Most Popular
1500 questions
63
votes
11 answers
Undergraduate algebraic geometry textbook recommendations
What are the best algebraic geometry textbooks for undergraduate students?
tobias
63
votes
3 answers
What is difference between a ring and a field?
The ring axioms require that addition is commutative, addition and multiplication are associative, multiplication distributes over addition.
A field can be thought of as two groups with extra distributivity law.
A ring is more complex: with…
zinking
- 1,089
63
votes
5 answers
Sum of two closed sets in $\mathbb R$ is closed?
Is there a counterexample for the claim in the question subject, that a sum of two closed sets in $\mathbb R$ is closed? If not, how can we prove it?
(By sum of sets $X+Y$ I mean the set of all sums $x+y$ where $x$ is in $X$ and $y$ is in…
ro44
- 633
63
votes
3 answers
Is "A New Kind of Science" a new kind of science?
A couple of years ago I was reading "New Kind of Science" (NKS) by S. Wolfram, and it presented lot of interesting ideas for a young Physics undergraduate. Now that I am studying Mathematics however, I realise that many ideas of NKS seem to be not…
Andrea
- 2,433
63
votes
5 answers
Good books for a high schooler self-studying Abstract Algebra?
Does anyone have any suggestions for abstract algebra books particularly suited to self-study?
Here is some background and motivation, if it's helpful.
I'm currently a junior in high school, but I have some familiarity with groups, rings,…
yunone
- 22,333
63
votes
8 answers
How can a set contain itself?
In Russell's famous paradox ("Does the set of all sets which do not contain themselves contain itself?") he obviously makes the assumption that a set can contain itself. I do not understand how this should be possible and therefore my answer to…
jimmyorpheus
- 765
62
votes
1 answer
Why is the absolute value function not differentiable at $x=0$?
They say that the right and left limits do not approach the same value hence it does not satisfy the definition of derivative. But what does it mean verbally in terms of rate of change?
user187397
- 621
62
votes
2 answers
What do eigenvalues have to do with pictures?
I am trying to write a program that will perform OCR on a mobile phone, and I recently encountered this article :
Can someone explain this to me ?
Patryk
- 741
62
votes
10 answers
What is the arithmetic mean of no numbers?
I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the arithmetic mean and how many numbers were given. However, when you don't give them any numbers, one says the arithmetic mean is…
Ky -
- 1,300
62
votes
6 answers
What should an amateur do with a proof of an open problem?
Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for verification or send to some authorities? Is there…
Ztalloc
- 627
62
votes
5 answers
Are functions of independent variables also independent?
It's a really simple question. However I didn't see it in books and I tried to find the answer on the web but failed.
If I have two independent random variables, $X_1$ and $X_2$, then I define two other random variables $Y_1$ and $Y_2$, where $Y_1$…
LLS
- 787
62
votes
6 answers
Why do differential forms have a much richer structure than vector fields?
I apologize in advance because this question might be a bit philosophical, but I do think it is probably a genuine question with non-vacuous content.
We know as a fact that differential forms have a much richer structure than vector fields, to name…
Jia Yiyang
- 1,053
62
votes
8 answers
Probability that random moves in the game 2048 will win
I have recently played the game 2048, created by Gabriele Cirulli, which is fun. I suggest trying if you have not. But my brother posed this question to me about the game:
If he were to write a script that made random moves in the game 2048, what…
N. Owad
- 6,822
62
votes
4 answers
Why is the Laplacian important in Riemannian geometry?
As I've learned more Riemannian geometry, many of my teachers have said that studying the Laplacian (and its eigenvalues) is very important. But I must admit, I've never fully understood why.
Fundamentally, I would like to know why the Laplacian…
Jesse Madnick
- 31,524
62
votes
20 answers
Coin flipping probability game ; 7 flips vs 8 flips
Your friend flips a coin 7 times and you flip a coin 8 times; the person who got the most tails wins. If you get an equal amount, your friend wins.
There is a 50% chance of you winning the game and a 50% chance of your friend winning.
How can I…
Jason
- 3,563