I last taught Linear Algebra during Summer 2012. At the end of the course I gave a survey where the last question was - What advice would you give to an incoming student to this class? The unedited responses are below.
Don't procrastinate. Understand, don't cram the proofs.
Dont slack off even a little. Don't daydream in class or you will fall behind instantly. Do all homework. Ask questions.
It's a good idea to do your homework before it will be discussed in class. That way you could contribute to asking questions and/or understand the problems better. Be very careful on proving, since the professor only grades what he THINKS is best. So, just follow and accept his way and you'll be fine.
Test questions are almost all from HW, make sure you do and understand all of them. Some of the big proofs might appear to be confusing at first, but stick with it, memorizes it even if you don't understand it, because those proofs and concepts will be used again in the following chapters and you will eventually understands it very well.
Do Homework, review and don't study at the last 20 minutes :))
Do homework everyday after class because that will keep you on track with the pace of the course. If you get lazy and decide to not do homework everyday then you'll find yourself falling behind very very quickly. A good 1 1/2 - 2 hours of doing homework each day will save you from cramming/studying the night before a test. So just work diligently and ask questions in class so you won't screw yourself over. :)
Do the homework and understand the material. It isn't that hard but if you start slacking off it is very hard to brin your grade up. This class had a very straight forward grading system, no dropes no replacements.
If he does something in class, it's likely to be on a test at some point. If little or no emphasis is made on a certain topic in class, then there is a slim chance it will appear on a test. Pay attention when he says he REALLY LIKES a certain proof. It will be on the test.
If you stay on top of homework and study a small amount each day, this class will be a breeze. Do NOT wait until the day before the test to do homework... it is a TERRIBLE idea. Trust me. . . I know. If you don't do the homework and don't study... drop ... NOW, you will not do well.
Just a head's up: There's a quiz in the first week of school. And you'll have a lot of proofs. But trust me, they're not that hard to understand. A lot of the topics are pretty straightforward, as well as the proofs. Only a couple of weird proofs. So just study daily on the proofs and review your notes/homework. if you do that, you'll do fine
Understand all the material and practice the homework and the proofs. Just DO it.
COPY PROOFS, PROOFS, PROOFS!
study the proofs, not memorize them. Make sure that you understand what the proofs mean and what they are proving.
Study, study, study the proofs. If you don't understand some things, create a study group and go to the math lab. It really helps.
Study the proofs, re-write them and be on top of the hw. Try to even get ahead on the hw if you can cause it helped me having done the hw before seeing the lecture (of course there were some problems I had to skip though). Last thing, do all the hw and keep your hw as notes! I would copy the problem and then do the problem so when I studied for the final I had a whole packet of hw for each chapter to study off of.
It's a very easy class, I assure you that you are going to do very well on the first and the second tests. And you may get a little cocky afterwords. Don't be cocky because the third one is going to be a trick.
Work hard and do not memorize those proofs, understanding firstly.
Be careful of the answering 'Linera Algebra we covered this semester' question. I misread the title and I lose some points for the interesting question.
Do as much homework as you can after a lecture, keep up with it. The amount of material piles up as you go along on the chapters, you have to keep up with it and make sure you give yourself enough time to review theory problems before an exam. Do not memorize problems or theory problems!!! It will not help you !! Read the book if you don't feel too confident or understand a concept, because everything you learn in one chapter you will use in the next.
Try to keep up with all the work and focus on understanding the proofs from the notes
Do your Hw everyday and understand all the proofs in this class. It will help you more on the exams and final
Do all of the homework each day; don't wait until the last day to do it all at once. If you pay attention in class and
do the homework as you learn the material, you should be able to do well in this course. The class is cumulative in nature, so make sure you keep up with everything as you're most likely going to be using it for the rest of the semester.
Review the homework at least twice before an exam. There is more than likely going to be question on the exam that is similar.