Hey everyone. I've just gone back to university after a number of years off, and I'm looking to take Calculus in the fall of 2008. My problem is that it's been 9 years since I did Precalculus, so I was thinking of self studying through the summer. I've picked up Precalculus by James Stewart along with the Student's Solution Manual as my learning resources and was wondering what the best way was to go about it through the summer. I'll also be working close to full time in the summer, so my time is somewhat limited. Does anyone know of any websites with quizes/exams that I could do while I'm progressing through this book? Does anyone have any general tips about self studying in math? Should I just be going for short sessions like 2 hours a day, 5 days a week? Thanks for your responses in advance.
Don't think you understand stuff because you do the reading and it seems to make sense and seem familiar. Be sure to work the problems, and judge your progress from the ability to work the problems correctly. Use the solution manual for help only when you are stuck. Understanding how the author worked a problem is different from learning to do it on your own. There should be enough problems so that you can prove your ability to work the problems without the manual (perhaps after using the manual for assistance in a few.) Two hours a day, five days a week is a good committment level. I would expect success. I have never seen a student fail with this level of committment, and I've had a lot of students come back to school after long periods away. Older students with an appropriate level of committment and interest make very good students. Michael Courtney
I really don't think it's necessary to go back to precalculus. I don't really remember any similarities with it and calculus (but then again I don't remember any of the courses I took in high school, which is when I took precalc). I remember throughout high school I got C's in all my math classes (geometry, algebra trig, precalc) - my high school had terrible math teachers. So I figured I'd have no clue at all when I took calculus in college. What I did first was take a refresher course in basic college algebra (1 semester), and then I took short calculus (1 semester). And then a year later I took Calculus 1 and 2 and Aced them both. My tips are to just really pay attention to the concepts in the texts (I pretty much highlighted everything and worked out every example) and do a ton of practice problems (don't look at the solutions first - work out the problem until you've worked out a solution of your own or have completely exhausted every option). I also had a REALLY ****ING GREAT calculus teacher who kind of helped me relearn some of the stuff from previous courses that I was "supposed to" already know. So that helped (check on rateyourprofessor.com for good math professors at your institution before you go out and choose one blindly). Good luck!
greenneub: your going to be suprised how much you have forgotten. I took a 6 year break, and I had to get algebra and trig books to supplement my precalc book. But after such a long break, your focus and dedication will be different, and once things start rolling, you will absorb information quicker and better than before. best of luck.
It's vital that you master precalculus before calculus. If your algebra skills are weak, you will really struggle in calculus. It will be difficult to stay motivated working alone and also if you get stuck it might be hard to find help. If you audit or even take a precalculus class from a local community college it will be easier to stay motivated and on task. Also you will have lifelines in the form of the teacher and your fellow students. If you can't do that a good way to accomplish self study is to take classes online. If you really don't want to entertain either option I suggest preparing for yourself study guides. When you go through the text there are three levels that you might follow in order-- (a) Make sure that you know and write down the important vocab and results (b) Understand the reasoning behind each argument, fill in any steps that are missing (c) Solve the exercises So you might want to actually plan out and write up a worksheet for each chapter based on those steps, and then construct a time table with due dates to accomplish each worksheet. Even if you're only accountable to yourself, creating an explicit strategy with tangible proof that you're reaching your goals will help you stay on task during the summer.
Hey greenneub. I'm sort of in the same position as you, and doing more or less the same thing. (The main difference being that I never learned pre-calculus in the first place, so I can't really skip it). I'm doing 2-3 hours each day, and I've found that more than that is meaningless. If I cover too much ground too quickly, I don't learn it as well as I want to. I guess the mind needs some time to process things on its own for it to stick. I believe doing more than 3 hours on a single day is ok if you have enough material and problems for a single topic, but that is rarely the case. I do every single problem in the main book as well as a companion book with problems. I make a note on the areas where I feel like it's not "flowing" the way it is supposed to, and when I'm done with the book I go back and do those chapters again, taking my time and trying to really understand how each step works and why. A tip that I have "discovered" is this: When you start on a new topic, read the definitions, skip the examples and try the problems. When you get stuck, look at them for atleast a couple of minutes. If you still cant see the answer, THEN read the examples. I can only speak for myself, but atleast I get more "Aha!"'s that way, rather than the "Oh"'s of reading examples first. You only really appreciate the solution if you have tried the problem yourself. Another thing that I learned, is that I have to be very aware of when I am doing "shortcuts". IE: 4 * 3^x = 9 * 2^x lg( 4 * 3^x ) = ( lg 9 * 2^x ) lg 4 + x * lg 3 = lg 9 + x * lg 2 x * lg 3 - x * lg 2 = lg 9 - lg 4 x(lg 3 - lg 2) = lg 9 - lg 4 x = ( lg 9 -lg 4 ) / ( lg 3 - lg 2 ) It's a lot to write out, and I frequently find myself thinking "well, I know where this is going" and jumping from the second to the last line without writing the other steps. Then I feel clever. The thing is, that when I get used to this, after a while I tend to forget what the middle part actually did and looked like, and when the problems get more complex, I get stumped. So, I try to be very aware of when I am doing a shortcut, and at least go through the steps in my mind. (Of course, there are some shortcuts in the example above as well, but those are tried and tested over a long period of time, not new material). On those days when a lot of the end results are wrong, because I did an early mistake which followed through on the entire problem (wrote down the problem wrong, messed up a sign, multiplied powers instead of adding or whichever), I try to tell myself that it is ok, look at the book: It is written by a professor, proof read by multiple people, and still some of the answers are wrong. Getting to the wrong place now and again is a part of math, and it is ok. What is NOT ok, is using a erroneous approach or failing to understand the problem. Another really helpful thing are these forums. Looking at what other people has problems with works on many levels. Sometimes you can help (and this reinforce what you know), sometimes you can learn something new or read an explaination which makes something click, and sometimes you get help on problems of your own. There is a lot of highly overqualified people here that take time out of their day to help people like you and me. God bless them. k
Tutors at the school? Or a private tutor? Buy a web based program that teaches it and has online tutoring and tests and practice problems? Look at You tube videos and tutorials in calculus topics?
Went back to school 5 years after I finished high school, and I finished high school math in grade 11. Don't worry too much about it. Really. Refresh yourself on your basic algebra (exponent rules especially) and basic trig (identities, unit circle, special triangles) and you'll be fine. I found that after about the first month I was on a level playing field with all the fresh from high school kids in all my classes.
The best advice for self-study? Focus more on doing and mastering problem sets rather than trying to "get" the concepts.