Okay here's the story,
I always loved maths, but for some reasons i dropped out of school.
Now at 22 i want to start studying maths again, but i do not know where to start from..
tl;rd suggest me some books that cover the basics and the advanced stuff of mathematics, algebra and geometry.
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Anonymous2007-05-06 17:56 ID:OklpgP0z
do you really love maths?
find email addresses of lots of professors, tell them what youve completed, and ask for recommendations on where to begin and what books would be good, maybe a reading list, thank them for any response. don't forget libraries exist.
how much do you already know?
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Anonymous2007-05-06 19:13 ID:Y7llkwmq
>do you really love maths?
with passion
>how much do you already know?
Not much, but i'm a good programmer and everything i've learned, i've learned it myself reading books and manuals.
plus i have time and i'm not in a hurry.
I'm single, i do a small job, i live in a tiny apartment and i'm lost.
But to answer your question, oh well.. hmm i'm not good with english terms, but i guess i know some basic geometry, i have read about pythagoras and euclid (mostly historical stuff, the book i had didn't have much about their theories but i know most) and generally, i might not be a genius, but when it comes to something i really like (eg maths or programming) i can learn it myself
I'd prefer if someone could tell me some books to get instead of talking to professors, i don't think they would take me seriously anyway.
And anyway, i don't know how serious i am either; With programming i didn't knew if it was my thing or not, i tried it and i loved it and here i am, a good programmer with a shitty job.
If you're really serious, you can try Art of Problem Solving by Richard Rusczyk. The book's not easy, but I'm pretty sure it starts from scratch (ie doesn't assume you know everything ahead of time).
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Anonymous2007-05-07 4:35 ID:Phi9sCT2
It'd help if you were more specific about what math you know. A list of math classes you've taken beyond high school level would help. Are you planning to learn on your own or at a college? Do you have access to a math/science library? Do you have a specific area of math in mind? Do you have no clue what the areas of math are and whether they interest you?
If you wanted to learn the important parts of a college degree in math then you'd want to cover the following subjects in roughly this order:
Calculus, Linear Algebra, Multivariable Calculus, Topology, Real Analysis, Abstract Algebra
Extra topics: Differential Equations, Combinatorics, Number Theory, Differential Geometry
Your best bet is to read textbooks. One trick is to look at college websites and cruise their course lists to see which subjects are using which book. This also gives you an idea of difficulty and prerequisites.
If you want to just take random walks in mathematics try reading mathematical journals. A journal article will assume a certain level of mathematical background but they are easy to read.
Textbooks are generally pretty expensive because they have a narrow market. If you don't have access to a math/science library at a university or something it'd be tough to learn on your own.
>>7 A list of math classes you've taken beyond high school level would help.
I never took any Are you planning to learn on your own or at a college?
My own, i don't go to a college. Do you have access to a math/science library?
Maybe, there's a library here but i never asked if they have math/science related books.
i can order books from a bookstore Do you have a specific area of math in mind?
When i started programming i didn't knew why i am learning that stuff or what i am going to do with it, but after some years i made up my mind. Do you have no clue what the areas of math are and whether they interest you?
to be honest; no. but i like maths and i have lots of time and nothing to lose If you wanted to learn the important parts of a college degree in math then you'd want to cover the following subjects in roughly this order:
I don't care about a college degree, but ofcourse if this is the correct order (if there is a correct order) i'll follow it. Textbooks are generally pretty expensive because they have a narrow market. If you don't have access to a math/science library at a university or something it'd be tough to learn on your own.
I might download them off the internet if i find them or get them from a library.
If i cannot get them from any of those i'll buy them i guess.
But anyways, i don't think the "tought" part is to buy the books, but to understand their content.
What i am looking for here is some names of those 'textbooks' >>4,6 suggested some (thanks ;)
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d2007-05-07 6:43 ID:otjOvDPf
You will never succeed at learning advanced mathematics without attending a university, no matter how smart you are. Here's why:
* Maths books are a didactic nightmare for people learning on their own.
* It's impossible to do exercises without knowing "tricks" that they teach at universities. These "tricks" aren't written down anywhere, because it's silently assumed that anyone interested will simply attend the relevant courses.
* Mathematics is hard. Without peers to exchange advice and the pressure of exams, you will learn very, very slowly and only through great effort. This might not sound so bad now, but one day you'll regret that you didn't spend the time fucking hot bitches or building your own personal empire, or whatever.
* Learning mathematics on your own is useless. Nobody will ever ask you to give an example of a contravariant functor, and if the world economy collapses, you're better off with a tin opener than a thesis on unbounded operators.
* It won't help you in life. Without academic credentials, the jobs you'll find will be the same as now. Fantasize about employers asking you trick maths questions all you like, it won't happen. Without access to the academic community, it will be very difficult to find people who appreciate knowledge of mathematics. So know you how to integrate on locally compact groups, but what kind of car do you drive?
Still not convinced? Buy (the hardcover version of) _The Principles Of Mathematical Analysis_. This is your new Bible - it's used all over the world and is absolutely perfect, and very hard. You'll have to read a lot of other books to understand it. But when you finish, when you understand it and can do most of the exercises, you can start calling yourself a mathematician. No other book can give you that.
As for the reasons you gave me why i should go to a uni or stop now, well
* It's impossible to do exercises without knowing "tricks" that they teach at universities. These "tricks" aren't written down anywhere, because it's silently assumed that anyone interested will simply attend the relevant courses.
