Math 324: Linear Algebra and Matrix Theory II

Math 324: Linear Algebra and Matrix Theory II Spring 2019, Section 01, CRN 653

Schedule: MWF 1:00pm-1:50pm
Location: Fitzelle Hall 204
Text: Linear Algebra (3rd edition), by Hefferon

Professor: Jonathan Brown
Office: Fitzelle Hall 260
Email: jonathan.brown@oneonta.edu
Phone: 436-3720
Office Hours: Monday 2:00-2:50, Thursday 12:00-12:50, Friday 12:00-12:50, or by appointment
Website: http://employees.oneonta.edu/brownjs/

SUNY General Education Attributes: LA

Catalog Description:
Finite dimensional vector spaces; linear transformations and their matrix representations; eigenvalues; rational and Jordan canonical forms; inner product spaces; quadratic and bilinear forms; applications.

Prerequisites: Math 224 or Math 205 with a "C" or better. It is strongly recommended that Math 205 be considered a co-requisite.

Course Content: We will be covering Chapters 3 - 5. Topics covered include matrix algebra, change of basis formula, determinants, eigenvalues and eigenvectors, characteristic polynomial, minimal polynomial, and Jordan Canonical Form of a matrix.

Grades:
Homework: 22%
2 in class exams: 23% each
Final: 32%

Your letter grade will be determined from the following heuristic:
A : 93 - 100
A-: 90 - 92.99
B+: 87 - 89.99
B : 83 - 86.99
B-: 80 - 82.99
C+: 77 - 79.99
C :73 - 76.99
C-: 70 - 72.99
D+: 67 - 69.99
D : 63 - 66.99
D-: 60 - 62.99
E : 0 - 59.99

Homework:
Problem sets to be turned in will be assigned every 1-2 weeks. These will be collected and graded.
Homework from the text will be assigned regularly. This homework will not be collected or graded, however it is mandatory that you do these problems. Learning, development, and growth require time and sustained effort. Most of the knowledge and skills you obtain from this course will come from the time you spend with these problems. Solutions to nearly every problem from the text can be found at http://joshua.smcvt.edu/linearalgebra/.

Tentative Exam Schedule:
Exam 1: 2/22
Exam 2: 4/12

Final Exam Schedule:
Wednesday May 8, 11:00am - 1:30pm.

Attendance Policy:
Missing class is a very bad idea. Anyone who misses more than 25% of classes starting in week 2 may be removed from the course.

Emergency Evacuation Procedures:
In the event of an emergency evacuation, classes meeting in this building are directed to reassemble in the IRC Lobby so that all persons can be accounted for. Complete details of the College's emergency evacuation, shelter-in-place, and other emergency procedures can be found at http://www.oneonta.edu/security/.

ADA (American with Disabilities Act):
Students Diagnosed with a Disability, all individuals who are diagnosed with a disability are protected under the Americans with Disabilities Act, and Section 504 of the Rehabilitation Act of 1973. As such, you may be entitled to certain accommodations within this class. If you are diagnosed with a disability, please make and appointment to meet with Student Disability Services, 209 Alumni Hall, ext. 2137. All students with the necessary supporting documentation will be provided appropriate accommodations as determined by the SDS Office.

Getting Help
You are expected to spend anywhere between 6 and 12 hours per week outside of class on the material. The amount of time necessary to pass, or obtain the grade you expect, depends heavily from person to person. Typically, a student spending less than 6 hours per week outside the class should expect to earn a "C" or worse.

If you are struggling with the material, be aware that you have options:
(1) Struggle a bit. Part of the learning process is the internal struggle of trying to understand how all of the pieces fit together. It can be frustrating, but it can also be rewarding. If you make progress, however slow, then it is time well spent. If you feel that your time is not productive, then you should talk to me, or other students, about how you can make better use of your study time.
(2) Visit my office hours. It is part of my job to be available to help you understand the material. There is not enough time in the classroom to get everything across, and you are not expected to do it all on your own.
(3) Find alternate instructional material online. Different people have different styles, and while you might have found my way of discussing something to be confusing, there may be someone else out there who can discuss it in a away that makes sense to you. There are a number of free text books, lessons, and video lectures available online. Feel free to ask me about other sources.
(4) Talk to your fellow students who are taking or who have taken the class. Learning is a social activity; you are not expected to do it all on your own.
(5) If after availing yourself of the above options, you still find that you are struggling regularly to understand the material, find a regular tutor. If you are in this situation, you will likely have to spend significant extra time on the material to ensure a passing grade.

