrices over arbitrary fields, Chapters 1-2; practice problems, Chapter 2, section 1, exercises on dimensions, 1 - 7, section 2, 1 - 4, section 3, 17 -18, 35 - 39

Week 3 Jan. 20 - 23, dimension, linear transformations - finishing Chapters 1 and 2, beginning chapter 3; practice, Chapter 3, section 2: #5, 10, 16, 17; section 3, # 9, 13 - 16; section 4

Week 4 Jan. 27 - Jan. 30, more on linear maps, fields, polynomial rings and factorization; practice Chapter 3, section 4, #4, 5, 10 - 13, 17 - 18, 20 - 21; Chapter 4, section 3, #2, 8 - 11

Week 5 Feb. 3 - Feb. 6, polynomials applied to operators, triangularization, Chap. 9, 10 first test on Feb. 6. practice problems, Chapter 9, section 2, #2 - 5

Week 6 Feb. 10 - Feb. 13, Cayley-Hamilton Theorem, decomposition of vector spaces, Chap. 10, 11, section 1 - 2. Practice problems, Chapter 11, section 1, #2, section 2, #1 - 3

Week 7 Feb. 24 - Feb. 27, decomposition of vector spaces, Jordan canonical form, Chap. 11, sections 4 and 6. Practice problems, Chapter 11, section 4, #2 and 3, section 6, #1, 4, 5

Week 8 Mar. 3 - Mar. 6, conclusion of Jordan canonical form, determinants, Chap. 6, sections 6 and 7 although it will be helpful to review the other sections in Chap. 6. Practice problems, Chapter 6, section 6, #1 - 3 (read the section to understand Lang's notation); section 7, #1, 2

Week 9 Mar. 10 - 13, second test on Mar. 13, systems of homogeneous linear equations, matrix exponentiation

Week 10 Mar. 17 - 20, matrix exponentiation continued, Chap. 5, section 1, 2 and 6: scalar products; practice problems, section 1, #1 - 3, section 2, #3 - 5, 7, 8, 10, section 6, #4, 7

Week 11 Mar. 24 - 27, Chap 5, cont'd; Chap 8, sections 3 - 6; practice problems, section 3, #3; section 4, #3, 5, 10, 12, 21, section 5, #1, 4, 5

Week 12 Mar. 31 - Apr. 1, Chap. 8 cont'd; Chap. 10, section 3, practice problems #1, 2

Week 13 Apr. 7 - 8, catch-up