Math 323: Linear Algebra and Matrix Theory I

Math 323: Linear Algebra and Matrix Theory I Fall 2018, Section 01, CRN 916

Schedule: MWF 11:00am-11:50am
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: Wednesday 12:00-12:50, Thursday 11:00-11:50, 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 1 - 3. Topics covered include solving systems of linear equations, matrix algebra, vector spaces, and linear transformation.

Grades:
Homework: 18%
3 in class exams: 18% each
Final: 28%

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: 10/5 (Friday)
Exam 2: 11/16 (Friday)

Final Exam Schedule:
Wednesday December 12, 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

8/27
8/29 One.I.1 Solving Linear Systems: Gauss's Method 17-20, 24 23, 37-41

8/31
9/5 One.I.2 Describing the Solutions Set 15-21 23, 29-34

9/7
9/10 One.I.3 General = Particular + Homogeneous 14-21 24, 25

9/12 One.II.1 Linear Geometry: Vectors in Space 1-7 11, 12

9/14 One.II.2 Length and Angle Measures 11-15 36, 40, 41

9/17 One.III.1 Reduced Echelon Form: Gauss-Jordan Reduction 8-14 19,20

9/19 One.III.2 The Linear Combination Lemma 11-16 24, 27

9/21
9/24 Two.I.1 Vector Spaces: Definition and Examples 18-22 23, 37, 41

9/26
9/28 Two.I.2 Subspaces and Spanning Sets 20-25 29, 32, 47

10/1
10/3 Two.II.1 Linear Independence: Definition and Examples 20-24 43, 44

10/5 Exam 1

10/10 Two.III.1 Bases 18-23 31, 37

10/12 Two.III.2 Basis and Dimension 16-20, 22, 26 39

10/15 Two.III.3 Vector Spaces and Linear Systems 16-22, 27 37, 41, 43

10/17 Two.III.4 Combining Subspaces 20-24 31, 37, 38

10/19
10/22 Three.I.1 Isomorphisms: Definitions and Examples 13-17 25, 30, 38

10/24 Three.I.2 Dimension Characterizes Isomorphism 9-12, 14, 15 23, 28

10/26 Three.II.1 Homomorphisms: Definition 18-20 26, 30, 38

10/29
10/31 Three.II.2 Range and Null Space 21-26 37, 44

11/2 Three.III.1 Representing Linear Maps with Matrices 12-17, 20, 26 31, 33

11/5
11/7 Three.III.2 Any Matrix Represents a Linear Map 12-16 29, 30

11/9 Three.IV.1 Matrix Operations: Sums and Scalar Products 8, 9, 11 13, 17

11/12 Three.IV.2 Matrix Multiplication 14-16 28, 31, 32

11/14 Three.IV.3 Mechanics of Matrix Multiplication 24-27 30, 31, 32, 44

11/16 Exam 2

11/19 Three.IV.4 Inverses 13-17 18, 33, 35

11/26 Three.V.1 Change of Basis: Changing Representations of Vectors 7-11 16, 24

11/28 Three.V.2 Changing Map Representations 10, 11, 13, 16 21, 30, 31

11/30 Three.VI.1 Orthogonal Projection Into a Line 6-8 15, 17

12/3 Three.VI.2 Gram-Schmidt Orthogonalization 10-15 24, 25

12/5
12/7 Three.VI.3 Projection Into a Subspace 10-13 18, 20

12/10 Review

12/12 Final Exam 11:00-1:30

Date	Section	Topic	Mandatory Problems	Fun/Challenge Problems
8/27 8/29	One.I.1	Solving Linear Systems: Gauss's Method	17-20, 24	23, 37-41
8/31 9/5	One.I.2	Describing the Solutions Set	15-21	23, 29-34
9/7 9/10	One.I.3	General = Particular + Homogeneous	14-21	24, 25
9/12	One.II.1	Linear Geometry: Vectors in Space	1-7	11, 12
9/14	One.II.2	Length and Angle Measures	11-15	36, 40, 41
9/17	One.III.1	Reduced Echelon Form: Gauss-Jordan Reduction	8-14	19,20
9/19	One.III.2	The Linear Combination Lemma	11-16	24, 27
9/21 9/24	Two.I.1	Vector Spaces: Definition and Examples	18-22	23, 37, 41
9/26 9/28	Two.I.2	Subspaces and Spanning Sets	20-25	29, 32, 47
10/1 10/3	Two.II.1	Linear Independence: Definition and Examples	20-24	43, 44
10/5	Exam 1
10/10	Two.III.1	Bases	18-23	31, 37
10/12	Two.III.2	Basis and Dimension	16-20, 22, 26	39
10/15	Two.III.3	Vector Spaces and Linear Systems	16-22, 27	37, 41, 43
10/17	Two.III.4	Combining Subspaces	20-24	31, 37, 38
10/19 10/22	Three.I.1	Isomorphisms: Definitions and Examples	13-17	25, 30, 38
10/24	Three.I.2	Dimension Characterizes Isomorphism	9-12, 14, 15	23, 28
10/26	Three.II.1	Homomorphisms: Definition	18-20	26, 30, 38
10/29 10/31	Three.II.2	Range and Null Space	21-26	37, 44
11/2	Three.III.1	Representing Linear Maps with Matrices	12-17, 20, 26	31, 33
11/5 11/7	Three.III.2	Any Matrix Represents a Linear Map	12-16	29, 30
11/9	Three.IV.1	Matrix Operations: Sums and Scalar Products	8, 9, 11	13, 17
11/12	Three.IV.2	Matrix Multiplication	14-16	28, 31, 32
11/14	Three.IV.3	Mechanics of Matrix Multiplication	24-27	30, 31, 32, 44
11/16	Exam 2
11/19	Three.IV.4	Inverses	13-17	18, 33, 35
11/26	Three.V.1	Change of Basis: Changing Representations of Vectors	7-11	16, 24
11/28	Three.V.2	Changing Map Representations	10, 11, 13, 16	21, 30, 31
11/30	Three.VI.1	Orthogonal Projection Into a Line	6-8	15, 17
12/3	Three.VI.2	Gram-Schmidt Orthogonalization	10-15	24, 25
12/5 12/7	Three.VI.3	Projection Into a Subspace	10-13	18, 20
12/10	Review
12/12	Final Exam	11:00-1:30