# Fall 17 - Math 115A - Linear Algebra

This is the course website for Math 115A in Fall 2017. Most relevant information and links can be found here.

Please note that we are using Piazza for this class (see below).

## Instructor, TAs and office hours

### Instructor

Jens Eberhardt (myfirstname@math.ucla.edu)
Mondays 9:30-11AM, MS 6118 (115a students preferred),
Fridays 9:30-11AM, MS 3974 (31a students preferred).

### TAs

Frank White (flastname1618@ucla.edu)
Thursdays 10am-12pm, MS 2963 (for 115a),
Tuesdays 11am-12pm, MS 2963 (priority to 32a students).

Please check back here as office hours and locations may change.

## Schedule

The lectures take place Monday, Wednesday and Friday at 2:00 to 2:50PM in the Mathematical Sciences Building Room 5147. Time and date of the discussions can be found here.

In the following table you can see the preliminary lecture schedule and find your weekly problems list and homework.

# Date Content Homework
1 F, 09/29 Introduction, Vector Spaces over a Field (1.2) Week 0: None!
2 M, 10/2 Subspaces (1.3) Week 1
Problems:
Appendix C: Prove Thm. 1 (a)
1.2: 1, 2, 3, 4aceg, 8, 9, 11, 21 (one also writes $V\oplus W$ for the vector space $Z$ and calls it the direct sum of $V$ and $W$)
1.3: 1, 2abc, 3, 5, 8abf, 10, 11, 12, 15, 16, 20
1.4: 1, 2ab, 3ab, 5ab, 11, 13
1.5: 1, 2abc, 3, 4, 5, 9, 10, 12, 14, 15, 19
Homework:
Appendix C: Prove Thm. 1 (a), 1.2.21, 1.3.10, 1.4.5a
3 W, 10/4 Linear Combinations and Systems of Linear Equations (1.4)
4 F, 10/6 Linear Dependence and Linear Independence (1.5)
5 M, 10/9 Bases and Dimensions (1.6) Week 2:
Problems:
1.6: 1, 2, 4, 7, 9, 11, 13, 14, 15, 23, 25, 29, 30
Homework:
6 W, 10/11 Bases and Dimensions (1.6)
7 F, 10/13 Review, Linear Transformations, Null Spaces, and Ranges (2.1)
8 M, 10/16 Midterm #1 Week 3:
Problems:
2.1: 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 14, 17, 18, 19, 22, 37
2.2: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16
Homework:
2.1.1, 2.1.6, 2.1.14, 2.1.18
9 W, 10/18 Linear Transformations, Null Spaces, and Ranges (2.1)
10 F, 10/20 Linear Transformations, Null Spaces, and Ranges (2.1), The Matrix Representation of a Linear Transformation (2.2)
11 M, 10/23 The Matrix Representation of a Linear Transformation (2.2) Week 4:
Problems:
2.3: 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15
2.4: 1, 2abde, 3, 4, 5, 6, 10, 14, 15, 20
Homework:
2.1.17, 2.2.2a, 2.2.5abcd, 2.2.8, 2.3.2a, 2.3.4abcd
12 W, 10/25 Composition of Linear Transformations and Matrix Multiplication (2.3)
13 F, 10/27 Invertibility and Isomorphisms (2.4)
14 M, 10/30 Invertibility and Isomorphisms (2.4), The Change of Coordinate Matrix (2.5) Week 5:
Problems:
2.5: 1, 2, 3ac, 4, 6ab, 8, 12, 13
4.4: 1, 2, 3abg, 4, 5
Homework:
2.4.2abde, 2.4.3, 2.4.15, 2.5.2.abc, 2.5.3c
15 W, 11/1 The Change of Coordinate Matrix (2.5)
16 F, 11/3 Summary - Important Facts about Determinants (4.4)
17 M, 11/6 Eigenvalues and Eigenvectors (5.1) Week 6:
Problems:
5.1: 1, 2, 3abc, 4adh, 5, 6, 7, 8, 11, 15
Homework:
4.4.1, 4.4.3a, 5.1.3b
18 W, 11/8 Eigenvalues and Eigenvectors (5.1)
Friday, 11/10: Veterans Day Holiday!
19 M, 11/13 Midterm #2 Week 7:
Problems:
5.2.: 1, 2abd, 3ab, 7, 8, 10, 11, 12, 13, 18, 19, 20
Homework:
5.1.4g, 5.1.11, 5.2.1, 5.2.2a
20 W, 11/15 Diagonalizability (5.2)
21 F, 11/17 Diagonalizability (5.2)
22 M, 11/20 Diagonalizability (5.2) Week 8: No Homework!
23 W, 11/22 Inner Products and Norms (6.1)
Friday, 11/23: Thanksgiving Holiday!
24 M, 11/27 Inner Products and Norms (6.1), The Gram-Schmidt Orthogonalization Process and Orthogonal Complements (6.2) Week 9:
Problems:
6.1:1, 2, 3, 5, 8, 9, 13, 17, 22
6.2: 1, 2acdg, 4, 6, 7, 8, 10, 12
Homework:
25 W, 11/29 The Gram-Schmidt Orthogonalization Process and Orthogonal Complements (6.2)
26 F, 12/1 The Gram-Schmidt Orthogonalization Process and Orthogonal Complements (6.2)
27 M, 12/4 The Adjoint of a Linear Operator (6.3),Normal and Self-Adjoint Operators (6.4) Week 11:Problems:
6.3: 1, 2, 6, 7, 11, 12
Homework:
6.2.1, 6.2.2ab, 6.2.4
28 W, 12/6 Normal and Self-Adjoint Operators (6.4)
29 F, 12/8 Review

