033 AH - Honors Linear Algebra and Applications - Winter 2012 - UCLA

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Time: 10am MWF for lectures and 10am T for discussion.
Place: Lectures: MS 7608. Discussion: MS 7608..

E-mail: antieau@math.ucla.edu.
Phone: 310-825-3068.
Course webpage: www.math.ucla.edu/~antieau/201201-033ah.html
Course discussion site: piazza.com

Office hours: 1-2 Monday, 11-12 Wednesday, and 11-12 Friday in my office, MS 6617D.
TA: Anton Malyshev (amalyshev@math.ucla.edu).
TA office hours: 11-12 Tuesdays and 10-11 Thursdays in MS 3921.

Book: Strang, Introduction to Linear Algebra, Fourth Edition, Wellesley, ISBN-13: 978-0-980232-71-4. Note that any version of the book is acceptable. However, if there are differences in numbering between the editions (I don't know if there are), then it is your responsibility to read the correct sections and do the correct exercises.

Course outline:

01/09 - Vectors and linear combinations, lengths and dot products (1.1, 1.2).
01/11 - Matrices (1.3).
01/13 - Vectors and linear equations (2.1).
01/16 - Martin Luther King's Birthday. No class.
01/18 - The idea of elimination (2.2).
01/20 - Elimination using matrices (2.3).
01/23 -
01/25 -
01/27 -
01/30 - Midterm 1. Practice midterm: [pdf].
02/01 -
02/03 -
02/06 -
02/08 -
02/10 -
02/13 -
02/15 -
02/17 -
02/20 - Presidents' Day Holiday. No class.
02/22 -
02/24 - Midterm 2. Practice midterm: [pdf].
02/27 -
02/29 -
03/02 -
03/05 -
03/07 -
03/09 -
03/12 -
03/14 -
03/16 -
03/23 - Final. The final will be cumulative. The final will take place from 11:30am to 2:30pm on Friday 23 February. Practice final: [pdf].

Homework: (note that you should show all work to receive full credit.)

Week 1 (due 01/13) - 1.1: 1-10, 15-19, 28-29. 1.2: 1-3, 5-9, 12-15, 17, 27-29.
Week 2 (due 01/20) - 1.3: 1-9, 14. 2.1: 1-5, 9-18, 20, 31, 32, 35. 2.2: 1, 2, 4, 7, 11-15, 18, 21, 31. 2.4 (optional): 1-7, 14, 16-20, 28, 36-37. You don't need to turn the problems from Section 2.4 in, but you are responsible for being familiar with matrix multiplication. Thus, I strongly encourage you to do the selected problems.
Week 3 (due 01/30) - 2.3: 1-4, 6-10, 12-14, 18, 20, 25, 27, 31. 2.5: 1-2, 5, 7-12, 21, 23-25, 30, 32, 40. 2.6: 3-7, 12, 15, 23. 2.7: 1-4, 6, 8-12, 17, 22, 24, 28, 36, 38, 40.
Week 4 (due 02/03) - 3.1: 1-2, 9, 11-13, 19-20, 23, 29. 3.2: 1-4, 16, 21-22, 26-27, 35.
Week 5 (due 02/10) - 3.2: 35. 3.3: 3, 7, 17-19, 27. 3.4: 1, 4, 34, 36. 3.5: 2, 23, 41, 45. 3.6: 2, 3, 11, 14, 26, 32. Problem: A square matrix A is nilpotent if A^n=0 for some n. Give two different proofs of the fact that a strictly upper triangular matrix is nilpotent, where an upper triangular matrix is strictly upper triangular if its diagonal entries are all zero.
Week 6 (due 02/17) - 4.1: 9, 10, 13, 24, 25, 30. 4.2: 2, 5, 17, 18, 26, 30, 31, 34. Problem: An orthogonal matrix is a square matrix such that A^T=A^{-1} (the transpose of A is the inverse of A). Show that A is orthogonal if and only if the columns of A are mutually perpindicular unit vectors. Then, prove that if A is orthogonal, then for any two vectors x and y, the dot product x.y is the same as the dot product Ax.Ay.
Week 8 (due 03/02) - 4.3: 7, 9, 10, 17, 26. 4.4: 14, 15, 21, 23. 5.1: 15, 18, 27. 5.2: 1, 12. 5.3: 6, 39. 6.1: 1, 2, 3, 15, 35, 36.
Week 9 (due 03/09) - 6.2: 7, 8, 16, 18, 19, 33, 36. 6.4: 3, 8, 30. 8.3: 1, 2, 3.
Week 10 (due 03/16) - 6.5: 3, 6, 14, 15, 17, 25, 33, 35. 6.6: 6, 10, 14, 22. 6.7: 1, 2, 3, 4, 14. Let A be a positive definite matrix. Try to prove that no permutations are required to do elimination, or find a counterexample. If there are permutations are required, show that the number of permutations required is even.

Policies:

I encourage everyone to work in groups on the homework.
I encourage everyone to use the free discussion board piazza.com for discussion of the class. You may go to their website, and enroll in MATH 31 AH. This is a site that allows everyone to ask and answer questions. It is my hope that you will help each other out on the site, but I would prefer you restrict the questions to questions about the content, instead of simply about the homework. I don't want to see all of the homework solutions posted there. If there are questions about policies, exams, etc, please post them on piazza as well. I will answer them there so that the answers will be public and useful to other students.
I encourage everyone to play around with matrices using sagenb.org. I will create some examples there to help you figure it out.
There will be 9 homework assignments. Homework is due in lecture on Fridays.
No late homework will be accepted.
The grade will be based on 20% homework, 20% midterm 1, 20% midterm 2, 40% final.
If you wish to request an accommodation due to a disability, please contact the Office for Students with Disabilities as soon as possible at A255 Murphy Hall, (310) 825-1501, (310) 206-6083 (telephone device for the deaf). Website: www.osd.ucla.edu.
This class will use the myUCLA gradebook facility.
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 phones is strongly discouraged during class.
Come to office hours!
There is a Student Math Center, located in MS 3974, which offers free individual and group tutoring for all lower division math courses. This is a walk-in service. No appointments are necessary. Its hours are 9am-3pm Monday-Thursday, and it opens Monday 26 September 2011.

Catalogue description: Lecture, three hours; discussion, one hour. Requisite: course 3B, 31A or 32A with a grade of C- or better. Introduction to linear algebra: systems of linear equations, matrix algebra, linear independence, subspaces, bases and dimension, orthogonality, least-squares methods, determinants, eigenvalues and eigenvectors, matrix diagonalization, and symmetric matrices. P/NP or letter grading.