Honors Linear Algebra Fall 2019

Honors Linear Algebra, 110.212, Fall 2019
W. Stephen Wilson

Professor: W. Stephen Wilson: wwilson3@jhu.edu or wsw@math.jhu.edu

Textbook: Linear Algebra Done Right, 3rd Edition, 2015 Edition. By Sheldon Axler.
ISBN-13: 978-3319110790
ISBN-10: 3319110799
A pdf of the textbook is available for free download through the JHU library.

Errata file for the text.

The official departmental Course Syllabus.

Monday, Wednesday, 1:30-2:45, Section, Friday, 1:30-2:20, all held in Croft G02, which I suspect isn't that great a room and have tried to change it. If you hear they changed it, let me know. Likewise, if I hear, I'll tell you.

Office hours are Wednesday, 2:45-3:45. (Krieger 421.) This is right after class, so if you want to come to office hours, you arrange that in class, or I won't be there. You can always email me with questions or to set up a meeting if the office hours don't work for you or aren't enough.

In addition, you should all know about the math department help room that is open nearly all day and most evenings during the week. It is in Krieger 213. Your TA will be there in the help room at a time not yet determined as of this writing, so ask him in section. Anyone in the help room can help you with linear algebra. Also, I am very responsive to emails. Need help, send an email to me.

The text comes with videos

Linear algebra videos made by me that are relevant to the course, and many of them will be assigned "reading." This is because the text we use actually assumes you've had a computationally based linear algebra course already. That really isn't necessary, but you need to learn computations as you go, thus the videos. For gluttons, there are Linear algebra videos made by the Khan Academy. And then there are Linear algebra videos made by Gil Strang at MIT. Feel free to make use of these resources in your "spare time".

The Honors Linear Algebra course is designed for students with the mindset of a math major even if the student is not majoring in math. It is for students who have self selected because they are brighter, harder working, and more motivated. In particular, they are happy to be free to learn. The prerequisites are 113, Calc II, or a 5 on the AP BC exam.

All students must attend every class and maintain a high level of consciousness during the entire class. You will have something serious to do during the entire class, every class (except the first one on August 29).

Students are expected to make the transition to proving things in this course if they have not already made that transition. Few will have done this already. It is a great introduction to proving things because everything in the course is simultaneously geometric and algebraic. Great material, and you use linear algebra in nearly every math, science, and engineering course you take. More important, the intellectual development associated with learning to prove things is invaluable for all future endeavors in life.

The transition to proving things is a difficult one and the course will be fast paced. It is best for students to keep an eye on the regular linear algebra course so they can drop down to it if it looks like the honors course will not go well. If you don't learn the material each week and learn how to prove things by the 3rd week, you will not get a good grade in the course. This is an HONORS course and assumes that you can and will do this.

The flow of the course. The normal flow is to have a reading assignment, then to be examined as to whether or not you did the reading. Next, homework on that reading will be assigned and then, of course, it will come due. When it is turned in, you get another exam to see if you understood it.

The reading assignments are already set for the entire course and are at the bottom of this website.

The pattern for the above is, somewhat in reverse order because our week is really Wednesday to Monday:

Monday: Your homework is due at the start of class on Monday. A test will be given immediately. The test will cover the material that you read for the homework just handed in. There will probably be two problems, one from the homework just handed in, and one from the sections the homework was based on. I reserve the right to ask whatever I want though. Most such tests will be open book unless I ask for a proof of a simple theorem in the book.

Monday Continued: After the test, I will assign small groups to work on a sequence of problems. These problems will be from the material you read for the homework you just handed in, so you should be really good at it. The group will do as many of them as they can, sequentially, and write them up to be handed in at the end of the class for the whole group. The whole group will get the same grade on this. The groups will vary day to day.

More Monday: I will give a very short lecture on the material you are about to read for Wednesday so you'll know the high points to look out for.

Even More Monday: While groups are at work, I will tend to pull someone out of group work to talk and work with. Sometimes this will be at random, and sometimes because you need it.

Wednesday: I give you a quiz when you walk into class to see if you have done the reading for that week. It will cover really basic things like definitions and statements of theorems. No understanding is required to do well on this, but I want people prepared to work, not read, when they come to class on Wed. You can teach a 10 year old to do this perfectly, so don't embarrass yourself.

News flash. The "quiz" just got promoted to a serious exam. It will most likely be an opportunity to reproduce some basic theorem that was in the reading. Not likely to be a long complicated theorem though.

Wednesday continued: You will then be assigned to small groups to work on a sequence of problems. These problems will be for the reading you were just quizzed on. As above: The group will do as many of them as they can, sequentially, and write them up to be handed in at the end of the class for the whole group. The whole group will get the same grade on this. The groups will vary day to day.

More Wednesday: I will post the homework on the next reading assignment sometime before the end of the day on Wednesday.

Even More Wednesday: While groups are at work, I will tend to pull someone out of group work to talk and work with. Sometimes this will be at random, and sometimes because you need it.

Friday: This is your TA section.

Friday continued The TA will grade your homework and in-class work. In section he can go over common problems s/he sees when grading your proofs and/or give guidance on the homework due next. If students don't go to section regularly, we will start an exam in section as well as the other two days.

Grades: As you can see, you have an exam that gets graded every day you have class. We call the Wednesday exam on reading a "quiz" and the Monday exam on content a "test."

Homework: In addition, you have homework. Three problems of my choice, unknown to you, will be graded by the TA. The idea here is that with only 3 problems to grade, the TA can give serious feedback. If you are not getting useful feedback, you need to report that to me. Also, on Mondays and Wednesdays you will be working problems in groups most of the class. Some of these problems will be graded. All in all, there are lots of things that get graded that will go into your grade. How they will all be weighted will get worked out during the semester, but historically, it has been 25% each for in-class work, homework, quiz, and test. But your individual work will dominate the grade.

Group work: You are welcome to, even encouraged to, work together on homework, but you must write up your own homework. If you write up your own, it will not be the same as that written up by students you worked with.

The syllabus, subject to, but not likely to, change.

The first class will be a bit of a dud since you won't know anything yet. It is on an unusual day, Thursday August 29. JHU has redefined that day as a Monday, and, yes, you have section the next day, which is still a Friday.

Videos assigned for Sept 4.

Reading assignment # 1: Sections 1ABC. Quiz to see if you read them, Sept 4.

Problem set # 1.

Homework # 1 due Sept 9. Test to see if you understood it same day.

Reading assignment # 2: Sections 2ABC. Quiz to see if you read it, Sept 11.

Problem set # 2.

Homework # 2 due Sept 16. Test to see if you understood it same day.

Reading assignment # 3: Sections 3AB. Quiz to see if you read it, Sept 18.

Problem set # 3.

Homework # 3 due Sept 23. Test to see if you understood it same day.

Reading assignment # 4: Sections 3CD. Quiz to see if you read it, Sept 25.

Problem set # 4.