I've finished singe variable calculus and I want a taste of pure mathematics before I go to university next September. I'm going to get a grasp of sets and proof first but what next? Number theory, analysis or what? Book recommendations would be ideal!
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Anonymous2007-12-22 19:19
I'm planning on going into topology or analysis. Both of those are fucking badass.
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Anonymous2007-12-22 19:21
Oh, and this is more of a physics book, but Sir Roger Penrose's The Road to Reality is great. I recommend it for post-calculus level, and it seems to sit well even with higher mathematicians. A good read, even if you don't know all of the maths yet.
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Anonymous2007-12-22 21:52
Linear Algebra
Differential Equations
Discrete and Combinatorial Algebra
Vector Calculus (including multivariable calculus if you haven't gotten to it yet)
Those are basically the math topics that you could handle right about now. Use google or something to learn more about them, I've enjoyed all of them except probably diffEq, and thats more of the professors fault I think.
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Anonymous2007-12-23 1:01
In no particular order:
Linear algebra
Abstract algebra (number theory first is preferred)
Topology
Analysis (real, complex, functional)
Differential equations
Differential geometry is for after topology, and analysis (and possibly differential equations). Tensors and Riemannian geometry usually go with this, as does vector calculus.
Algebraic geometry is for after abstract algebra and analysis
Algebraic topology is after abstract algebra and topology
Linear algebra and differential equations are more for applications rather than something in themselves. Lots of things require it linear algebra, but differential equations are usually less seen (they usually appear in functional analysis), but obviously very important in applied math. Analysis and topology are very important; measure theory is something very important, but is usually presented along with Analysis. I don't know about abstract algebra because I don't know it, nor has it popped much in other things that I do know.
In all, mathematics is roughly divided into three interests of study: algebra, analysis, and topology.
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Anonymous2007-12-23 2:10
Elementary differential equations are not exciting by any means. They are useful, and the advanced stuff can get really fun, but they should not be used in a survey of higher math. Algebra is LOTS of fun - check out "Contemporary Abstract Algebra" by Gallian - its only prerequisite is a tiny amount of set theory and familiarity with the concept of a function. There's an elementary book on topology by Michael Henle (the title of which escapes me) which you might like.
>>8
Agreed. Pure math is pointless unless you have time enough or money enough to study it. You could also go to some engineering school. In any case, biomedical engineering is perhaps worth pursuing. Contribute to health, and so that people can live longer to study pure math.
>>10
I did all the 100 and 200 maths (the math versions too, not the life science version) and got an A in every one of them (except for the B+ in Calc I, LOL).
Anyways, the point here is that both can be as hard as you want them to be, it's just biochemistry and cell biology are more useful and financially rewarding than pure maths.
If you like math do engineering. That way someone will care when you're dead.
Wrong. If you like math, become a mathemetician. If you like problem solving, become an engineer.
While problem solving and math skills have high correlation, there is a big difference between liking math and liking problem solving, and that difference leads to some people being better academics and others being better engineers.
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Anonymous2007-12-28 14:00
>>17 Wrong. If you like math, become a mathemetician. If you like taking credit for things mathematicians came up with, become an engineer.
Fixed.
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Anonymous2007-12-28 15:46
We need engineers more than we need mathematicians. If I asked a mathematician to build a sewer plant, it would cost 10 times as much, and always be half-finished.
>>20
engineers are a subset of mathematicians, yes
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Anonymous2007-12-28 17:49
>>21
Uh, you got the first part right. Engineers are not mathematicians, though.
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Anonymous2007-12-28 17:58
If I need a toilet installed, I call a plumber. If I needed a sewer network, I'd call an engineer. If I need an inscrutable process examined for manipulatable numbers, I call a mathematician.
The thing is, I can install my own toilet, -and- I can manipulate my own equations, but I cannot install a sewer network.
But, you know, you're right. Mathematicians are worthless. Calculus is worthless. Engineering r great.
Also, just because you're an ignorant fucktard who can't install a sewer network, doesn't mean a mathematician can't.
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Anonymous2007-12-28 20:55
but I cannot install a sewer network.
Neither can an engineer. Design it, sure, but so can any mathematician and most people with half a brain. For the actual installation, you're going to need blue-collar peons.
Mathematicians don't do "we've found a problem which is useful to solve, let's solve it." Instead, they do "we've solved a problem, it seems. Perhaps this can be expanded upon so that it may become useful for other things." In other words, mathematicians work in generalities in that it MAY become useful, whereas engineers don't do problems unless they already know that it is useful.
But other than that, engineers do things that are frequently actually useful for the economy, and permanently useful in that matter. I don't know how the economy could be affected by mathematicians.
A Mathematician's Apology. Read it you fucking faggots.
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Anonymous2007-12-29 0:24
>>28
Because a person's worth can only be judged in terms of his direct usefulness to the economy.
Congratulations, capitalism, you've become the new communism.
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Anonymous2007-12-29 0:26
>>28
The fact that real economics work is done by mathematicians should prove you sufficiently wrong to shut you the fuck up.
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Anonymous2007-12-29 0:56
>>31
I meant all that theoretical work in areas like topology, differential geometry, analytic number theory, algebraic geometry, and so on.
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Anonymous2007-12-29 1:07
>>32
Theoretical work in those areas contributes to physics. You know, that whole thing about EVERYTHING?
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Anonymous2007-12-29 2:05
Pure mathematicians are fine. We put up with teaching your engineers "useful" maths, we develop your field (even if unintentionally), and be a consultant for them later. Now fuck off, you twat.