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1500 questions
79
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0 answers
Does the $32$-inator exist?
Background
It is common popular-math knowledge that as we extend the real numbers to complex numbers, quaternions, octonions, sedenions, $32$-nions, etc. using the Cayley-Dickson construction, we lose algebraic properties at each step such as…
pregunton
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79
votes
3 answers
String Theory: What to do?
This is going to be a relatively broad/open-ended question, so I apologize before hand if it is the wrong place to ask this.
Anyways, I'm currently a 3rd year undergraduate starting to more seriously research possible grad schools. I find myself in…
Jonathan Gleason
- 7,861
79
votes
4 answers
A simple explanation of eigenvectors and eigenvalues with 'big picture' ideas of why on earth they matter
A number of areas I'm studying in my degree (not a maths degree) involve eigenvalues and eigvenvectors, which have never been properly explained to me. I find it very difficult to understand the explanations given in textbooks and lectures. Does…
robintw
- 943
79
votes
9 answers
What is the math behind the game Spot It?
I just purchased the game Spot It. As per this site, the structure of the game is as follows:
Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 different symbols through the deck. The most…
Javid Jamae
- 894
79
votes
10 answers
Examples of finite nonabelian groups.
Can anybody provide some examples of finite nonabelian groups which are not symmetric groups or dihedral groups?
kalpeshmpopat
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79
votes
7 answers
What exactly are eigen-things?
Wikipedia defines an eigenvector like this:
An eigenvector of a square matrix is a non-zero vector that, when multiplied by the matrix, yields a vector that differs from the original vector at most by a multiplicative scalar.
So basically in layman…
Eigeneverything
- 793
79
votes
8 answers
Difference between Fourier transform and Wavelets
While understanding difference between wavelets and Fourier transform I came across this point in Wikipedia.
The main difference is that wavelets are localized in both time and frequency whereas the standard Fourier transform is only localized in…
chatur
- 1,132
79
votes
3 answers
Two curious "identities" on $x^x$, $e$, and $\pi$
A numerical calculation on Mathematica shows that
$$I_1=\int_0^1 x^x(1-x)^{1-x}\sin\pi x\,\mathrm dx\approx0.355822$$
and
$$I_2=\int_0^1 x^{-x}(1-x)^{x-1}\sin\pi x\,\mathrm dx\approx1.15573$$
A furthur investigation on OEIS (A019632 and A061382)…
zy_
- 2,961
79
votes
18 answers
Conjectures (or intuitions) that turned out wrong in an interesting or useful way
The question
What seemingly innocuous results in mathematics require advanced proofs? prompts me to ask about conjectures or, less formally, beliefs or intuitions, that turned out wrong in interesting or useful ways.
I have several in mind, but…
Ethan Bolker
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79
votes
8 answers
Why do books titled "Abstract Algebra" mostly deal with groups/rings/fields?
As a computer science graduate who had only a basic course in abstract algebra, I want to study some abstract algebra in my free time. I've been looking through some books on the topic, and most seem to 'only' cover groups, rings and fields. Why is…
GeorgW
- 799
79
votes
5 answers
Use of "without loss of generality"
Why do we use "without loss of generality" when writing proofs?
Is it necessary or convention? What "synonym" can be used?
Pedro
- 122,002
79
votes
2 answers
Distinguishing probability measure, function and distribution
I have a bit trouble distinguishing the following concepts:
probability measure
probability function (with special cases probability mass function and probability density function)
probability distribution
Are some of these interchangeable? Which…
Marc
- 3,285
79
votes
10 answers
Is there a shape with infinite area but finite perimeter?
Is this really possible? Is there any other example of this other than the Koch Snowflake? If so can you prove that example to be true?
Chris Truong
- 791
78
votes
10 answers
Best Algebraic Geometry text book? (other than Hartshorne)
Lifted from Mathoverflow:
I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best.
Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc.
One suggestion per answer please.…
user218
78
votes
2 answers
What are the formal names of operands and results for basic operations?
I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far:
Addition: Augend + Addend = Sum.
Subtraction: Minuend - Subtrahend = Difference.
Multiplication: Multiplicand × Multiplier = Product. Generally,…
trw
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