Hint: If you are using your phone, turning the screen horizontal makes the table easier to read.

# Textbook

S. Friedberg, et al, Linear Algebra, Custom UCLA 4th Ed., Prentice Hall.

Owning a copy of the textbook will be very helpful and is recommended however you might not find it necessary.

Hint: You might also try to buy used and older versions of Linear Algebra by Friedberg and Mathematical Thinking by D’Angelo and West. In my understanding Linear Algebra, Custom UCLA 4th Edition is just a combination of those two books.

## Homework

Solving problems on your own is one of the most important parts of this course. It will teach you how to apply your new knowledge and also be the best preparation for the midterms and final exam.

I encourage you to discuss the problems in teams but write up the solutions on your own. Simply copying your homework will not prepare you for the exams at all and is also not allowed (i.e. considered academic misconduct/cheating).

Hint: You can use Piazza to find teammates!

Every week you will be able to find a list of problems in the lecture schedule. They will be covering the material of the lectures and similar to exam questions.

Certain problems will be your homework which you will have to hand in during the lecture every Friday. Your homework has to be submitted in a form obeying the following rules:

• In the upper right corner of the first page put:

 Last and first name Student ID Date, Homework number 

• In the upper right corner of every additional page, put your name.
• Write only on the front side of every sheet of paper.
• Write legible. No crumpled, torn paper.
• Label each solution with the section and problem number (e.g. 7.2 #2).
We will not accept your homework if it violates any of the above rules.

# Exams

There will be two midterms and a final exam. Apart from the exceptions mentioned below, only writing equipment will be allowed in exams. Exams must be written in pen.

• Midterm 1: 2-2:50pm Monday, 16 October, 2017
• Midterm 2: 2-2:50pm Monday, 13 Novemver, 2017
• Final Exam: 8-11am Thursday, 14 December, 2017

Cheatsheets: For each exam, students may bring a cheat sheet. Each student must prepare their own handwritten cheat sheet. For the midterms, the cheat sheet may consist of one side of half a standard (A4 or letter) sheet of paper (i.e. A5 or letter folded in half lengthways). For the final, the cheat sheet may consist of one side of a standard sheet of paper. Cheatsheets that do not meet these requirements will be confiscated at the beginning of the exam.

Calculators: You may use a non-programmable, non-graphing calculator in exams. Calculators not meeting this specification will be confiscated.

Study: Here I will post some practice exams which might aid your study.

The midterm scores will be adjusted to account for any difference in difficulty. Your final grade will be calculated using the maximum of the following two grading schemes. Your letter grade will then be determined by your rank in the class. Unless something very out of the ordinary occurs I expect to give approximately 20-30% A’s and 55-65% A’s and B’s combined.

Option 1:

10% (7 best homework scores) +
40% (combined midterm scores) +
50% (final exam score)


Option 2:

10% (7 best homework scores) +
30% (best midterm score) +
60% (final exam score)


Effectively, this will mean that unless you score worse in the final than both midterms, your lowest midterm score will be dropped. This also means missing one midterm probably will not impact your grade in any serious way.

## Questions and Help

Mathematical questions should be asked on Piazza. You can either do so anonymously or with you full name. You are also encouraged to answer or take part in the discussion of the questions of others!

Obviously homework questions and solutions should not be posted on Piazza. Offences will be treated as academic dishonesty/cheating.

You can also visit me and the TAs in our office hours.

Administrative questions should in the first instance be directed to your TA. If your TA cannot resolve your query then you should contact me.

If you need to email me, the subject line must include the string math115. If not, then there is a good chance your email will slip through the cracks and remain unanswered.