## MAT 310-02 (Elementary Linear Algebra) Fall 2016

Linear systems, matrices, determinants, eigenvalues and eigenvectors, finite-dimensional vector spaces, linear transformations.

- Pr. grade of at least C in MAT 292

The class meets TTh 9:30 - 10:45 am in Petty 217. The final exam is Thursday, December 8, 2016, 8:00 - 11:00 am.

All announcements and handouts will be posted on Canvas. Be sure to check your UNCG email regularly.

### Documents (pdf)

- Syllabus (PDF)
- Discrete Dynamical System Example (Python)
- Handout on proof writing (PDF)
- Handout for induction proofs (PDF)
- All additional documents will be posted on Canvas.

### Homework

The exercise list below will be updated as the semester progresses. Of these, only submit the ones in square brackets to be graded.

Make sure the assignments you turn in are in compliance with the Homework Guidelines for Mathematics.

- 1.1 (1-4, 7-14, 17-26) [3, 4, 8, 10, 12, 14, 18, 23, 24, 25, 26]
- 1.2 (1-4, 7-16, 19-27, 30, 31) [2, 8, 10, 12, 21, 22, 23, 24, 26, 30, 31] Note: The instructions on problems 1-2 are unclear, since some matrices in echelon form are in reduced echelon form, and some matrices in echelon form are not in reduced echelon form, and some are not in echelon form. You should distinguish between these three types as reduced echelon form, echelon form, and not echelon form, respectively.
- 1.3 (3-14, 21-28, 33, 34) [4, 6, 10, 12, 14, 22, 23, 24, 28, 33]
- 1.4 (1-20, 23-26, 28-30, 32) [2, 4, 8, 10, 12, 14, 23, 24, 25, 32]
- 1.5 (1-16, 19, 20, 23-26, 28-37) [2, 6, 10, 12, 14, 16, 20, 23, 24, 25]
- 1.7 (1-30, 33-40) [2, 6, 8, 14, 21, 22, 27, 28, 38, 39]
- 1.8 (1-12, 13-18, 20-25, 31, 32, 35) [4, 6, 10, 16, 17, 21, 22, 31, 35]
- 1.9 (1-6, 15- 20, 23-28, 31-36) [4, 6, 16, 18, 20, 23, 24, 26, 27, 33, 34]
- 1.10 (1, 2, 9, 10, 12) [2, 9, 10]
- 2.1 (1, 2, 5-8, 10, 12, 13, 15, 16, 18-22, 28, 29, 32, 34) [2, 6, 8, 10, 15, 16, 18, 20, 29, 34]
- 2.2 (3, 4, 6-12, 14, 16, 18, 22, 24, 31, 32, 35) [3, 6, 7, 8, 9, 10, 14, 22, 24, 32]
- 2.3 (1-8, 10-14, 18-25, 34, 36) [4, 6, 8, 11, 12, 13, 20, 23, 34, 36]
- 2.8 (1-6, 8, 15-24, 26) [4, 6, 8, 16, 18, 20, 21, 22, 23, 24, 26]
- 2.9 (1-6, 8, 9-18, 22, 24, 25, 27) [4, 6, 10, 12, 14, 17, 18, 22, 27]
- 3.1 (1-12, 15-22, 24-26, 34, 35, 39-41) [2, 6, 10, 12, 20, 22, 24, 34, 35, 41]
- 3.2 (1, 2, 4, 5, 6, 8, 10, 15-18, 21, 22, 24, 25, 27, 28, 31, 34, 35, 40) [1, 2, 5, 6, 22, 24, 27, 28, 31, 34, 40]
- 3.3 (7, 19, 20, 22, 26-32) [20, 26, 27, 28, 29, 32]
- 4.1 (1-20, 23, 24, 32, 33) [1, 2, 5, 11, 14, 18, 20, 23, 24, 32, 33]
- 4.2 (1-37) [2, 6, 12, 16, 25, 26, 27, 28, 31, 35]
- 4.3 (1-16, 21-31) [2, 4, 8, 12, 14, 21, 22, 24, 26, 31]
- 4.4 (1-32) [2, 6, 12, 15, 16, 17, 20, 24, 28, 32]
- 4.5 (1-32) [4, 8, 10, 19, 20, 22, 29, 30, 31]
- 4.6 (1-30) [1, 2, 6, 13, 17, 18, 20, 27, 28, 30]
- 4.7 (1-14) [1, 2, 6, 7, 8, 11, 12, 13, 14]
- 5.1 (1-36) [2, 4, 6, 12, 16, 18, 21, 22 omit c, 24, 25]
- 5.2 (1-27) [4, 6, 9, 10, 16, 18, 21, 22, 23, 24]
- 5.3 (1-32) [2, 4, 8, 12, 21, 22, 24, 25, 27, 31]
- 5.4 (1-31) [2, 3, 5, 8, 12, 16, 17, 19, 20, 25]
- 5.5 (1-26) [4, 12, 15, 18, 22, 23, 25]
- 5.6 (1-18) [1, 2, 6, 10, 12, 18a]
- 6.1 (1-31) [2, 6, 10, 14, 16, 20, 24, 26, 28]
- 6.2 (1-34) [2, 6, 12, 14, 16, 23, 24, 27, 34]
- 6.3 (1-24) [2, 6, 8, 12, 14, 15, 19, 21, 22, 23]
- 6.5 (1-25) [2, 3, 5, 7, 14, 17, 18a-d, 19, 24, 25]
- 6.6 (1-12) [2, 3, 7a, 9]