Yes, i understand what you mean here, that's sad but i guess i can't do much about it. you will learn very, very slowly and only through great effort.
I'm not in a rush .. * Learning mathematics on your own is useless.
That's like saying knowledge is useless, well it might be useless. Our whole existence is useless so what's your point :P * It won't help you in life. Without academic credentials, the jobs you'll find will be the same as now. Fantasize about employers asking you trick maths questions all you like, it won't happen.
It's ok that wasn't my goal anyway.
thread over i guess (except if someone wants to add something helpful)
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Anonymous2007-05-07 8:12 ID:Phi9sCT2
7 here, I say go for it regardless of what others say (which sounds like what you've already decided, great!).
I'm looking through my old textbooks to give you some good recommendations as per your request. I really love my Calc book by Larson, Hostetler and Edwards (just titled 'Calculus'). It's a solid book all around: covers all of Caclulus (even goes into multivariable and diffeq a little), has complete proofs for everything, most importantly it is easy to read and gives refershers for lots of things preceeding Caclulus. If you get frustrated with the difficulty of learning math on your own, try this book.
As mentioned, "The Principles Of Mathematical Analysis" by Rudin is the best book for Analysis, hands down. The area of math called 'Analysis' is basically everything which directly follows (and encompasses) Calculus. While reading Rudin keep in mind his style is to prove things *very* concisely, which can be intimidating. Logically one could do Rudin right after (or instead of) Calculus, but realistically one has to work their way up to this difficulty.
For Algebra I like the book by Artin. There aren't any prerequisites for Algebra besides knowing what a set is and a little Linear Algebra, and he does cover I think all of what you need from Linear Algebra in the first chapter.
Don't be too intimidated by the thought that there are tricks which aren't taught in textbooks. You can pick up lots of those tricks slowly anyways, and even so these tricks are generally not teaching you anything too important. What's in the meat of the textbooks is the most important part.
The hardest part for someone just starting to study mathematics is learning how to *prove* things rigorously, which is something that is not emphasized in high school mathematics. It is vital that you try to understand every proof when you read a textbook. It should be your aim to eventually understand all the proofs. Even better you would like to be able to commit to memory the general idea of each proof so that from the general idea you can reconstruct the entire proof by hand.
A final thought is that many textbooks have exercise solutions available online written up by students. I know you can find most of the solutions to Rudin online, for example.
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Anonymous2007-05-07 8:34 ID:jqJ9hy0G
I found this list of math books
(http://www.pastebin.ca/475392)
The books you guys recommended are there, i'm going to download them.
If anyone wants a book from this list post here and i'll upload it at rapidshare/megaupload/whatever you want.
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4tran2007-05-07 9:00 ID:kPrYhAza
If you're up for the challenge go for it. Do be aware that mathematics is among the most difficult subjects in all of academia. If you can pull this off, I'll be amazed.
Yea, seriously. The math should become as clear as common sense if you think about it hard enough. If you're going up into higher math and you know that things work, but don't know why then maybe you should switch over to another profession.
Being a mathematician isn't a hobby, it's a way of life. Teaching yourself the math will give you a much better understanding of the math, but it will take a lot more time and dedication.
Many of the greatest mathematicians in history were self taught.
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Anonymous2007-05-10 1:20 ID:P/X3Al4p
Find a good calculus book. Start doing as many problems as you can until you are stumped. Also, keep an algebra/trig book nearby in case your math skills really suck. Pay special attention to the word problems which try to borrow from physics or geometry. If you can do those, then you might be able to develop some skills for higher mathematics.
DO NOT USE A GRAPHING CALCULATOR. Use pen and pencil like everyone else had up to the 1990s.
If you somehow manage to avoid quitting, you're gonna be doing Linear Algebra and Differential Equations next.
Ugggh, not Baby Rudin. Good reference, but lousy textbook.
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Anonymous2007-05-10 2:58 ID:9aiwN/Df
Search your favorite torrent site for "Tom Apostle's" Calculus books.
This series should give you a rigorous introduction to many different areas in college math. Then pick some areas you're interested in and/or find practical. Linear Algebra? Advanced Calculus? Find a local university and sit in the relevant classes.. you don't have to register and pay tuition.. just keep going till the prof kicks you out.
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4tran2007-05-10 4:24 ID:fkaIbNku
>>26
I wish to disagree. I don't think chugging through random calculus problems/word problems will be very helpful for someone attempting higher math. If you want accuracy/speed/competance with computations, then yes it will help. If you want skill with abstract thinking and proof work, then it will be of negligible help.
Look for The Teaching Company's calculus lectures by Michael Starbird. If you download it you'll only find the audio, but it's still worthwhile as it'll force you to use your imagination and learn to think abstractly. Even if you already know calculus it should help you get a different perspective on why it is you do the things you do.
Also, while you're reading text books try and play around with the formulas you're given (not entirely blindly, try to understand what you're doing and why). This will help you not only understand the concept and how the formula was derived, but you will retain the information for much longer and with much less effort than if you just try to memorize it by rote learning (using it over and over again until you're "used" to the process and can do it even if you don't understand it).
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Anonymous2007-05-12 0:35 ID:wJQv4COq
purplemath.com ftw?
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Anonymous2009-03-18 2:30
I'm feeling really keen, for some of that good ol' green