Favourite field of mathematics

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I myself love anything and everything to with algebra, particularly Galois theory. Number theory is a close second.
 

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Admittedly my mathematics background is extremely shallow (nothing higher than Calculus I), I have been working independently through a few modern abstract algebra books, I am enjoying this field of mathematics more than any other field I have been exposed to. I have just started learning group theory and will eventually move through fields, rings, Galois Theory, etc.

How far can someone go into this field of mathematics, because I am really enjoying it a lot. Of course, I am reserving my selection of specilization until I am exposed to more mathematics. I really enjoy the abstractness that this field of maths develops. It is refreshing to do something, which to me, is a lot different than calculus.
 
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I will also admit that I do not truly have deep knowledge in any particular area of mathematics to really pick a favorite, but currently I would say my favorite is algebra(even with my limited experience in it), but of the subjects I have had classes in I find complex analysis, and partial differential equations very interesting as well.
 
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Differential topology...was like discovering sex.
 
Gib Z
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>.< Number Theory, But I wouldn't say it was like discovering sex...lol. Both things are equally beautiful :p. Thats a BIG compliment for Number Theory, trust me :)
 
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I was fascinated with the idea of studying functions of a complex variable. Later I found out I could study functions on n- dimensional complex space. I currently studying function theory of several complex variables. I also like differential geometry.

So my hope is to study complex (differential) geometry (i.e., geometry of complex manifolds)
 
quasar987
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So far, the subject in math that was the most enthralling to me is functional analysis.
 
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>.< Number Theory, But I wouldn't say it was like discovering sex...lol. Both things are equally beautiful :p. Thats a BIG compliment for Number Theory, trust me :)
You're only 15, how would you know?
 
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I'm somewhat partial to complex analysis and differential geometry. But I'm on an algebraic geometry kick at the moment, simply because I feel that Groebner bases are far cooler than they're given credit for.
 
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differential topology, differential geometry
 
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Differential topology and geometry are my current obsessions.
 
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dynamical systems (flow, collisionless or collisoin)

edit: oh and graph theory and 3D engine mathematics.
 
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It's so hard to say. I like analysis, differential geometry, algebraic and point set topology, combinatorics, logic, algebraic geometry, group theory, representation theory and commutative algebra.

But I hate non-commutative rings.
 
CRGreathouse
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Number Theory.
 
disregardthat
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I prefer addition.
 
Gib Z
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Rofl we got a comedian here!

Quote theperthian (dunno if i spelled right): How would you know, your only 15?
Quote d_leet : I was thinking the same thing

I got lucky :p

EDIT: I Spelled "Spelled" as "slept"...Im pretty bad at slepting :p
 
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Gib Z
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That gives me an idea, ima start a thread in PF lounge on when people lost their..innocence, thatll be a nice thread :p

Just need a mentor to tell me i wont be banned for doing so before i make it lol.

Btw: Last post, i was kidding.

Its like, f'(x)= d/dx (sex) and I don't know f(x), but Im using 10 Riemann Midpoint sums :P Im such a nerd
 
J77
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Currently I'm doing some research in higher dimensional interior angles, which is a fun topic, dealing with the infamous gamma vector, but I particularly enjoy differential equations and am starting to develop a love for Complex Analysis.
 
Aren't we all :biggrin:
I prefer intellect. Intellects acquire knowledge because they have a passion for discovery and exploration and simply because they can. Nerds acquire knowledge because it's all they are good at.

I can never have a social, intellectual conversation with stereotypical 'nerds' because they always seem to lack good conversation skills and word formation. This is why I prefer the term intellect, we blend in with society and act like we don't care but secretly do homework in our closets.

<333

In France, intellects are celebrities, (e.g. Jean Paul Sartre - one of my favorite philosophers).

This is of course, purely anecdotal.
 
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mathwonk
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a more difficult and useful exercise is to regain ones innocence.
 
a more difficult and useful exercise is to regain ones innocence.
Innocence distorts one's ability to transcend the tangible, concrete foundations of reality and expand their awareness across the plane of infinite imagination. Corrupt yourself as much as you can and you will feel an inextricable, interconnectedness between your perceptions and reality.

Actually, I have no idea what innocence you were describing, I was focusing on the embodied consciousness and how we can disassociate and disconnect it from the usual flow of perception.
 
mathwonk
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i was thinking of grohendieck's notion of the innocence of a child in research, in being willing to conjecture things too simple minded for the sophisticated to attempt, like the prime spectrum of an arbitrary ring as the right framework for algebraic geometry and number theory.

or picassos innocence in relearning to draw with the freedom and creativity
again of a child. As he put it, he could draw like raphael as a child himself, and it took him years to regain the free expression of the ordinary child.
 

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