Math 2270-3 Linear Algebra

Instructor: Mladen Bestvina

Office: JWB 210

Web page: http://www.math.utah.edu/~bestvina/2270

Office Hours: after class or by appointment

Textbook: Linear Algebra 3rd Edition, by Serge Lang, Springer Verlag

Time: MWF 16:35-17:50

Room: JWB 308

The course is an honors version of 2270 and it will be taught in a more abstract manner than the regular sections. I plan to cover at least the first 8 chapters of the textbook, and maybe more if the time permits.

The grades will be based on homework and class participation.

There are a few more books you might find useful:

Introduction to Linear Algebra, by Serge Lang. This is a more elementary version of the textbook, intended for regular sections. We may occasionally refer to it.

Linear Algebra done Right, by Sheldon Axler. This is at the same level as our textbook.

Linear Algebra done Wrong, by Sergei Treil. Same as above, but with a dose of humor (and sarcasm). It can be freely downloaded from here.

If a concept we discuss is unclear you may want to consult some of these books.

You can contact me by email.

Homework 1, due Sept 2.

We'll discuss how to solve a system of linear equations, which is not in Lang's book. I'll follow Treil's book above, the first 4 sections of chapter 2.

Homework 2, due Sept 11. Lang p.36-42: #18(e), 19, 20, 32, 35, 39.
    Hint for 32: Use that ^t(AB)=^tB^tA
    Hint for 35: Show that if A has entries 0 below the k^thdiagonal (i.e. j-i<k implies a_ij=0) and B has entries 0 below l^th diagonal then AB has entries 0 below (k+l)^th diagonal. By popular demand, here is the solution to #35.

Homework 3, due Sept 16. Treil's book Ch.2: p.46: 2.2, p.51: 3.1, 3.2, 3.3 a,c, p.54: 4.1
    Hint for 3.3c: Rearrange the order of vectors and then it's already in echelon form!

Homework 4, due Sept 23. Lang p.58:#15,18, p.63:#3,5, p.70 #8a,10

Homework 5, due Sept 30. Lang p.93, #1(b), 8(e), 8(f), p.103 #1,2, p.111 #0,1

Homework 6, due Oct 7. Lang p.103, #3, p.111 #2b, p.117 #1g,3,6. Read Treil's book sections 4-5 on p.136-146 and do #4.1,4.4 on p. 141.

Homework 7, due Oct 21.

Homework 8, due Oct 28: Lang p.154 #1a,5b, Treil p.85 #3.4,3.9,3.10, p.89 #4.1, also write the given permutation as a product of transpositions

Homework 9, due Nov 4: Treil p.94 #5.2,5.3,5.4,5.5, Lang p.177, #2.

Homework 10, due Nov 11: Lang p.199: #4,5 (hint: use the char poly), p.213: #8d, 10,11,15 (hint: if ABv=λv apply B but watch out for λ=0)

Homework 11, due Nov 18: Lang p.183: 1,2,6,11,12,15 (warning: this homework is a bit harder than usual)

Homework 12, due Nov 25: Lang p.218 #3, p.223 #9f, 16d, p.226 #1,4, Treil p.170 #2.6,2.8.

The last homework will be assigned on Monday and will be due the following Monday. Happy Thanksgiving!

Homework 13, due Dec 7: Lang p.260 #2, p.261 #2, p.266 #1,2. Hint on #1: Define D to be multiplication by λ on the generalized λ-eigenspace.

    I am not assigning #6,7 on p.267, but if you want to try a little "research project" you could give it a shot.

That's all folks! If you feel like it look at the collection of linear algebra problems by Prof. Jerry Kazdan and see how many you can solve.