Course
Material for Linear Algebra, 110.201. Fall 2020.
Professor: W. Stephen Wilson, wwilson3@jhu.edu
Head TA: Daniel Fuentes-Keuthan, dfuente6@jhu.edu
In
times of need, you can contact either one of use. For bureaucratic issues, best to try the Head
TA first.
Textbook: Linear Algebra with
Applications, Fifth Edition, by Otto Bretscher
ISBN-13: 978-0-321-79697-4
ISBN-10: 0-321-79697-7
What is going on here?
Some of you may have noticed.
This is not a normal semester.
But, for those of you who are new, this isn’t how we usually do
things. It used to be that I would give
a lecture in front of all of you at once.
This would happen 3 days a week.
That’s not going to happen this fall.
However, that’s not all that bad.
I’ve recorded lectures in short spurts, seldom much more than 10 minutes
and often shorter. The advantage here is
that when I made a mistake, I could start over.
Another advantage is that when you watch them, you can rewind and watch
them over and over again until you understand.
That was hard to do in a regular lecture room with 100+ students all
with different questions. Another thing
is that I’ll be generally available for “office hours” and we can Zoom together
and it will feel like we are only 3 feet apart.
This will all work out, however weird and
different it might be.
This document.
What I’m going to do here is lay out what will happen in the
course. Most everything will be organized
through Blackboard
https://blackboard.jhu.edu/webapps/login/
There you will find modules for
every week of the course. They will tell
you what is expected of you for the week.
The reading assignment for the week is there as are links to all of that
week’s video lectures. Instructions are
there for the weekly quizzes and problem sets.
As you should know by now, you are required to be in the PILOT program
as well. In addition, the Head TA will
organize and monitor a discussion forum.
Although it is on Blackboard, here
is a link to the guide to the course video lectures.
http://www.math.jhu.edu/~wsw/F20la/Video-guide-for-fall-2020-Linear-Algebra.pdf
Just to get this out of the way
early, the grade breakdown is as follows:
Quizzes: 15%
Homework 15%
PILOT 10%
Discussion 10%
Exam 1 15%
Exam 2 15%
Final 20%
The default grading for all courses is S/U
(satisfactory/unsatisfactory = ABC/DF).
However, all students can ask for a real official grade, so grades will
be made up for all but only given to those who want them. I will, of course, always be happy to write
letters of recommendation for student who need them later on. If you ask for a letter of recommendation
from me, I will assume you have given me permission to use the grade I have
made up for you unless you specify otherwise.
Quizzes: The weekly open book quizzes are given online
and they are timed. They are explained
in Blackboard. They are single attempt, 10
questions, one point each, with a timer of 30 minutes. The quizzes are set up to automatically give
1.5x or 2x time to any students who need more time for accessibility reasons. The quizzes are computer generated and graded.
Homework: Each
week you can download the homework from Blackboard. When you are done with it you can upload it
back to Blackboard. You will need some
sort of scanning software for your phone or computer for this and other things
in the course. Your TA will grade 3
problems each week. You won’t know which
ones. This is in hopes of being able to
give you real feedback. You are allowed, even
encouraged, to work in groups. When it comes to handing in the homework though,
please do your own solutions. Homework, that is, working problems, is THE
essential educational part of the course.
PILOT: All students are required to be in the PILOT
Program for this course. The grade will
be based on attendance.
Discussion forum: Using the Blackboard
discussion board, the head TA will create weekly open ended
prompts. Students will be required to answer a subset of the questions
posted with an initial response due by end of day Thursday and two response
posts due by end of day Sunday. Discussion forums will be graded directly
in Blackboard using a rubric.
Exams: There will be two open book midterms (Friday,
Oct 2, and Friday, Nov 6) and an open book final exam (TBA). The midterms will be offered in 2 time
slots: 8am - 9:30am and 5pm - 6:30pm, to accommodate students in
different time zones. You will be given
60 minutes, but you must start and end during your time slot. You can take the exam in either slot. We will be available for questions by
email. The exam will be online and you
will input your answers online but then upload your work before 10am and 7pm
respectively. Work must accompany your
exam. The TAs and I will grade them. The final will have a longer time slot.
A typical week. Because we don’t have regular lectures, the
typical week is, well, atypical. I will
hold a Zoom class at the regular time (10am Baltimore time) on Fridays. By then you should all have watched the
lectures and started on the homework and be ready with any questions you might
have (use chat). I might do some true/false
questions that you can answer on zoom but the class will no doubt degenerate
into the equivalent of office hours where I’ll answer questions or, if none, we
will disperse. Although you are not
required, my preference is that you have your camera on during Zoom meetings.