Tentative Schedule and Textbook Homework Problems

Date Section Topic Mandatory Problems Fun/Challenge Problems

1/16
1/18 Review Review of Linear Algebra I p.87 # 19, 20, 22
p.97 # 20, 22, 23
p.110 # 21
p.119 # 18, 19, 20
p.188 # 18, 19
p.212 # 18, 19
p.233 # 14

1/21
1/23 Four.IV.3 Mechanics of Matrix Multiplication 24-27 30, 32, 38, 41, 44, 45

1/25
1/28 Four.IV.4 Inverses 13-18 24, 26, 29, 30, 35

1/30 Four.V.1 Changing Representations of Vectors 7-10 14, 21

2/1 Four.V.2 Changing Map Representations 10-13 26, 30

2/4 Four.VI.1 Orthogonal Projection Into a Line 6-8 14, 17

2/6
2/8 Four.VI.2 Gram-Schmidt Orthogonalization 10-14 22, 23

2/11
2/13 Four.VI.3 Projection Into a Subspace 10-13 20, 27

2/15
2/18 Five.I.1 Determinants: Exploration 1-5 6, 9, 14, 15

2/20
2/25 Five.I.2 Properties of Determinants 8-11, 13 12, 18, 23

2/22 Exam 1

2/27
3/1 Five.I.3 The Permutation Expansion 17-22 29, 34, 35, 40

3/11
3/13 Five.I.4 Determinants Exist 11-14 15, 16

3/15
3/18 Five.II.1 Determinants as Size Functions 8, 9, 12 19, 21, 22

3/20
3/22 Five.III.1 Laplace's Formula 11-20 26, 28

3/25 Topic: Cramer's Rule 1, 2 3, 5

3/27 Five.I.1
Five.I.2 Polynomial Factoring and Complex Numbers
Complex Representations

3/29
4/1 Five.II.1 Similarity: Definition and Examples 5-9 13, 14, 24

4/3
4/5 Five.II.2 Diagonalizability 7, 14, 15 17

4/8
4/10 Five.II.3 Eigenvalues and Eigenvectors 21-30 39, 42, 43

4/12 Exam 2

4/15 Five.III.1 Nilpotence: Self-Composition 9, 10 13

4/17 Five.III.2 Strings 20-22, 24 30, 34

4/19
4/22 Five.IV.1 Polynomials of Maps and Matrices 13-17 20, 29

4/24
4/26 Five.IV.2 Jordan Canonical Form 19, 20, 22 23, 28, 32, 36

4/29 Review

5/8 Final Exam 11:00-1:30

Date	Section	Topic	Mandatory Problems	Fun/Challenge Problems
1/16 1/18	Review	Review of Linear Algebra I	p.87 # 19, 20, 22 p.97 # 20, 22, 23 p.110 # 21 p.119 # 18, 19, 20 p.188 # 18, 19 p.212 # 18, 19 p.233 # 14
1/21 1/23	Four.IV.3	Mechanics of Matrix Multiplication	24-27	30, 32, 38, 41, 44, 45
1/25 1/28	Four.IV.4	Inverses	13-18	24, 26, 29, 30, 35
1/30	Four.V.1	Changing Representations of Vectors	7-10	14, 21
2/1	Four.V.2	Changing Map Representations	10-13	26, 30
2/4	Four.VI.1	Orthogonal Projection Into a Line	6-8	14, 17
2/6 2/8	Four.VI.2	Gram-Schmidt Orthogonalization	10-14	22, 23
2/11 2/13	Four.VI.3	Projection Into a Subspace	10-13	20, 27
2/15 2/18	Five.I.1	Determinants: Exploration	1-5	6, 9, 14, 15
2/20 2/25	Five.I.2	Properties of Determinants	8-11, 13	12, 18, 23
2/22	Exam 1
2/27 3/1	Five.I.3	The Permutation Expansion	17-22	29, 34, 35, 40
3/11 3/13	Five.I.4	Determinants Exist	11-14	15, 16
3/15 3/18	Five.II.1	Determinants as Size Functions	8, 9, 12	19, 21, 22
3/20 3/22	Five.III.1	Laplace's Formula	11-20	26, 28
3/25	Topic: Cramer's Rule		1, 2	3, 5
3/27	Five.I.1 Five.I.2	Polynomial Factoring and Complex Numbers Complex Representations
3/29 4/1	Five.II.1	Similarity: Definition and Examples	5-9	13, 14, 24
4/3 4/5	Five.II.2	Diagonalizability	7, 14, 15	17
4/8 4/10	Five.II.3	Eigenvalues and Eigenvectors	21-30	39, 42, 43
4/12	Exam 2
4/15	Five.III.1	Nilpotence: Self-Composition	9, 10	13
4/17	Five.III.2	Strings	20-22, 24	30, 34
4/19 4/22	Five.IV.1	Polynomials of Maps and Matrices	13-17	20, 29
4/24 4/26	Five.IV.2	Jordan Canonical Form	19, 20, 22	23, 28, 32, 36
4/29	Review
5/8	Final Exam	11:00-1:30