### Lecture log

**Tuesday, 8/23/2016:** I gave out the syllabus and lectured on 1.1 and
1.2. I will define echelon form next time, but you should be able to
complete the other exercises in 1.1. and 1.2. The quiz on Thursday
will focus on definitions from 1.1. Read 1.1-1.3 for Thursday.

**Thursday, 8/25/2016:** I finished 1.2 and 1.3. We
talked about echelon form, vector equations, and linear combinations.
Exercises 1.1, 1.2, 1.3 are due Tuesday. When you work word problems
(like 1.3.28), be sure to include units in your answers. On
true/false problems, justify your answer by giving a reference for
true statements and a counter-example for false ones. Read 1.4-1.5
for Tuesday.

**Tuesday, 8/30/2016:**I lectured on 1.4 and 1.5. I will finish 1.5 and 1.7 next time, but you should be able to complete the other exercises in 1.4. and 1.5. The quiz on Thursday will focus on material since the last quiz. Read 1.7 for Thursday.

**Thursday, 9/01/2016:** I did an example from 1.5 and
lectured on 1.7. The homework 1.5 and 1.7 exercises are due
Tuesday. Read 1.8 and 1.9 for Tuesday. I updated the main page of
Canvas to include a folder where I will put solutions to exercises and
other handouts.

**Tuesday, 9/06/2016:** I lectured on 1.8 and
1.9. I will finish the theory for 1.9 next time, but you should be able to
complete all of 1.8 and many of the exercises in 1.9. I will only
collect 1.8 on Thursday. The quiz on Thursday
will focus on material since the last quiz. Read 1.10 for Thursday.

**Thursday, 9/08/2016:** I finished 1.9 and worked some
examples from 1.10. The homework 1.9 and 1.10 exercises are due
Tuesday. Read 2.1 and 2.2 for Tuesday. I updated the course page to
include some additional resources.

**Tuesday, 9/13/2016:** I finished 2.1 and started 2.2.
The homework 2.1 exercises are due
Thursday. Read 2.2 and 2.3 for Thursday. I updated the shared folder
with more HW solutions and a sample test. Test 1 is next Tuesday.

**Thursday, 9/15/2016:** I finished 2.2 and 2.3.
The homework 2.2 and 2.3 exercises are due
next Thursday, but you should work through them before the test on
Tuesday. I updated the shared folder with more HW solutions and
another sample test. Read your email for a vocabulary list for Test 1.

**Tuesday, 9/20/2016:**
Test 1.

**Thursday, 9/22/2016:**
I lectured on 2.8 Subspaces. Turn in the 2.8 exercises on Tuesday.
Read 2.9 for Tuesday. Test 1 grades will be uploaded by Monday.

