115b/1 - Winter 2011 - UCLA

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Time: 1pm MWF for lectures and 1pm R for discussion.
Place: MS 5147.

E-mail: antieau@math.ucla.edu.
Phone: 310-825-3068.
Course webpage: www.math.ucla.edu/~antieau/201101-115b.html

Office hours: 2-3:30pm Monday, 2-3 Wednesday in my office, MS 6617D.
TA: Pietro Carolino (pietro@math.ucla.edu).
TA office hours: 11:30am-1pm Thursday, MS 2903.

Book: Friedberg, et al, Linear algebra, 4th Edition, Prentice-Hall.

Course outline: Bold numbers in parentheses indicated the number of lectures on a given topic during that week.

Week 01 - Introduction and review (1), dual spaces (2).
Week 02 - Review of 5.1-5.2 (1); invariant subspaces and the Cayley-Hamilton theorem (2).
Week 03 - Invariant subspaces and the Cayley-Hamilton theorem (1); the minimal polynomial (1) [short week, guest lectures].
Week 04 - The minimal polynomial (1); review of 6.1-6.4 (2).
Week 05 - Unitary and orthogonal operators and their matrices (3).
Week 06 - Midterm; orthogonal projections and the spectral theorem (2).
Week 07 - orthogonal projections and the spectral theorem (1); the geometry of orthogonal operators (2).
Week 08 - The geometry of orthogonal operators (1); the Jordan canonical form (1) [short week].
Week 09 - The Jordan canonical form (2); other canonical forms and decompositions (1).
Week 10 - Other canonical forms and decompositions (3).

Important dates:

Monday, 10 January 2011: HW1 due.
Monday, 17 January 2011: Martin Luther King, Jr. day; no class.
Wednesday, 19 January 2011: HW2 due.
Monday, 24 January 2011: HW3 due.
Monday, 31 January 2011: HW4 due.
Monday, 7 February 2011: Midterm. Sample midterm.
Monday, 14 February 2011: HW5 due.
Monday, 21 February 2011: President's day; no class.
Wednesday, 23 February 2011: HW6 due.
Monday, 28 Febraury 2011: HW7 due.
Friday, 11 March 2011: HW8 due.
Friday, 18 March 2011: Final examination, 8:00am-11:00am.

Policies:

No late homework will be accepted.
The grade will be based on 40% homework, 20% midterm, 40% final.
This class will use the myUCLA gradebook facility.
Requests for re-grading will only be considered within 14 calendar days of the due date of the original assignment or midterm and no later than the day before the final. All such requests are to be directed to the instructor; the TA may not make changes to the grades.
A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including the midterm, but who, for a legitimate, documented reason, miss the final.
Use of electronics is strongly discouraged during class.
Come to office hours!

Catalogue description: 115B. Linear Algebra. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading.