Joan E. Licata

Joan E. Licata

Math 113: Linear Algebra and Matrix Theory (2011)

Office Hours:

Monday 2:30-3:30

Tuesday 1:30-3:30

or by appointment

380-382E

Course Details:

Monday, Wednesday, &

Friday, 10:00-10:50

380-380W

Course CA:

Jose Perea, 381D

Office Hours: Tuesday &

Thursday, 5:30 - 7:00

Math 113 is a linear algebra course which emphasizes abstract properties of vector spaces and linear maps. Depending on your interests, you may prefer Math 104, which emphasizes applications of linear algebra. This class has no formal pre-requisites.

Outside of my office hours, the best way to reach me is by email; I try to respond to weekday emails within 24 hours.

The text for the course is Linear Algebra Done Right, by Sheldon Axler (2nd ed.). A copy of the text may be found on reserve in the Math Library.

Homework: The weekly problem sets (below) are your best opportunity to master the course material. You’re encouraged to work with other members of the class, but each student is responsible for writing up his or her own solution. Please acknowledge any collaborators by name in a note at the end of your problem set. All assignments will be evaluated on both content and exposition, so it’s a good idea to approach problems in two steps: first, figure out the logical structure of your solution. Then decide on the clearest way to explain your argument and write it up carefully.

Evaluation: The course grade will be based on problem sets (30%), a midterm (30%), and a final exam (40%). Thoughtful participation in class can help a borderline grade, as can improvement over the course of the quarter.

... and now for the fine print:

No late homework assignments will be accepted, and if your assignment isn’t stapled, only the first page will be graded. Your lowest homework score will be dropped at the end of the quarter. Per math department policy, any students found guilty of an Honor Code violation will receive an automatic NP in Math 113.

Exams: The midterm exam is scheduled for May 4 from 7:00 to 9:00 p.m in Hewlett 201, and there’s a practice exam here. The final exam is scheduled for June 8, from 8:30 to 11:30 a.m. in 380-380C. Here’s a practice final, together with some hints if you get stuck. Update: The average on the final exam was 41/75, and the quartiles were roughly 30, 40, and 55. If you have already left campus and would like to see your final exam, let me know and I’ll send you a scanned copy of the graded test.

Syllabus and Assignments: Problem sets are due to the envelope in my mailbox by noon each Wednesday. You may also turn assignments in during class on Wednesday morning. Solutions are posted on Coursework in the Materials section.

Week 1: (March 28 - April 1) Vector spaces, subspaces, linear combinations, direct sums

Read Chapter 1 and ProofTips.pdf.

Due March 30: Send me a short email introducing yourself. Why are you taking 113?

Week 2: (April 4- April 8) Linear independence, bases, dimension

Read Chapter 2

Due April 6: Ch. 1, problems 4, 6, 7, 9, 12, 13, 14, 15, Additional Problems

Week 3: (April 11- April 15) Linear maps, isomorphisms

Read Chapter 3

Due April 13: Ch. 2, problems 2, 3, 7, 8, 9, 11, 15, Additional Problems

Week 4: (April 18- April 22) Matrices, complex numbers, polynomials, eigenvalues

Read Chapter 4 and Chapter 5, pp. 76-80

Due April 20: Set A: Ch. 3, problems 2, 3, 5, 6, 14

Set B: Ch. 3, problems 22, 24, and Additional Problems

Week 5: (April 25 - April 29) Eigenvalues, eigenvectors,

Read Chapter 5, pp. 80-93

Due April 27: Set A: Ch. 4, problems 3, 5; Ch. 5, problems 1, 3, 4

Set B: Ch. 5, problems 7, 8, 10, 13, matrix exercises (ungraded)

Week 6: (May 2 - May 6) Generalized eigenvectors, characteristic polynomial

Read Chapter 8, pp. 164-176

Due May 4: Set A: Ch. 5, problems 15, 16, 18

Set B: Ch. 5, problems 20, 21, 22

Midterm May 4, 7:00 - 9:00 p.m.

Week 7: (May 9 - May 13) Minimal polynomial, Jordan normal form

Read Chapter 8, pp. 179-187 (you may skip the section on square roots)

Due May 11: Set A: Ch. 8, problems 2, 3, 8, 9

Set B: Ch. 8, problems 10, 11, 14, 16

Week 8: (May 16 - May 20) Inner products, orthonormal bases, linear functionals, adjoints

Read Chapter 6

Due May 18: Set A: Ch. 8, problems 20, 21, 23, 25

Set B: Ch. 8, problems 27, 30, 31, and Additional Problems

Week 9: (May 23 - May 27) Fourier series, self-adjoint and normal operators, Spectral Theorem

Read Chapter 7, pp. 128-137, 147- 152

Due May 25: Set A: Ch. 6, problems 5, 9, 12, 15, 18

Set B: Ch. 6, problems 19, 25, 28, 29

Week 10: (May 30 - June 1) Spectral Theorem, perhaps determinants or isometries

Due June 1: Set A: Ch. 7, problems 1,3, 4, 7

Set B: Ch. 7, problems 9, 10, 15, Additional Problem