PAUL BALMER
Professor of
Mathematics
UCLA

TEACHING
MATH 115A  LINEAR ALGEBRA  Fall 2017  Lectures 3 and 4.
DO NOT TAKE THIS CLASS IF YOU HAVE A TIME CONFLICT WITH ANY OF THE EXAMS!
 Schedule & TAs

Lecture 3: MWF 1010:50, MS 5147. TA: Don Laackman.
Lecture 4: MWF 1111:50, MS 5147. TA: Redmond McNamara.
 Textbook

S. Friedberg, et al, Linear Algebra, Custom UCLA 4th Ed., Prentice Hall. See details at UCLA store.
 Calendar and outline

Week 01: §§ 1.21.4: Vector spaces and subspaces. Linear combinations.
Week 2: §§ 1.51.6: Linear (in)dependence, bases and dimension.
Week 3: §§ 2.12.2: Linear transformations and matrices.
Week 4: (Friday October 20: Midterm 1) § 2.3: Composition and matrix multiplication.
Week 5: §§ 2.42.5 & § 4.4: Invertibility and change of coordinates. Recalling determinants.
Week 6: §§ 5.15.2: Eigenvalues and eigenvectors. Diagonalizability.
Week 7: § 5.2 & § 6.1: Diagonalizability. Inner products. Review.
Week 8: (Monday November 20: Midterm 2) § 6.1: Norms.
Week 9: §§ 6.26.3: GramSchmidt. Adjoint operators.
Week 10: §§ 6.4: Normal and selfadjoint operators. Review.
 Testing

Weekly homework due every Friday in class  see details below.
1st midterm: Friday, October 20, in class.
2nd midterm: Monday, November 20, in class.
Final exam: Saturday, December 9, TBA (lec.3) and TBA (lec.4), in class (MS 5147).
 Missed it?

If you miss an exam or a homework deadline, don't worry! The system is flexible: You can miss two homework without consequences. Also, if you miss one midterm, your final will simply weigh more. Things happen  I understand. However, instead of giving makeup exams, I build in some flexibility in the grading scheme. So, you don't need to come and tell me what happened because
there will be NO MAKEUP AT ALL, under no circumstances, neither for homework, nor for the midterms, nor for the final exam.
 Grading

Homework will simply record regularity of your work, independently of the quality. So, do not waste your time copying other people's work! Returning 8 out of the 10 weekly homework gives you full HW score.
Midterms count for 15% each. However, if you do better on the final than on one of the midterms, your lowest midterm grade is dropped and the final counts 75% instead of 60%.
In short, your overall final grade will be the best of the following two variants:
 10% homework + 30% for both midterms + 60% final.
 10% homework + 15% best midterm + 75% final.
Regrades on midterms must be requested upon reception of your copy, no later than two weeks after the exam date. After this time, no requests for corrections will be honored.
 Homework

The numbers correspond to problems in the corresponding section of the textbook.
Week 
Due date 
Exercises in textbook 
1 
Fri, Oct 6 
§ 1.2: Ex: 6, 7, 9, 15, 16, 19, 20, 22;
§ 1.3: Ex: 6, 8, 19, 24, 29, 30, 31.

2 
Fri, Oct 13 
§ 1.4: Ex: 2, 3, 8, 10, 12, 14, 15, 16;
§ 1.5: Ex: 3, 6, 7, 13, 17, 18, 19;
§ 1.6: Ex: 4, 9, 11, 14, 15, 17, 22, 29, 32.

3 
Fri, Oct 20 
§ 2.1: Ex: 3, 5, 11, 13, 14, 17, 18, 21, 24, 26, 31, 36.

4 
Fri, Oct 27 
§ 2.2: Ex: 2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16;

5 
Fri, Nov 3 
§ 2.3: Ex: 3, 4, 11, 12, 13, 16, 17;
§ 2.4: Ex: 2, 3, 4, 7, 9, 13, 14, 15, 17, 19, 23.

6 
Wed, Nov 8 
§ 2.5: Ex: 3, 5, 6, 8, 9, 10, 11, 13, 14;
§ 4.4: Ex: 1, 3, 4, 5, 6.

7 
Fri, Nov 17 
§ 5.1: Ex: 3, 4, 6, 7, 9, 12, 13, 22, 23;
§ 5.2: Ex: 3, 8, 9, 10, 11, 12, 13, 14, 16.

8 
Wed, Nov 22 
§ 6.1: Ex: 2, 8, 9, 10, 12, 14, 15, 16, 18, 21.

9 
Fri, Dec 1 
§ 6.2: Ex: 2, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18;
§ 6.3: Ex: 7, 8, 9, 10, 11, 12, 13, 14.

10 
Fri, Dec 8 
§ 6.4: Ex: 3, 4, 6, 7, 9, 11, 13, 17, 21.

Here is a list of past courses.