I will hold class on the first day of class, Aug 31, Monday, at 10
am. On that day I will run a poll to
find another time slot during the week for those who might not be able to make
it on Friday or just want a second class.
After the first week, we will have class at that new time as well as the
Friday time.
Your TA will meet at their assigned time the first week as
well. During that time
they will find a second time to meet each week.
Their section meetings will run only 20 minutes or so, once at their
assigned time and, after the first week, at the second time.
The TAs and I will generally be there to answer questions, but we
will not introduce new material that is required for the course. That is all handled through the textbook and
the video lectures.
Office hours. There will be no formal office hours (no
office for that matter). However, I am
generally available and like to talk about math. I live right across the street from the
office I won’t be in. In fact, I have
not been in another building since early March.
I have some time on my hands. If
you want to come to my “office hours”, you just email me and we’ll set up a
Zoom time to get together. Unless it is something
personal, I will notify and invite the rest of the class to come and listen in
(or participate). I find that if one
student has the nerve to ask a question, stupid one or not, it is likely that
many other students have the same question.
You can request the meeting to be private, but if it is math question, I
urge you not to do that.
Old Exams (http://www.math.jhu.edu/~wsw/S18/201/): are
posted on the web. These are from many years of previous versions of this
course. There are lots of exams and some solutions. Lots of great practice
materials. As with homework, I encourage
you to work in groups on these old exams. They are very good study materials and
solutions are not always available. However, as with homework, you must use the
groups carefully or they will work against you rather than for you. So, some
suggestions for study groups. All members should work all problems before the
study group meets. At the meeting, the group should hash out differences and
help those who couldn't work certain problems. The day after the group meets,
each student should work those problems they couldn't work before. A student
who goes to a study group and ``learns by watching'' is not likely to do well
in the course. I do not grade on the basis of how well you can watch others do
problems.
Personal Problems: If you anticipate, or actually
experience, serious problems with an exam because you have physical, mental or
psychological problems, then email me immediately, preferably before the exam,
but better to do it during the exam than after. Exams are for the purpose of
finding out if you know the material, not to see if you can function when you
are seriously stressed for external reasons. This suggestion applies to any aspect of the
course, not just the major exams. To cut
down the stress, there is no part of the grading system that counts a lot. Under normal circumstances the final might be
40% of the grade and thus be much more high stakes than anything we have in
this course this fall.
Grades: Roughly speaking, depending on how
the class goes, you can sort of expect that the middle grade might be about a
B/B-/C+ and about 30-40% of the class might get As. However, if you
all learn the material really well, then I would be delighted to give you
all As. I like to give hard exams because I don't think the best
students should be cheated out of their tuition; they should have something to
do too. So, don't get demoralized if the average is 50%, I grade on the
proverbial 'curve'.
Grade disputes. Every semester there are a number of students who are unhappy with
their course grade. Only one or two of these students push very hard for a
grade change. These students are usually ones who neglected some important part
of the course like doing the homework, studying, or they want some sort of
special consideration. Special consideration is patently unfair to all of the
other students. I will not do something for one student that I
would not do for all. I will not be unfair to the many students who would like
a better grade but who do not bug me daily for a week or two. Students who do
push hard for a grade change will experience my insistence on fairness for all
students as personal brutal abuse. I will be able to defend any grade I give
and my chairman and my dean will back me up. The point of this little tirade is
two-fold. First, I would really like to save the incredible amount of time
these one or two students cost me each semester, and, second, I want to
reassure all of the other students that I will not unfairly change someone
else's grade just because they made a pest of themselves. I take grades
seriously because I know most students do too. That means that they should be
fair.
HOURS YOU OWE: This is a 4
credit course. I assume that you take 15 credits and you work 45 hours a
week. That means you owe this course 45 x (4/15) = 12 hours. Since there are no in person lectures, most
of this time will be reading the text, watching video lectures, and in the
PILOT program. You can attend classes,
but they are now quite limited. If you
are not working 12 hours then don't be surprised if you're not doing well. Work
harder before you complain or even before you ask for too much help. You are
not working hard in this course until you put over 15 hours a week into it. If you are taking more credits then you have
chosen to work more hours.
