For many students, this is your first college-level course in mathematics. In high school, you may have taken calculus courses that taught you to perform (sometimes rather involved) mechanical procedures for computing derivatives, integrals, and the like. About half of this course will be similar, except instead of computing integrals, you'll learn to solve systems of linear equations of various forms.
The other half of this course, however, will likely be more abstract in nature than anything you've seen before. You are at the Georgia Institute of Technology, after all — this is not high school any more. We will focus on conceptual ways of understanding equations and their solution sets. We will ask questions like, what is the dimension of a set of solutions? What are all ways we can write them down? Are there any properties of the matrices involved that we can exploit to describe the solution sets, without actually solving the equations in the first place? What kind of geometric questions can we associate to a system of linear equations?
For these reasons, the methods you used to approach your previous mathematics courses may not suffice any more. For instance:
You will probably notice that there are lots of vocabulary words in this course, such as span, linearly independent, eigenvector, invertible, etc. You have to not only learn what they mean, but learn to make them work for you. The language of mathematics is very powerful, but also very precise; having a vague idea of what a term signifies is not useful.
You may be tempted to ask, "so what's the recipe for solving this kind of problem?" or "what kinds of problems will be on the exam?" About half of the problems will not reduce to some kind of mechanical procedure, so there really is no recipe. We can't tell you that you'll only have problems of a certain form, and that we'll just fiddle with the numbers on the exams. If Wolfram Alpha can do the problem faster than you can, it doesn't count as problem solving. Problem solving is the part where you figure out what to ask Wolfram Alpha (or Mathematica, etc.) in the first place. And this is as it should be: nobody is going to hire you to do calculations that a computer can do better.
If you've read this far, then you may be worried that your usual approach is useless, and that you're in for a tough semester. Don't worry, you're smart and hardworking. You wouldn't have been admitted if we didn't think you'd succeed. You'll figure it out! Plus there are lots of resources available, so you won't be on your own.
Read on for more specific advice.
Do the homework assignments carefully
This is the only graded portion of the course where you have a full week to
think about your answers. The only way to truly learn to do math is by
practicing doing math — just like the only way to learn to play tennis
is by spending time on the practice court.
Keep up with the daily coursework
Trying to learn everything the night or the week before an exam is like
trying to learn to hit serves and backhands in one long day of practice
with a big match the next day.
Work with your classmates
In addition to being a great way to get to know people, you'll find you may
learn as much from your classmates as you do from your professors. I'm of
the firm opinion that the advantage of being at a prestigious institution
such as Georgia Tech is as much the quality of your peers as the quality of
instruction.
Read the textbook before the lecture
The purpose of lecture time is to fill the gaps in your understanding, not to
communicate all of the content of the course. You don't need a Georgia Tech
professor to teach you the easy stuff, so we will concentrate on the
tricky points.
Come to class and to recitation, and pay attention
We prepare lectures carefully, and the online lecture notes will not
mean much to you unless you were there to hear them explained. If you're not
in class, then you won't hear us say the word "span" four hundred times in
one week, and therefore you might be surprised to see it on the midterm.
Besides, attendance is part of your grade.
Take advantage of the resources provided
We know that learning linear algebra can be hard. There are lots of ways to
get help. Come to office hours! Read the textbook! Go to Math Lab! Ask
questions on Piazza! We want you to succeed, but you can lead a horse
to water...
Don't look for answers on the Internet
This is not because it's considered dishonest; rather, it is hard to find
quality information on the Internet, and even harder to judge the
reliability of any information you do find.
At the very least, only use the Internet as a last resort, after you've already
been stuck for a while.
Math Lab
This is essentially a free walk-in one-on-many tutoring service provided by
the School of Mathematics, and is staffed by graduate teaching assistants.
Its hours are very flexible. Here you will find people who are willing to
spend lots of time helping you and answering your questions. Note that it's not
necessary to find a time when you can meet with a graduate instructor who is
currently teaching 1553: any math grad student is very comfortable with
basic linear algebra.
The textbook and course materials.
If you get stuck,
Go back and actually read through the
textbook carefully. Your instructor
will post new material throughout the semester on their website or on Canvas.
The exercises in the textbook
There are many good exercises at the end of every section and every chapter
of Lay. These are ideal for use as practice problems.
Piazza
This is an online space for this class where you can post questions
and help other people by answering their questions. We will also check Piazza
. It can be accessed through the course
site on Canvas.
See the discussion on the
organization page. Please login to it at least
once, since you will not receive class announcements posted through Piazza otherwise.
One-on-one tutoring
If you decide you need extra, personalized help beyond what is freely
available, you can consider hiring a tutor.