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1500 questions
66
votes
1 answer
Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?
This question is inspired
by my answer to the question
"How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$?".
The sums
$f(k) = \sum_{n=1}^{\infty} \frac{1}{(n!)^k}$
(for positive integer $k$)
came up,
and I noticed that
$f(1) = e-1$ was…
marty cohen
- 107,799
66
votes
3 answers
What is the geometry in algebraic geometry?
Coming from a physics background, my understanding of geometry (in a very generic sense) is that it involves taking a space and adding some extra structure to it. The extra structure takes some local data about the space as its input and outputs…
d_b
- 955
66
votes
2 answers
What does "communicated by" mean in math papers?
[This question involves mostly math papers, and may be relevant to graduate students learning to write and cite papers, although this is my only justification for this being a math question.]
Usually papers start out with the title and then the…
user2055
66
votes
6 answers
How do you show monotonicity of the $\ell^p$ norms?
I can't seem to work out the inequality $(\sum |x_n|^q)^{1/q} \leq (\sum |x_n|^p)^{1/p}$ for $p \leq q$ (which I'm assuming is the way to go about it).
user1736
- 8,573
66
votes
2 answers
Why doesn't Cantor's diagonal argument also apply to natural numbers?
In my understanding of Cantor's diagonal argument, we start by representing each of a set of real numbers as an infinite bit string.
My question is: why can't we begin by representing each natural number as an infinite bit string? So that 0 =…
usul
- 3,724
66
votes
1 answer
Abstract nonsense proof of snake lemma
During my studies, I always wanted to see a "purely category-theoretical" proof of the Snake Lemma, i.e. a proof that constructs all morphisms (including the snake) and proves exactness via universal properties. It was an interest little shared by…
Jesko Hüttenhain
- 14,792
66
votes
10 answers
List of problem books in undergraduate and graduate mathematics
I would like to know some good problem books in various branches of undergraduate and graduate mathematics like group theory, galois theory, commutative algebra, real analysis, complex analysis, topology etc. The books should contain solution to…
Mohan
- 14,856
66
votes
8 answers
How much Math do you REALLY do in your job?
I am writing this, as I am a currently an intern at an aircraft manufactur. I am studying a mixture of engineering and applied math. During the semester I focussed on numerical courses and my applied field is CFD. Even though every mathematician…
Thomas
- 4,363
66
votes
5 answers
Is there any branch of Mathematics which has no applications in any other field or in real world?
Is there any branch of Mathematics which has no applications in any other field or in real world ?
for instance , maybe : number theory ? mathematical logic ?
is there something like this ?
FNH
- 9,130
66
votes
4 answers
Calculate on which side of a straight line is a given point located?
I am a programmer without really good knowledge in math. :/ So I have to write an algorithm that changes the color of pixel(dot) P to opposite if it's on left side of the straigt line in coordinate system (and the line is not vertical, with that I…
Ritvars
- 763
66
votes
5 answers
Help understanding Algebraic Geometry
I while ago I started reading Hartshorne's Algebraic Geometry and it almost immediately felt like I hit a brick wall. I have some experience with category theory and abstract algebra but not with algebraic or projective geometry.
I'm wondering if…
user25470
- 1,033
- 2
- 9
- 15
66
votes
2 answers
Differences between the Borel measure and Lebesgue measure
I'm having difficult time in understanding the difference between the Borel measure and Lebesgue measure. Which are the exact differences? Can anyone explain this using an example?
Mark Hyatt
- 745
66
votes
3 answers
Necessity/Advantage of LU Decomposition over Gaussian Elimination
I am reading the book "Introduction to Linear Algebra" by Gilbert Strang and couldn't help wondering the advantages of LU decomposition over Gaussian Elimination!
For a system of linear equations in the form $Ax = b$, one of the methods to solve the…
66
votes
9 answers
Prove every odd integer is the difference of two squares
I know that I should use the definition of an odd integer ($2k+1$), but that's about it.
Thanks in advance!
papercuts
- 1,873
66
votes
3 answers
Recognizable vs Decidable
What is difference between "recognizable" and "decidable" in context of Turing machines?
metdos
- 957