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Apr
16
comment Undergraduate Research Thesis
If you don't want to take this approach at your university then approach professors and researchers in your listed fields at other universities and ask them for ideas. Be prepared to ask 10 people and hear 9 Nos or answers you don't need to get to the 1 Yes that you need.
Jan
1
comment What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?
This is a great question. It would be interesting to see a graph with the age of discovery distribution of the math at different levels - grade school, high school, undergrad. My intuition is that it would mostly skew to older discoveries (Though I did study groups theory in O Level math in UK which is more recent). With undergrad being more recent (1850-1950 mostly). Has anyone seen such a graph?
Apr
15
comment Are there surfaces with more than two sides?
What is the proof that there is not a global 3rd side? I could use the categorization of compact surfaces to show all of them have 1 or 2 sides. But that does not include non-compact surfaces and it seems to me that a hidden assumption in the categorization proof is that the surfaces have 1 or 2 sides...
Apr
9
comment Are mathematical articles on Wikipedia reliable?
@KRyan: wikis and internet education resources in general are in competition with paid universities professors. As they become good enough there will be less demand for high priced schools and downward pressure on professor jobs. Don't expect someone to talk up their competition... see the book "The Nearly Free University and the Emerging Economy" for more on this topic oftwominds.com/CHS-books.html
Apr
9
comment Are mathematical articles on Wikipedia reliable?
The way a wiki gives links to terms used in the article so you can look those wiki articles up too makes learning about a new math subject much easier than a book. I still use books and the wiki is fast way to get started. Often when starting a new subject I don't know not just the main topic but the definitions and related terms and topics...
Apr
9
comment Are mathematical articles on Wikipedia reliable?
In my experience wikipedia math articles on all degree level topic are good. I have read hundreds of them and not seen an issue. I did a math degree and masters in math at Cambridge and still actively study math.
Mar
6
comment Proof that a certain subset of the reals is not a ring
Yes you are right. Thanks for clarifying. Now I get that 2 sin(1) is just 1 sin(1) + 1 sin(1) and Steven showed the set is not closed under addition.
Mar
6
comment Proof that a certain subset of the reals is not a ring
Aha I had missed that point. Thanks for explaining! So given we are using the 1 from R here in regular way it seems like we must be assuming the ring has identity.
Mar
5
comment Proof that a certain subset of the reals is not a ring
Now I am curious if you assume that there is not a 1 in the ring if you can still prove the statement :-)
Mar
5
comment Proof that a certain subset of the reals is not a ring
True that is unclear from the question if they mean ring with identity or not. The other answer also assumes there is a 1 in the ring when it say there is an n such that 2 sin 1 = n sin n. Because the 2 here is an element 2 in the ring to multiply 1 sin 1 by. Hence it assumes there is a 1 in the ring to make the element 2 from.
Mar
1
comment Tough contest problem
As sin(ix) = i sinh(x) (for real x) it is purely imaginary. So sin(sin(ix)) = i sinh(sinh(x)). Similarly for any more iterations of sin() and sin(sin(sin(sin(ix) = i sinh(sinh(sinh(sinh(x)))) is purely imaginary too. However cos(ix) = cosh(x) is purely real and taking cos() of this value three more times cos(cos(cos(cos(ix)))) is also purely real. Hence there is no solution to this equation on the imaginary axis. The imaginary solution(s) must lie somewhere else.
Feb
28
comment Tough contest problem
Alternative just looking at the imaginary axis putting ix for x and using cosh(x) = cos(ix) and i sinh(x) = sin(ix). I will play around with this a bit.
Feb
28
comment Tough contest problem
Cool use of Picard's Theorem! Makes sense to me. I was thinking of converting the sin() and cos() to expressions in exp()s but it gets pretty complex due to the nesting.
Feb
27
comment Tough contest problem
I know the question was for real x. I am curious if we allow complex x if there are solutions.
May
23
comment Fractional Derivative Implications/Meaning?
You are right it can have a geometric interpretation just as the single integral can be interpreted as the area under the curve. And it is not a local geometric property as the tangent is. I am having trouble reading the small print in your question and if you are asking can you have arbitrary real numbers in the power of the derivative operator then I believe the answer is yes. Actually I have read you can even put complex numbers in there!
Feb
27
comment Fractional Derivative Implications/Meaning?
I added to my answer to say why it is non-local
Feb
13
comment To what extent is the taylor polynomial the best polynomial approximation?
@5PM Thanks - that makes sense. I had misread the formula as f(k) with k = 0 to n. Works for f = p giving zero norm.
Feb
12
comment To what extent is the taylor polynomial the best polynomial approximation?
I may be misunderstanding something here but if I set f = p in your metric the first term is zero but the second term is not zero. But isn't the norm of 0 supposed to be zero?
Dec
5
comment Difference of differentiation under integral sign between Lebesgue and Riemann
In your right hand side is it supposed to be df/dx(x,t)dt evaluated at x = x0 and not df/dx(x0,t)?
Nov
20
comment What do we lose passing from the reals to the complex numbers?
Does losing ordering define the complex numbers? Ie is there only one field (strictly) containing the reals that can not be ordered but is complete?