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View Poll Results: Which is most interesting, or which are you best at?
Discrete Math (such as Number Theory) 11 39.29%
Algebra (Group Theory, Linear Algebra, Abstract Algebra) 3 10.71%
Analysis (Calculus, The Real Line, Differential Equations) 5 17.86%
Geometry/Topolgy 1 3.57%
Statistics/Computation 4 14.29%
Other (please post) 4 14.29%
Voters: 28. You may not vote on this poll

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Old 2011-10-28, 16:45   #1
Dubslow
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Default What kind of math do you prefer?

It's time I contributed here.

I'm often lost in the theory around here because discrete, integer, number theory stuff just aint my thing.

What do you all like? (And please don't all respond Number Theory.)

Edit: I've just pegged myself as a complete and total American.

Analysis type stuff is the only stuff I've studied in depth, which means basic differential calculus and partway through a DiffEq course. I also have taken a Linear Algebra course, though I thought the coolest part of that was extending inner products to functions, which according to this falls under Harmonic Analysis.

Last fiddled with by Dubslow on 2011-10-28 at 16:50
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Old 2011-10-28, 18:27   #2
xilman
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Quote:
Originally Posted by Dubslow View Post
What do you all like? (And please don't all respond Number Theory.)

Edit: I've just pegged myself as a complete and total American.
The type with an 's' in the spelling.

Paul
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Old 2011-10-28, 18:29   #3
ET_
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"Luigi"
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Quote:
Originally Posted by Dubslow View Post
It's time I contributed here.

I'm often lost in the theory around here because discrete, integer, number theory stuff just aint my thing.

What do you all like? (And please don't all respond Number Theory.)

Edit: I've just pegged myself as a complete and total American.

Analysis type stuff is the only stuff I've studied in depth, which means basic differential calculus and partway through a DiffEq course. I also have taken a Linear Algebra course, though I thought the coolest part of that was extending inner products to functions, which according to this falls under Harmonic Analysis.
I'd prefer a multiple choice poll, as I am interested in Number Theory, Algebra and Topology...

Luigi
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Old 2011-10-28, 18:51   #4
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Quote:
Originally Posted by ET_ View Post
I'd prefer a multiple choice poll, as I am interested in Number Theory, Algebra and Topology...

Luigi
Why is it called "multiple choice" when you only get one choice?
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Old 2011-10-28, 18:56   #5
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Quote:
Originally Posted by Dubslow View Post
Analysis type stuff is the only stuff I've studied in depth...
I wouldn't dare to claim to have studied anything "in depth", given the company.

Topics I've barely scratched the surface of include abstract algebra, topology, set theory, category theory, logic, and of course, number theory.
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Old 2011-10-28, 19:12   #6
ET_
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Quote:
Originally Posted by Mr. P-1 View Post
I wouldn't dare to claim to have studied anything "in depth", given the company.
I just said "I'm interested in", not "I know about"...

Luigi
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Old 2011-10-28, 19:23   #7
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Quote:
Originally Posted by Mr. P-1 View Post
Why is it called "multiple choice" when you only get one choice?
When you set a poll up you have the option of allowing more than one answer to be selected.....hence "multiple choice" that ET_ was referring to.
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Old 2011-10-28, 20:23   #8
Dubslow
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Quote:
Originally Posted by Mr. P-1 View Post
I wouldn't dare to claim to have studied anything "in depth", given the company.

Topics I've barely scratched the surface of include abstract algebra, topology, set theory, category theory, logic, and of course, number theory.
Consider it in depth compared to how much I've studied anything else. And it's also the most interesting for me. Inner products with integrals on polynomials is much cooler than matrices. Those are just icky.

Last fiddled with by Dubslow on 2011-10-28 at 20:31
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Old 2011-10-28, 21:03   #9
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Quote:
Originally Posted by Dubslow View Post
Inner products with integrals on polynomials is much cooler than matrices. Those are just icky.
I discovered that knowing how to use the matrices was the key to aceing my Introduction to Quantum Mechanics exams.
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Old 2011-10-28, 22:13   #10
R.D. Silverman
 
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Quote:
Originally Posted by Dubslow View Post
It's time I contributed here.

I'm often lost in the theory around here because discrete, integer, number theory stuff just aint my thing.

What do you all like? (And please don't all respond Number Theory.)

Edit: I've just pegged myself as a complete and total American.

Analysis type stuff is the only stuff I've studied in depth, which means basic differential calculus and partway through a DiffEq course.
You have not studied analysis in depth. I would recommend reading,
e.g. Rudin's "Principles of Mathematical Analysis" as a solid introduction
to analysis. All you have studied is a basic intro to calculus. Have you
e.g. worked through a proof of the intermediate value theorem?
Can you prove the chain rule for derivatives? Can you perform
epsilon-delta proofs for evaluating limits?

Do you know what it means for the reals to be complete? Do you
understand the construction of the reals by Dedekind cuts or Cauchy sequences?
Do you know what Borel measure is? Lebesgue Measure?
Do you know the difference between a Riemann and Stieljes integral?

