How to get along fast in math. while retaining all the info

[andrewkg]

Hello my name is Andrew I'm also in high school a sophmore. I got sort of behind my 8th and 9th grade years in math currently to catch up I'm at the university in my town. I've always loved math, but its taking time to get through all the basics for calc and so on. I mainly want to get to some of the latter topics in linear algebra, differential geo, and DE so that I can understand QM. My major question is does anyone have any ideas on a fast maybe 3 week way that i can learn all of the things needed before calculus. Mainly just trig .I'm taking precalc now and then this summer I'm taking calc 1. I want to get ahead with some speed more so then the path of just taking classes, but also I want to have a very concrete knowledge of this subject.

Now for the questions. How did you go about getting ahead like you have? Did I miss the boat? Is there a way I can get through trigh and logs in a relitively small amount of time, in say 5 months to get to DE topology or DG? And if so through personal study how would you suggest I get there? Does anyone know of a good linear algebra book that requires no fore knowledge of calc? I have Shilov I think that's it, but I want one that could be done with some more ease seeing as I have little understanding of determinants and I noticed they use some parts with integrals, and there is some function analysis that i do not comprehend. Also I am decent at math, by no means an genius but i love the subject and am willing to invest as much time as necessary.

Thank you a ton.

 

[TomServo]

I'll just repost what I posted on another forum:

I am a former math tutor/current physics and computer science major who is very strong on math, and I am also self-taught. I'm not saying this to brag, I'm saying it so you will take my advice seriously. IF YOU DON'T FOLLOW MY ADVICE, YOU WILL CONTINUE TO FAIL. And here it is:

Practice every day. Math is like learning to play an instrument. Some people have a knack for it, but even they will practice every day. Practice steps:

1) Do a set of practice problems, either from the examples in the book or from the problems in the book that you can get the answers for in the back. Were you assigned problems 1-20, even? Then do 1-20 odd so you can get the answers (or flip the even/odd depending on how your book does it), and do those as practice. The end of each chapter should have a chapter review set of problems or even a practice exams. These are perfect for studying before an exam.
2) Check your answers. Mark each one you did wrong.
3) Redo the ones you did wrong until you get the correct answer.

When doing the example problems in the first part of each chapter section, don't just read through, actually do the problem with pen and paper, reproducing each step. Make sure you understand how to get from one step to another.

Here are some BAD ways to study that you should avoid:
1) studying once or twice a week
2) learning new material before a test (studying before a test is to reinforce material you've covered already, not introduce you to it)
3) just reading through the book and not actually doing problems
4) getting a problem wrong but not redoing it
5) not going through homework and exam problems you got wrong to fix them
6) not asking somebody, like your professor or TA, about a question you have
7) not getting free tutoring either in the form of office hours or the free tutoring services that most colleges seem to offer (usually called peer tutoring)
8) studying around distractions (tv, smartphones, laptops, noisy places)
9) not doing enough practice problems
10) over-reliance on calculators (they are for checking answers and doing arithmetic)

 

[TomServo]

I also said:

I taught myself pre-calc with this book:

Amazon.com: PreCalculus the Easy Way (Barron's E-Z) (9780764128929): Lawrence Leff: Books

I taught myself calculus with this book:

Amazon.com: Teach Yourself Calculus (9780071421287): Hugh Neill: Books

And then moved on to this book:

Amazon.com: Calculus of a Single Variable (9780618503032): Ron Larson, Robert P. Hostetler, Bruce H. Edwards: Books

I got all A's in my math classes because I DID EVERY PROBLEM in the first two books and select odd-numbered problems in the third book, and then if I got one wrong I did it again until I got it right. Take it from a great math student and a former math tutor, the secrets to doing well in math are:

--study every day, going through the book's examples and explanations. Take your books and go to McDonald's or a park or something if you need to force yourself to study in a distraction-free environment. Don't take a laptop or smart phone or any procrastination tools with you if you can't resist them

--do the problems and correct your answers

--do the practice exams or chapter reviews in the book

--if the teacher hands out a practice mid-term or practice final exam, DO IT, MAKE TIME FOR IT, and fix your mistakes

--to prepare for a final, re-do your mid-term

--use a graphing calculator to become intimately familiar with the behavior of the various functions: polynomials, logarithms, trig (I'm assuming you have trig down pat or you wouldn't even be attempting calculus), exponential, etc.

To do well in calculus you must grasp the following concepts. Note: I said grasp the concepts, I'm NOT talking about memorizing the formulae (which you will do anyway):

--the limit concept
--the derivative and how it comes from the slope-secant line using the limit concept
--rates of change, what it means when a change in one variable means a change in another
--understanding how the integral is like adding up a bunch of infinitesimally tiny things Just remember this later as you cover these concepts.

 

[andrewkg]

Thanks for the advice. One thing though i don't know if the part was from the last post but I'm not failing. But again thank you, very thorough specific advice. Thanks

 

[andrewkg]

Sorry IDK if anyone has any ideas or if its possible. Is there a way i can learn trig in three weeks? If so how?

 

[Jorriss]

Don't try and learn it in 3 weeks? If you can learn trig in 3 weeks, great, it's not that complicated, but take the time you need.

Get a trig book, work through it.

Don't try and learn quantum based on a bad foundation of math.

 

[eumyang]

Don't try and learn it in 3 weeks? If you can learn trig in 3 weeks, great, it's not that complicated, but take the time you need.

Get a trig book, work through it.

Don't try and learn quantum based on a bad foundation of math.

I wanted to second what I've bolded above. From what I have seen, most math/science programs at colleges and universities in the US start with Calculus in the 1st year, so as long as you have a solid precalculus background by the time you graduate from high school, I wouldn't consider you "behind".

 

[andrewkg]

Yeah. Well we will be done with the trig part of precalc in 5 or 6 weeks anyways so I can just wait. Thanks for the advice.