BOSS: I'm the boss for the course,
although we have a Head TA who will handle much of the bureaucracy. If a TA
tells you something that contradicts what I (or the Head TA) said, get it
straightened out. This could be quite serious. If, for example, they said you
didn't have take a midterm because they don't count,
you probably should check with me because that contradicts what I said. If you
don't, and you listen to them, then you could lose big. We have very good TAs
so I do not anticipate any problems, but if you have problems with your TA then
you must bring it to my attention as quickly as possible if you want the
problem to end. For some reason students don't take this admonition seriously.
If you have complaints about your TA then email me about them. We'll fix it.
Study Habits: I should give you a little speech
here about study habits. All of you are good enough to get an A in the course.
What will determine the grade is a combination of motivation and study skills.
Motivation shouldn't be a problem since the material is great and you are
paying a fortune to get it (although I have met students who were unaffected by
these motivational tools). Study skills are harder to come by. I have
collected a number of useful things (http://www.math.jhu.edu/~wsw/S18/index2.html) that might help with learning how
to study. In a nutshell though, the point is, you learn math by doing. You can
watch people do math all day and not get much of an education. Do it. Work
problems. Memorize every theorem and definition in the book. You need to know
them all anyway, why make it up when you need it? Just learn it and remember
it. Then work every problem you can find. If you get help from someone, then go
back and work it again by yourself the next day. I cannot emphasize enough how
important that last statement is. Read it again. Do it. Many of you will notice
that there is a slight difference between this course and the last math course
you took in high school. We have over 100 students in this class. How big was
your last math class in high school? Did your teacher in high school actually
know your name? Did you have to read the book to learn the material in high
school or could you get it all out of the class? How many class hours did you
have in high school to learn one semester of Calculus? How many are you going
to get for Linear Algebra here? You MUST be able to read the book in this
class.
Linear Algebra: Linear algebra is everywhere.
You've been using it for years without naming it. The integral is linear, the
derivative is linear. Most applications of mathematics to the `real' world only
work when you only look at the linear part. It is great material which will be
with you always. One of the many
mathematical joys of linear algebra is that everything we do can be viewed both
geometrically and algebraically. Try to
keep both in mind as you study.
From the Course Catalogue: 110.201 (Q) Linear Algebra
Vector spaces, matrices, and linear transformations. Solutions of systems of
linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices.
Applications to differential equations. Prerequisite: Calculus I. 4
credits
The official Short Syllabus for
Linear Algebra
Calculus: Calculus I is a prerequisite for
this course. Technically, you can certainly do linear algebra without calculus,
but calculus supplies us with lots of examples so we use it. Even though there
are few real prerequisites, there is an abstraction about linear algebra that
makes it more difficult to grasp for some people. This is why many of you find
yourself taking it after Calculus III or differential equations. The more mathematical
sophistication you have, the easier it is to learn linear algebra. On the other
hand, the more linear algebra you know, the easier it is to understand the
content of courses like Calculus III and differential equations, because they
are full of linear things, obvious to those who have had linear algebra. Some
years back we found that students were getting random advice as to what order
to take courses in. I decided to figure out if there was a best order. What I
found didn't help. Students who took Calc III first and then Linear Algebra did
about the same in each. Students who did Linear Algebra first and then Calc III
didn't do as well in Linear Algebra as might have been expected (they didn't
have the advantage of the extra mathematical maturity of having taken Calc III)
but then they did better than expected in Calc III (because the content
knowledge of Linear Algebra that they had helped them with Calc III). We
decided not to tell people what order to recommend the courses be taken
in.
There are two distinct new levels
of abstraction in this course (abstract linear spaces and then inner products
on them). The intellectual transition for each of these is quite difficult so
if you find yourself having a hard time with the material it might not be your
imagination. The best way to make these transitions is, as usual, to work lots
of problems. Although these transitions can be difficult, they are well worth
the investment. Successfully making these transitions opens up a whole new type
of thought process which will remain available to you even if you never do math
again. Being able to absorb abstract
nonsense fast and then work with it is a great skill being offered in this
courses. As great as the material is and
as ever present as linear algebra will be for those who continue to use
mathematics, this ability to understand a new level of abstraction may well be
the most important thing in the course, should you manage it. Go for it!
Ethics: I have rarely had problems with
cheating in my classrooms and I don't expect to have it in this class. Although
everything is different this year, I believe that my students know the
difference between cheating and not cheating, right and wrong. In this syllabus I am supposed to tell you
about your responsibilities in this respect and also have you sign a pledge on
exams. I won’t do this because I
consider it insulting to you. This is an
advanced class full of students who actually want to learn and who need the
material, and I believe you know how to behave correctly.