Understanding Advanced Math Writings

For the discussion of math. Duh.

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vrek
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Understanding Advanced Math Writings

Postby vrek » Wed Sep 05, 2007 11:22 pm UTC

I was wondering if anyone could point me in a direction for understanding how to read math?
For examples look at http://mathworld.wolfram.com/ .
I like the idea of understanding how even simple operations actually work but I look at pages on the internet and I have no idea what they mean.
Take for example integration. We all know the basic idea but atleast I was never taught the actural theory behind it. So I look it up and I get this:http://mathworld.wolfram.com/Integral.html . I only understand about 1/4 of that page. Surely there has to be some resource to explain what in the world the rest means.

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Postby CodeLabMaster » Wed Sep 05, 2007 11:31 pm UTC

Generally, its always difficult to pick up random pieces of maths that you don't know and try to understand them without beginning at the beginning. Assuming you have a pretty good understanding of algebra and trig, and you know what logs and e are, then maybe you should try learning calculus, the field of math where you start learning about derivatives and integrals. Normally, I'd post up and recommend something like: http://tutorial.math.lamar.edu/ to learn Calculus, but right now that site seems to be down. I'm sure you'll find a good resource if you google Calculus 1 tutorial or something like that. Good Luck.

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Re: Understanding Advanced Math Writings

Postby jestingrabbit » Thu Sep 06, 2007 3:18 am UTC

vrek wrote:Surely there has to be some resource to explain what in the world the rest means.


Yes, they're called books.

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Re: Understanding Advanced Math Writings

Postby DrStalker » Thu Sep 06, 2007 3:49 am UTC

I prefer a decent text book over online pages. There are plenty of exceptions, but I find textbooks much better for learning and web pages much better to use as reference.

Checkout second-hand book stores; most (probably all!) the stuff you'll want to learn hasn't changed over the last few decades so unlike computer books ancient texts are just as good, if well written.

Work through the book systematically, and ask questions when you get stuck; forums are great for that sort of thing, you can get a dozen people explain something different ways and one of them should "click" with you.

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Re: Understanding Advanced Math Writings

Postby recurve boy » Thu Sep 06, 2007 4:36 am UTC

vrek wrote:I was wondering if anyone could point me in a direction for understanding how to read math?
For examples look at http://mathworld.wolfram.com/ .
I like the idea of understanding how even simple operations actually work but I look at pages on the internet and I have no idea what they mean.
Take for example integration. We all know the basic idea but atleast I was never taught the actural theory behind it. So I look it up and I get this:http://mathworld.wolfram.com/Integral.html . I only understand about 1/4 of that page. Surely there has to be some resource to explain what in the world the rest means.


That wolfram page is not too hard to understand if you have some university level math knowledge (proving them would probably require one to remember what one learned).

If you really want to know, buy a text book, start from the beginning and start working through problems and stuff.

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Re: Understanding Advanced Math Writings

Postby antonfire » Thu Sep 06, 2007 5:02 am UTC

jestingrabbit wrote:
vrek wrote:Surely there has to be some resource to explain what in the world the rest means.


Yes, they're called books.


Also, math professors. Taking a class might be a good idea, if that option is available.
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Postby Torn Apart By Dingos » Thu Sep 06, 2007 10:17 am UTC

Mathworld is only good as a reference for things you've already learnt once. The Mathworld pages are very obscure and hard to understand.

Wikipedia has very good articles on math, and you should definitely look there first, but be aware that it's written in an encyclopaedic manner. Definitions are sometimes omitted and proofs are scarce.

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Postby vrek » Fri Sep 07, 2007 2:00 am UTC

Ok so since everyone seems to be saying to read a book...What book?

I only have a HS education but I took up to Calculus in High school. I also have friends in a University who could help me(One is a Physics Major and Another is a Molecular BioChemist). Please Nothing extremly advanced like GEB but sometimes I can also learn and advance with. Thanks for your help.

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Postby Mathmagic » Fri Sep 07, 2007 2:15 am UTC

vrek wrote:Ok so since everyone seems to be saying to read a book...What book?


DrStalker wrote:text book


Ask one of your friends if you can borrow their first-year Calculus textbook. It's fairly simple to understand, and goes over your high-school calculus (ie. Limits, simple derivatives) and also is a very good intro/expansion to integrals.
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Postby Pathway » Fri Sep 07, 2007 2:51 am UTC

GEB doesn't really cover calculus, so we won't tell you to use it for that.

That said--it seems to be a wonderfully written book, and you might benefit a lot from forcing yourself to read it slowly and carefully.

Which is really the only way to read mathematics, incidentally.

As for calculus, if you already know the mechanics and surface-level justifications of integrals and derivatives (area under a curve, slope of a tangent line) then an ordinary textbook might not be satisfying enough.

Try to get a copy of Apostol's Calculus Vol. I from the library or something. There are copies on ebay for cheap as well.
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Postby Amicitia » Fri Sep 07, 2007 3:26 am UTC

I was just going to say Apostol.

Spivak's Calculus is easier to read, and still super rigorous. It has a good amount of foundations too, so even if your geography/algebra/trigonometry isn't too great, you'll be fine.

Apostol isn't witty though, so Spivak's Calculus is easier to read--cheaper too. :(

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Postby antonfire » Fri Sep 07, 2007 3:37 am UTC

vrek wrote:Please Nothing extremly advanced like GEB.


GEB (assuming you mean Gödel, Escher, Bach) is not that advanced. It has some sophisticated ideas, but it's meant to be read by the interested layperson. What made you think it's advanced?
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

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Postby Pathway » Fri Sep 07, 2007 4:16 am UTC

antonfire wrote:It has some sophisticated ideas


antonfire wrote:What made you think it's advanced?


I wasn't going to mention that, though, antonfire. Baby steps.
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Postby Amicitia » Fri Sep 07, 2007 4:42 am UTC

If calculus seems a bit too ambitious, then Set Theory & Metric Spaces by Kaplansky is conceptually not-too difficult, meaningful, and easy to read. If the notation seems to get you down in mathematical writing, just ask away in this thread, if you want. Formal mathematical language is a bit intimidating to swallow at first.


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