Math 2270 Syllabus, Fall 2014
October 29, 2014
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General Information
• Course: Linear Algebra (Math 2270, Section 002).
• Description: We will study vectors and matrices. We’ll begin by manipulating vectors
and matrices as arrays of numbers and gradually learn how to think about vectors as
elements of a vector space and matrices as linear transformations. Some of the key
concepts we’ll study are orthogonality, determinants, eigenvalues, and eigenvectors.
We’ll see many applications of vectors and matrices, such as solving systems of linear
equations and di↵erential equations, and we’ll end the course with applications to
engineering, computer science, statistics, and other areas of mathematics.
• Prerequisites: “C” or better in (MATH 2210 OR MATH 1260 OR MATH 1280 OR
MATH 1321 OR MATH 1320).
• Instructor: Thomas Goller. You can call me “Thomas”.
• Course Webpage: Google my name and follow the links. I will post all updates on
the webpage, so check it frequently!
• Time and Place: M,W,F 12:55 – 1:45 PM in ST 208; T 12:55 – 1:45 PM in LCB
225.
• Textbook: Chapters 1-8 of Introduction to Linear Algebra, Fourth Edition, by Gilbert
Strang, ISBN: 978-0-9802327-1-4. You can find video lectures by the author (and much
more!) at http://web.mit.edu/18.06/www/videos.shtml, and I strongly encourage you
to watch these videos if you find my lectures confusing, but I will make no e↵ort to
synchronize my presentation of the material with these videos.
• Quizzes: On Tuesdays. Quiz problems will be based on the recommended homework
problems posted the previous week. Your lowest quiz score will be dropped.
• Homework: Weekly sets of recommended problems to prepare you for the weekly
quizzes and tests. Homework will not be submitted.
• Tests: Roughly every third Tuesday. Tests will feature recommended homework problems from the previous week and all the material covered after the previous test.
• Final Project: You will each spend the last two weeks of class researching an application of linear algebra and writing up your findings. Example topics are the sections in
Chapter 8 of the textbook, but you may choose any topic that makes sufficient use of
the concepts we covered in class. There will be time in class to talk to me and to other
students. Expect to hear much more about these projects as the end of the semester
approaches.
• Final Exam: Comprehensive.
• Grading: 20% Quizzes, 40% Tests, 20% Final Project, 20% Final Exam. I will do all
of the grading for the course and try to return the work to you at the beginning of the
next class. I’ll assign letter grades using a curve, so forget about that awful “ 95% is
an ‘A’, don’t you dare make any mistakes!” nonsense. I will report average scores for
quizzes and tests as we proceed and give you a rough idea of how scores correspond to
letter grades. The average grade will likely be around a B-.
• Missing a Quiz or Test: If you are going to miss a quiz, contact me before class on
the Tuesday of that quiz. We can arrange for you to take the quiz early or possibly
later Tuesday afternoon, though I am fairly busy Tuesday afternoons and would much
rather give you the quiz early. If you are going to miss a test, we can arrange for you
to take the test early or later that week. If you take the test later in the week, I will
have to change the questions, so you should expect a slightly harder test. As in the
case of quizzes, you must contact me before class on Tuesday if you want to take a test
early or late.
• Problem Sessions: Mondays from 5 – 6 PM in JWB 333 and Thursdays 12:50 – 1:50
PM in LCB 225. Before coming to the Thursday problem sessions, please work on the
problems for the sections that were covered on Monday and Wednesday of that week.
During the Monday problem sessions, any problems from the previous week’s list of
recommended problems may be discussed, as well as questions about the upcoming
quiz or test. Bring any questions you may have about the material and expect me to
work through problems with you instead of presenting complete solutions.
• Office Hours: You can always talk to me right after class or e-mail me to set up an
appointment. You can also just drop by my office, JWB 307, at the risk that I might
be busy right at that moment.
• ADA Statement: The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, cognitive, systemic learning, and
psychiatric disabilities. Please contact me at the beginning of the semester to discuss
any such accommodations that you may require for this course.
• Disclaimer: Please remember that things on this syllabus can change! I will hold
you accountable for information that is communicated in class or posted on the course
webpage. Be sure to check the course webpage frequently throughout the semester.
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Course Timeline
Dates
Reading
Topics
Key Events
8/25, 8/26, 8/27, 8/29
1.1, 1.2, 1.3
introduction to vectors
LD, 9/2, 9/3, 9/5
2.1, 2.2
solving linear equations
quiz 1 on 9/2
9/8, 9/9 , 9/10, 9/12
2.3, 2.4, 2.5
solving linear equations
test 1 on 9/9
9/15, 9/16, 9/17, 9/19
2.6, 2.7, 3.1
vector spaces
quiz 2 on 9/16
9/22, 9/23, 9/24, 9/26
3.2, 3.3, 3.4
vector spaces
quiz 3 on 9/23
9/29, 9/30 , 10/1, 10/3
3.5, 3.6, 4.1
vector spaces
test 2 on 9/30
10/6, 10/7, 10/8, 10/10
4.2, 4.3, 4.4
orthogonality
quiz 4 on 10/7
10/20, 10/21, 10/22, 10/24
5.1, 5.2, 5.3
determinants
quiz 5 on 10/21
10/27, 10/28 , 10/29, 10/31
6.1, 6.2
eigenvalues, eigenvectors
test 3 on 10/28
11/3, 11/4, 11/5, 11/7
6.3, 6.4, 6.5
eigenvalues, eigenvectors
quiz 6 on 11/4
11/10, 11/11 , 11/12, 11/14 6.6, 6.7, 7.1
linear transformations
test 4 on 11/11
11/17, 11/18, 11/19, 11/21
7.2, 7.3
linear transformations
quiz 7 on 11/18
11/24, 11/25 , 11/26, TG
8.?
projects
test 5 on 11/25
12/1, 12/2, 12/3, 12/5
8.?
projects
12/8, 12/9, 12/10, 12/12
8.?
projects
projects due 12/12
chapters 1-7
final exam
Fall Break
12/16 (Tuesday), 1-3 PM
(Expect a test on the dates enclosed in rectangles.)
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Study Tips
Textbook
Strang’s writing is livelier, chattier, and more fun than what you will find in an average
math textbook. Strang works hard to motivate definitions and results before stating them.
While this writing style is refreshing, it is highly context dependent, so you may need to
read the whole section in order to understand a particular line of text. This is why you
will be rewarded if you read every word of every section carefully, but you will probably be
frustrated if you try to jump around in the textbook. Additionally, Strang’s notation often
isn’t as clear as it could be and there are some mistakes – please ask me if you are confused
by something! Like you, I will be reading every word of chapters 1-7 this semester.
Lecture
Absorbing a new concept usually takes longer than 50 minutes. I strongly encourage you to
read the section in the book before I lecture on that material. Try to understand the new
definitions and results in the examples in the book, and try to come up with a few of your
own examples too. One cannot claim to understand a mathematical concept if one cannot
give an example of it.
Quizzes and Tests
Work through all the recommended homework problems. Start them early so you have plenty
of time to get help! Make sure you understand all the new definitions and results and be able
to give examples of everything. Throughout the semester, compile these definitions, results,
and examples into a big list and study the entire list before every test.
You may notice that I emphasize certain concepts, results, or examples during lecture –
these are especially likely to pop up on a quiz or test!
Getting Help
In linear algebra, like in most math courses, the definitions build on each other quickly, and
once you fall behind you will likely stay behind. Work hard from the beginning and come to
office hours if you don’t understand something. The mathematics tutoring center is a great
resource if you want additional help.
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