Math 307 -Linear Algebra
Fall 2019

Instructor: Elizabeth Meckes

Office: Yost 208

Phone: 368-5015

Email: ese3 [at] cwru.edu

Office Hours: MWF, 2-3, or by appointment.

Textbook:

We'll be using the imaginatively named Linear Algebra by myself and Mark Meckes, published by Cambridge University Press.

Course web page:

http://www.cwru.edu/artsci/math/esmeckes/math307/.

All course information is posted here; Canvas is used only for grades.

About this course:

Math 307 is a theoretical course in linear algebra, geared primarily for students majoring in mathematics, mathematics and physics, and applied mathematics. (Although everyone is welcome, if you're not a math major, then depending on your interests and goals you may wish to consider taking Math 201 instead.) The major topics are linear systems of equations, matrices, vector spaces, linear transformations, and inner product spaces.

This is the official course description:

A course in linear algebra that studies the fundamentals of vector spaces, inner product spaces, and linear transformations on an axiomatic basis. Topics include: solutions of linear systems, matrix algebra over the real and complex numbers, linear independence, bases and dimension, eigenvalues and eigenvectors, singular value decomposition, and determinants. Other topics may include least squares, general inner product and normed spaces, orthogonal projections, finite dimensional spectral theorem. This course is required of all students majoring in mathematics and applied mathematics. More theoretical than MATH 201.

Saying that this is a theoretical course means that students will be expected to read and write proofs. If you don't yet feel comfortable with that, Math 305 (Introduction to Advanced Mathematics) is a course which is specifically designed to help ease the transition from calculus to proof-based math classes. Here is a self-diagnostic which you may find useful; I am happy to discuss it with you in office hours.

Even if you do feel comfortable with reading and writing proofs, I strongly suggest you read and work through this tutorial on proof comprehension.

Is this the course I'm looking for?

As it says above, this is a theoretical course designed for math, applied math, and math/physics majors. The goals are to build a strong foundation in the theory and practice of linear algebra, as well as to build comfort and fluency in advanced, proof-based mathematics. The math department also offers MATH 201, which is a linear algebra course aimed and science and engineering majors; it is less theoretical and more focused on problem-solving. For those who want to take MATH 307 but don't yet have the comfort with abstract mathematics which will be needed, MATH 305 is designed to help students successfully make the transition from calculus to advanced mathematics.

Topics and rough schedule:

We will cover essentially all of the book. The schedule will be roughly as follows:

Topics	Book chapter	Weeks
Linear systems, spaces, and maps	1,2	1-4
Linear independence and bases	3	5-7
Inner products, SVD, the spectral theorem	4,5	8-11
Determinants and the characteristic polynomial	6	12-14

Attendance:

You're supposed to come. (To every class.)

Reading and group quizzes:

We wrote the book to be read, by you! The reading and the lectures are complementary, and it's important to do both. Before each class, please read the section to be covered in the next lecture (we'll go through the book in order — I'll announce any exceptions in class). You will be placed in a group of four at the beginning of the semester, and each class will start with a short group quiz based on the material you read in preparation for class. The group's solution to the quiz problem(s) will be written up by that day's scribe; each group should establish a rotation so that all group members take turns serving as the scribe.

Homework Problems:

How much you work on the homework problems is probably the single biggest factor in determining how much you get out of the course. If you are having trouble with the problems, please come ask for help; you will learn much more (and probably get a rather better grade) if you figure out all of the homework problems, possibly with help in office hours or from your classmates, than if you do them alone when you can and skip the ones you can't. Students are welcome to work together on figuring out the homework, but you should write up the solutions on your own.

Each lecture has specific homework problems associated to it, as listed in the chart below. I strongly suggest doing the homework the same day as the corresponding lecture (see in particular this figure titled "The value of rehearsal after a lecture"). Homework will be collected at each class.

The homework is meant to be a mix of relatively straightforward exercises and really tough problems. Don't worry too much if you find some of it hard, but do continue to struggle with it; that's the way you learn.

The next stage after the struggle of figuring out a problem is writing down a solution; you learn a lot here, too. The homework assignments are writing assignments, and what you turn in should be polished (edited!) English prose with well-reasoned, complete arguments. I should be able to give your solutions to another student who has never thought about the problems (or did, but didn't figure them out), and she should be able to read and understand them.

Individual quizzes:

There will be four hour-long quizzes throughout the term. I know that sounds like a lot — it is! The quizzes are not just, or even mainly, for assessment; they are an important part of the learning process. Quizzes are closed book, closed notes. The dates are: September 16, October 9, November 8, and December 4.

Grading:

Your course grade will be computed as follows:

• Group quizzes 5% (the lowest three will be dropped)
• Homework 25%
• Individual quizzes 50%
• Final exam 20%

A couple articles worth reading:

Forget What You Know About Good Study Habits appeared in the Times in Fall 2010. It offers some advice about studying based on current pedagogical research.

Teaching and Human Memory, Part 2 from The Chronicle of Higher Education in December 2011. Its intended audience is professors, but I think it's worth it for students to take a look as well.

Investigating and Improving Undergraduate Proof Comprehension, Fall 2015. This is a fascinating description of attempts to help undergraduates improve at understanding and learning from proofs; it is the source of the tutorial on proof comprehension linked above. Again, it's really written with professors in mind, but you'll learn a lot by reading it.

Assignments:

Howework is posted below.