**Tuesday, 9/27/2016:**
I lectured on 2.9 Dimension and Rank and started Chpt 3 Determinants.
I will collect 2.9 exercises on Thursday. Test scores are in Canvas
and solutions are in the shared folder. Please check over your tests
to be sure I did not make any mistakes. Continue to utilize the Math
Help Center and my office hours to get additional help.

**Thursday, 9/29/2016:**
I lectured on 3.1-3.3 Determinants. Turn in the 3.1, 3.2 exercises on Tuesday.
I will finish 3.3 on Tuesday with an example. Read 4.1, 4.2 for Tuesday.

**Tuesday, 10/04/2016:**
We finished 3.3 by computing the area of an ellipse using linear maps
and determinants. We finished 4.1 and 4.2. Due to popular demand, I
will only collect 3.3 and 4.1 on Thursday. Read 4.3 for Thursday.

**Thursday, 10/06/2016:**
I lectured on 4.3 linear independence and bases. Read 4.4, 4.5 for
Tuesday.

**Tuesday, 10/11/2016:**
We finished 4.4 and 4.5 so that now we can answer many questions about
vector spaces by computing coordinate vectors. I will collect 4.4 and
4.5 on Thursday. Read 4.6 for Thursday.

**Thursday, 10/13/2016:**
We finished 4.6 today. I will collect 4.6 (and
4.5 if you didn't turn it in today) on Thursday. Read 4.7 for
Thursday. There is no class on Tuesday because of Fall break.

**Thursday, 10/20/2016:**
We finished 4.7 today. I will collect 4.7 on Thursday since we have
a test on Tuesday. You should work through the problems before the
test as you are responsible for 4.7 for the test.

**Tuesday, 10/25/2016:**
Test 2. Turn in 4.7 on Thursday. Read 5.1 and 5.2 for Thursday.

**Thursday, 10/27/2016:**
I covered eigenvalues and eigenvectors 5.1 and 5.2. Turn in 5.1 and
5.2 HW on Tuesday. Office hours are cancelled next week. Cliff Smyth
will lecture next Tuesday and Thursday. There is a quiz on Thursday.

**Tuesday, 11/01/2016:**
Cliff Smyth lectured on 5.3 and returned graded tests. Solutions are
in the shared folder.

**Thursday, 11/03/2016:**
Cliff Smyth lectured on 5.4 and gave a quiz.

**Tuesday, 11/08/2016:**
We covered 5.5 on complex eigenvalues. Read 5.6 for Thursday.

**Thursday, 11/11/2016:**
We covered 5.6 on discete dynamical systems.
Read 6.1 and 6.2 for Tuesday.

**Tuesday, 11/15/2016:**
We covered 6.1 and 6.2 on dot product and orthogonality.
Read 6.3 for Tuesday.

**Thursday, 11/17/2016:**
We covered 6.3 on orthogonal projection and reviewed for Test 3. The
old test with solutions is in the shared folder. Test 3 is Tuesday.

**Tuesday, 11/22/2016:**
Test 3. No class Thursday due to Thanksgiving.

**Tuesday, 11/29/2016:**
Cover 6.5 and 6.6.

**Thursday, 12/01/2016:**
Finish 6.6 and review.

**Friday, 12/08/2016:**
Final exam at 8 am.

### Additional resources

**The Art of Proof**by Matthias Beck and Ross Geoghegan is an excellent introduction to writing good proofs. Go to the UNCG Library Catalog to find this book. You can download a free copy by entering your UNCG information.**Linear algebra for everyone**by Lorenzo Robbiano is an excellent informal introduction linear algebra. Go to the UNCG Library Catalog to find this book. You can download a free copy by entering your UNCG information.- Math Help Center: Tutoring is provided on a walk-in first come first serve basis. No appointment is necessary. See the webpage for the schedule.
- Textbook website has student resources including selected material from the textbook and study guide, Getting Started with Technology, data sets, case studies and applications, and review materials.
- MIT OpenCourseWare 18.06SC Linear Algebra: lecture notes, video lectures, additional exercises.
- A Guide to Writing Mathematics, by Kevin P. Lee