Math 307 -Linear Algebra
Spring 2016

Instructor: Elizabeth Meckes
Office: Yost 208
Phone: 368-5015
Email: ese3 [at] cwru.edu
Office Hours: Tuesdays and Thursdays 11 – 12

Textbook:
We'll be using a draft of the imaginatively named Linear Algebra by myself and Mark Meckes. The text book is posted in Blackboard. It is there for the use of students in this course; please do not distribute it.

Course web page:
http://www.cwru.edu/artsci/math/esmeckes/math307/.

All course information is posted here; Blackboard is used only for posting the text book and for grades. (See Dave Noon's take on Blackboard.).

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.

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

TopicsBook chapterWeeks
Linear systems, spaces, and maps 1 1-4
Linear independence and bases 2 5-7
Inner products 3 8-11
Determinants and the characteristic polynomial 4 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; each class will start with a short group quiz based on the material you read in preparation for class.

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 the figure I passed out on the first day of class 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 five hour-long quizzes throughout the term. These are closed book, closed notes. The tentative dates are: January 29, February 19, March 18, April 6, April 25.

Grading:
Your course grade will be computed as follows:

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.

LectureGroup quizReading for next timeProblemsDue Date
M 1/11noneSec. 1.1, 1.2 Read this and do the exercise for practice proof 1
from the book: 1.1.3, 1.1.6		1/13
W 1/13pdfSec. 1.3 1.2.1, 1.2.21/15
F 1/15pdfSec. 1.4 1.2.5, 1.2.6, 1.3.11/20
W 1/20pdfSec. 1.5 1.4.1, 1.4.4, 1.4.7, 1.4.91/22
F 1/22pdfSec. 1.6 1.5.2, 1.5.4, 1.5.6, 1.5.71/25
M 1/25pdfnone 1.6.1, 1.6.2, 1.6.7, 1.6.91/27
W 1/27pdfnone study for quiz 11/29
F 1/29noneSec. 1.7 none2/1
M 2/1pdfSec. 1.7 1.7.1, 1.7.2, 1.7.3, 1.7.42/3
W 2/3pdfSec. 1.8 1.7.7, 1.7.8, extra problem2/5
F 2/5pdfSec. 1.9 1.8.4, 1.8.9, 1.8.10, 1.8.132/8
M 2/8pdfSec. 1.9 1.8.12, 1.9.1, 1.9.2, 1.9.42/10
W 2/10pdfSec. 1.10 1.9.5, 1.9.7, 1.9.9, 1.9.102/10
F 2/12pdfSec. 2.1 1.10.1, 1.10.22/15
M 2/15pdfnone 2.1.1, 2.1.5, 2.1.8, 2.1.102/17
W 2/17pdfSec. 2.2 study for quiz 22/19
M 2/22pdfSec. 2.3 2.2.3, 2.2.4, 2.2.6, extra problem 2/24
W 2/24pdfSec. 2.4 2.3.6, 2.3.9, 2.3.13, 2.3.152/26
F 2/26pdfSec. 2.4 2.4.1, 2.4.2, 2.4.3, 2.4.42/29
M 2/29pdfSec. 2.5 2.4.7, 2.4.8, 2.4.10, 2.4.133/2
W 3/2pdfSec. 2.5 2.5.1, 2.5.2, extra problem3/4
F 3/4pdfSec. 2.6 2.4.12, 2.5.3, 2.5.43/14
M 3/14pdfnone2.6.2, 2.6.3, 2.6.4, 2.6.6 3/16
W 3/16pdfnone study for Quiz 33/18
M 3/21pdfSec. 3.2 3.1.2, 3.1.4, 3.1.6, 3.1.73/23
W 3/23pdfSec. 3.3 3.1.8, 3.2.1, 3.2.2. 3.2.43/25
F 3/25pdfSec. 3.4 3.2.3, 3.3.5, 3.3.7, 3.3.83/28
M 3/28pdfSec. 3.5 3.4.1, 3.4.2, 3.4.3, 3.4.53/30
W 3/30pdfnone 3.3.9, 3.5.2, 3.5.3, 3.5.54/1
F 4/1pdfnone 3.5.6, 3.5.10, 3.5.11, 3.5.124/4
F 4/8pdfSec. 3.7 3.6.1, 3.6.3, 3.6.4, 3.6.54/11
M 4/11pdfSec. 3.7 3.6.7, 3.6.8, 3.7.3, 3.7.54/13
W 4/13pdfSec. 4.1 3.7.6, 3.7.7, 3.7.8, 3.7.94/15
F 4/15pdfSec. 4.2 4.1.2, 4.1.3, 4.1.4, 4.1.64/18
M 4/18pdfSec. 4.3 4.2.1, 4.2.2, 4.2.34/20
W 4/20pdfSec. 4.4 4.3.1, 4.3.2, 4.3.5, Quick Exercise #2, section 4.54/22
F 4/22pdfnone 4.4.1, 4.4.4, 4.4.5, 4.4.10not collected

Quiz 5 information

The fifth quiz will be Monday, April 25in class. The quiz will last all 50 minutes of lecture and is closed-notes, closed-book, with no calculators allowed.

The quiz will focus on sections 3.6 — 4.5 of the book.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context.

Quiz 4 information

The fourth quiz will be Wednesday, April 6 in class. The quiz will last all 50 minutes of lecture and is closed-notes, closed-book, with no calculators allowed.

The quiz will focus on sections 3.1 — 3.5 of the book.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context.

Quiz 3 information

The third quiz will be Friday, March 18 in class. The quiz will last all 50 minutes of lecture and is closed-notes, closed-book, with no calculators allowed.

The quiz will focus on material since the previous quiz; i.e., sections 2.2 — 2.6 of the book.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context.

Quiz 2 information

The second quiz will be Friday, February 19 in class. The quiz will last all 50 minutes of lecture and is closed-notes, closed-book, with no calculators allowed.

The quiz will focus on material since the previous quiz; i.e., sections 1.7 — 2.1 of the book.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context.

Quiz 1 information

The first quiz will be Friday, January 29 in class. The quiz will last all 50 minutes of lecture and is closed-notes, closed-book, with no calculators allowed.

The quiz will cover all the course material covered through January 25, including section 1.6 of the book. January 27 will be a review day.

Definitions

You will be asked for complete, precise definitions of about four of the following terms, including context (e.g., a span of what?). Remember that a complete mathematical definition leaves no room for ambiguity: if you give me a definition of what it means for a matrix to be in RREF, I need to be able to use it to decide whether or not any matrix I ever meet is in RREF.