Lecture	Group quiz	Reading for next time	Problems	Due Date
M 8/26	none	Sec. 1.1, 1.2	Read this and do the exercise for practice proof 1. From the book: 1.1.5 (a,b,d), 1.1.8, 1.1.10, 1.1.11	8/28
W 8/28	pdf	Sec. 1.3	1.2.4 (a,b,c), 1.2.6, 1.2.10, 1.2.14	8/30
F 8/30	pdf	Sec. 1.4	1.3.4, 1.3.6, 1.3.9, 1.3.12	9/4
W 9/4	pdf	Sec. 1.5	1.4.1, 1.4.6, 1.4.8, 1.4.16, 1.4.18	9/6
F 9/6	pdf	Sec. 2.1	1.5.2, 1.5.4, 1.5.10, 1.5.18, 1.5.20	9/9
M 9/9	pdf	Sec. 2.2	2.1.4, 2.1.5, 2.1.8, 2.1.10, 2.1.16	9/11
W 9/11	pdf	Review sections 2.1, 2.2	2.1.12, 2.1.14, 2.2.10, 2.2.14, 2.2.15	9/13
F 9/13	pdf	none	2.2.2, 2.2.4, 2.2.7, 2.2.17	9/18
M 9/16	none	Sec. 2.3	none
W 9/18	pdf	Sec. 2.4	2.3.2, 2.3.10, 2.3.11, 2.3.12 (a)	9/20
F 9/20	pdf	Sec. 2.4 (again)	2.4.2, 2.4.4, 2.4.19, 2.4.22	9/23
M 9/23	pdf	Sec. 2.5	2.4.6, 2.4.8 (c,d), 2.4.10(c,d) 2.4.17	9/25
W 9/25	pdf	Sec. 3.1	2.5.2, 2.5.4, 2.5.10, 2.5.11	9/27
F 9/27	pdf	Sec. 2.6	2.5.6, 2.5.12, 2.5.15, 2.5.16	9/30
M 9/30	pdf	Sec. 3.1 (again)	2.6.2, 2.6.4, 2.6.7, 2.6.8	10/2
W 10/2	pdf	Sec. 3.2	3.1.2(a,b), 3.1.8, 3.1.9, 3.1.14	10/4
F 10/4	pdf	Sec. 3.3	3.2.2 (a,b,c), 3.2.6 (a,b,c) 3.2.13, 3.2.14	10/7
M 10/7	pdf	none	3.2.4 (a,b,d), 3.2.11, 3.2.16, 3.2.18, 3.2.20	10/11
W 10/9	none	Sec. 3.3 (again)	3.2.4 (a,b,d), 3.2.11, 3.2.16, 3.2.18, 3.2.20	10/11
F 10/11	pdf	Sec. 3.4	3.3.2(b,e); 3.3.8, 3.3.9, 3.3.12	10/14
M 10/14	pdf	Sec. 3.5	3.4.2 (a,b,c), 3.4.3, 3.4.4, 3.4.8	10/16
W 10/16	pdf	Sec. 3.6	3.5.6 (a,b,c), 3.5.10, 3.5.12	10/18
F 10/18	pdf	Sec. 3.6 (again)	3.4.16, 3.5.14, 3.5.16	10/23
W 10/23	pdf	Sec. 3.7	3.6.10, 3.6.12, 3.6.18, 3.6.23	10/25
F 10/25	pdf	Sec. 4.1	3.7.4 (a,b,c), 3.7.7, 3.7.10, 3.7.14 (in 3.7.14, it should have said that the polynomial has to be nonzero!)	10/28
M 10/28	pdf	Sec. 4.1 (again)	4.1.2, 4.1.9, 4.1.10, 4.1.11	10/30
W 10/30	pdf	Sec. 4.2	4.1.4, 4.1.7, 4.14, 4.1.18	11/1
F 11/1	pdf	Sec. 4.2 (again)	4.2.4, 4.2.6, 4.2.10	11/4
M 11/4	pdf	Sec. 4.3	4.2.9, 4.2.16, 4.2.18, 4.2.20	11/6
W 11/6	pdf	Sec. 4.3 (for 11/11)	4.3.14, 4.3.16, 4.3.21, 4.3.22	11/11
M 11/11	pdf	Sec. 4.4	4.3.6(a,b,c), 4.3.8, 4.3.18, 4.3.20	11/13
W 11/13	pdf	Sec. 4.5	4.4.1, 4.4.16, 4.4.18, 4.4.19	11/15
F 11/15	pdf	Sec. 5.1	4.5.6, 4.5.12, 4.5.14, 4.5.16	11/18
M 11/18	pdf	Sec. 5.2	5.1.4, 5.1.6, 5.1.10, 5.1.14	11/20
W 11/20	pdf	Sec. 5.3	5.2.2, 5.2.8, 5.2.15, 5.2.21	11/22
F 11/22	pdf	Sec. 5.4	5.3.6, 5.3.8, 5.3.12, 5.3.18	11/25
M 11/25	pdf	Sec. 5.4(again)	5.4.2 (b,c), 5.4.5, 5.4.9, 5.4.10	11/27
W 11/27	pdf	Sec. 6.1	5.4.6, 5.4.7, 5.4.12, 5.4.18	12/2
M 12/2	pdf	none	6.1.8, 6.1.10, 6.2.3, 6.3.1(a,b), 6.3.17	12/6