You say that you have studied diffeqs. Do you know how to do an
existence proof [i.e. that a function satisfying a diffeq exists?]

Have you looked at analytic continuation of functions? Cauchy's residue
theorem, Picard's theorem??

No?? You have bare scratched the surface in your study of analysis.

Last fiddled with by R.D. Silverman on 2011-10-28 at 22:14 Reason: fix pagination
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Old 2011-10-28, 23:08   #11
Dubslow
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Quote:
Originally Posted by R.D. Silverman View Post
You have not studied analysis in depth. I would recommend reading,
e.g. Rudin's "Principles of Mathematical Analysis" as a solid introduction
to analysis. All you have studied is a basic intro to calculus. Have you
e.g. worked through a proof of the intermediate value theorem?
Can you prove the chain rule for derivatives? Can you perform
epsilon-delta proofs for evaluating limits?

Do you know what it means for the reals to be complete? Do you
understand the construction of the reals by Dedekind cuts or Cauchy sequences?
Do you know what Borel measure is? Lebesgue Measure?
Do you know the difference between a Riemann and Stieljes integral?

You say that you have studied diffeqs. Do you know how to do an
existence proof [i.e. that a function satisfying a diffeq exists?]

Have you looked at analytic continuation of functions? Cauchy's residue
theorem, Picard's theorem??

No?? You have bare scratched the surface in your study of analysis.
You sir, are an arrogant ass who looks down on everyone from an Ivory Tower and assumes that the common man can't possibly be intelligent as you. You've had how many years studying math?
Quote:
Originally Posted by Dubslow View Post
Consider it in depth compared to how much I've studied anything else.
Quote:
Originally Posted by R.D. Silverman View Post
Have you
e.g. worked through a proof of the intermediate value theorem?
Can you prove the chain rule for derivatives? Can you perform
epsilon-delta proofs for evaluating limits?
I'm fairly sure I have seen a proof, and depending on a source, go through it. I can prove the chain rule for derivatives, or at least I did that one time a year ago. Epsilon-delta proofs are not much harder than calculus, just harder to think about. Simple limits are trivial to prove with epsilon delta, and more complicated limits can be proven by proving the sum of limits = limit of sum and similar rules.
Quote:
Originally Posted by R.D. Silverman View Post
Do you know what it means for the reals to be complete? Do you understand the construction of the reals by Dedekind cuts or Cauchy sequences?
I had a rough idea, and 10 seconds of Wikipedia makes it more clear. Cauchy sequences are no harder than epsilon-delta limits. Dedekind cuts are a bit harder, taken me around ten minutes to grasp the idea, but that might be because Wikipedia's never been a good place to learn new math the first time.
Quote:
Originally Posted by R.D. Silverman View Post
Do you know what Borel measure is? Lebesgue Measure? Do you know the difference between a Riemann and Stieljes integral?
Off the top of my head, no. I believe that in a less-than-introductory Quantum Mechanics not-really-a-course, we had one of the math teachers come in a talk about measure theory in order to put physicists' use of the Dirac delta function in integrals on a firm basis. Being in high school at the time, I did not pay much attention. I do know what a Riemann integral is, though after a few minutes on Wikipedia, I fail to understand the subtle difference between the two kinds.
Quote:
Originally Posted by R.D. Silverman View Post
You say that you have studied diffeqs. Do you know how to do an
existence proof [i.e. that a function satisfying a diffeq exists?]
In class around a month ago we went over the E-U proof for first order equations y'=f(x,y) where f and df/dy (partials) are continuous. We did skip over a few of the details, like continuity of the solution, but it was still around 90% of the proof.
Quote:
Originally Posted by R.D. Silverman View Post
Have you looked at analytic continuation of functions? Cauchy's residue theorem, Picard's theorem??
I don't know about in general, but I have looked at the Gamma function (factorials extended to C) and obviously analytic continuation of the elementary functions of calculus is trivial with power series. A quick 2 minute glance at Wikipedia for Cauchy's theorem (one of the many Cauchy theorems) only interests my desire to take a complex analysis class. (I have a partial comprehension, not as good as others, but then again, I've never taken complex analysis.) Picard's theorem is easy enough to understand (again, Wikipedia) though the proof sections lost me half way through the first sentence.
Quote:
Originally Posted by R.D. Silverman View Post
No??
For the most part, yes.
Quote:
Originally Posted by R.D. Silverman View Post
No?? You have bare scratched the surface in your study of analysis.
Let me repeat for emphasis:
Quote:
Originally Posted by Dubslow View Post
Consider it "in depth" compared to how much I've studied anything else.

Keep in mind I turned 18 two months ago and have four years of undergraduate college ahead of me. I'm not even a math major. (Though I tried double majoring) (4 years minus half a semester, really.)

Last fiddled with by Dubslow on 2011-10-28 at 23:28
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