Table of topics and assignments

Table of topics and assignments

Starting with May 15, we'll meet for every class between 6:00-8:15pm (MWF). If DM 164 is free, we'll continue to use it. If not, we'll find an alternative room (maybe DM 409A).

I placed an older edition of Steven Leon's Linear Algebra --the undergraduate textbook -- on the shelves outside DM 416A. You can use it there, but please do not take it away from that area.

Besides the textbook by Sadun, I will also be using Peter D. Lax's book, "Linear Algebra and its Applications", 2nd edition, Wiley, ISBN 978-0-471-75156-4

Date	Topics covered	Suggested Assignment	Comments
May 13	Chapter 1 -- Introduction 2.1	Ex: 1-7 1-11 odd, 13-17all, 18, 19, 21	Also read Appendix A and all examples given.
May 15	2.2 2.3	1-11 odd 1-5 odd, 6-12 even	Homework 1 due Wednesday, May 22 (pb. 2 has been changed)
May 17	2.4 part of 2.5	1-11odd 1-4all
May 20	rest of 2.5 (quotient spaces) 3.1 3.2 3.5	5-8all 1-9all 1-14all 1-10all
May 22	3.3 applications of rank-nullity thm. (see class notes)	1-8all Exercises 11-15 from p. 30-31, handout	Homework 2 due Wednesday, May 29
May 24	Duality -- Chapter 2 and parts of 3 of P. Lax's book	Exercises 1-7 from p. 14-18, handout.	Here is a complete proof (by H.R. Parks, Oregon State University) for the statement that the dual of an infinite dimensional vector space is not isomorphic to the vector space. The special case presented in class is adapted from the link above. Homework 3 due Monday, June 3: Exs. 5, 6, p. 18 handout. (You don't have to do part (c1) of Ex. 6, as it was already done in class.)
May 27	No class --Memorial Day -- University closed
May 29	4.1 4.2 4.3 5.1	1-7all 1-6all 3-14all 1-5, 8-10all	The midterm exam on June 3 will cover all material done up to (and including) May 29. About 40-50% of the exam will be computational (exercises like those in the suggested assignments) and 50-60% will be more theoretical (like the theoretical problems in the assignments, exercises left in class, or parts of theorems proved in class).
May 31	4.4 4.5	1-5all,7-11odd (Do these after midterm) 1-9all (Do these after midterm)	Here is the midterm I gave in Fall 2011. Be aware that the one for this semester may be considerably different.
June 3	Midterm exam		You may do problem 7 (or 7', or both) as a take-home part of your final. Due date is Wednesday, June 5. I will consider one of them, but as a take-home, I value more Pb. 7 than 7', so the score may reflect that.
June 5	4.6 4.7	1-11all (for all students) 1-8all (for all students)	The statements in this lecture should be known by all students, the exercises left during the lecture are for GM's only (GM = graduates in math)
June 7	Spectral Theory handout 4.9	all exercises in handout (for GM's) 1-15 (for GM's only), 16-21 (for all)	The statements in this lecture should be known by all students, the exercises left during the lecture are for GM's only (GM = graduates in math) Homework 4 due Wednesday, June 12: Pbs. 4, 7, page 85 textbook
June 10	4.8 5.2 5.3 5.4	1-12all (for all students) 1-4all, 6-10all (for all students) 1, 2 (for all students), 4-9 (for GEO's only) 1, 3, 4, 6, 8 (for all students)	Exam Topics for GEO's only: know to derive the systems for coupled oscillators, + eqns. for Pbs. 8, 9 1-5 from Exploration Difference Equations (for GEO's only)
June 12	5.5 5.6 5.7	1,3, 4, 6-9all (for all students) 1,3-8, 15, 16 (for all students) 1-11 all (for all students)	Theorem 5.1 from Sadun assuming Peron (for all students), Peron's Theorem from handout (for GM's only) This is the wikipedia link for the (first) Cat & Mouse game presented in class
June 14	Class cancelled		Homework 4 is extended for Monday, June 19 Homework 5 due Wednesday, June 19
June 17	Bilinear forms, inner products, self-adjoint operators	section 7.2 #1-6 all (for all students)
June 19	Orthogonal, Unitary, Normal operators Receive the theoretical final exam topic		Exam topic for GM's: Fill in the class sketch for the spectral theorem for normal operators
June 20	Problem solving		This is a replacement for the June 14 class
June 21	Final Exam		Final exam will have a take-home component with one theoretical topic that you will receive earlier and an in-class component with 2 problems that you will solve during the final exam.
		Here are your scores and grades for the course.	The column "FE" contains your total score on the final exam out of 120 points possible. The in-class and take-home parts were worth 60 pts each. The "Grade" column is your grade for the course. Have a good summer and good luck with your further studies!