Tagged Questions
5
votes
4answers
85 views
Intuitive Explanation of Morphism Theorem
Is there an intuitive explanation for the morphism theorem from introductory abstract algebra?
First Morphism Theorem: Let $K$ be the kernel of the group morphism $f: G \to H$. Then $G/K$ is ...
3
votes
1answer
39 views
Expected Value of Students on a Bus
There's a question in my probability book that says there are $148$ students on $4$ buses containing $40, 33, 25, 50$ students, respectively. If we let $X$ denote the number of students that were on ...
11
votes
3answers
121 views
Are matrices best understood as linear maps?
Any linear map between finite-dimensional vector spaces may be represented by a matrix, and conversely. Matrix-matrix multiplication corresponds to map composition, and matrix-vector multiplication ...
22
votes
3answers
472 views
Intuition on fundamental theorem of arithmetic
I'm sorry ahead if time if this is overly trivial for this site.
Currently in school, much of what I enjoy is number theory - based. Currently, I lean pretty heavily on the FTA for a good deal of my ...
4
votes
0answers
68 views
Is there any equivalence between the category of schemes over $\mathbb R$ and the category real manifolds
The equivalence of the category of smooth projective curves over $\mathbb C$ and the category of compact Riemann surfaces is, I believe, well documented. For example, it is mentioned on the wiki page: ...
2
votes
1answer
133 views
Explain Zermelo–Fraenkel set theory in layman terms
What does Zermelo–Fraenkel set theory mean?
According to Wikipedia, Zermelo–Fraenkel set theory is a set theory that is proposed to overcome issues in naive set theory. I really appreciate if ...
4
votes
2answers
199 views
start mathematics from scratch
I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(.
I love mathematics but time passed ...
3
votes
2answers
65 views
Intuition Of Conditional Probability Equation
I was wondering if any one of you had any intuitive insight regarding the conditional probability equation, $P(A\mid B) = \large \frac{P(A \cap B)}{P(B)}$. In my textbook, they give a mere definition, ...
1
vote
1answer
75 views
How to understand the duality between Dilworth's theorem and Mirsky's theorem?
Dilworth's theorem states that for any partial order, the size of the largest antichains is the size of the smallest chain partitions. Mirsky's theorem states that for any partial order, the size of ...
2
votes
1answer
93 views
Hydra game and quantum superposition
Goodstein's theorem is not provable in Peano Arithmetic showed by Kirby and Harrington in 1982 [Wolfram Mathworld].
Any reference of a "quantum" hydra game where a head can remain in a state of ...
4
votes
2answers
259 views
Geometric intuition behind gradient, divergence and curl
I learned vector analysis and multivariate calculus about two years ago and right now I need to brush it up once again. So while trying to wrap my head around different terms and concepts in vector ...
6
votes
1answer
200 views
Age of Stochasticity?
Today I came across D. Mumford's 1999 article The Dawning of the Age of Stochasticity, which is quite remarkable even after more than a decade. The title already indicates the theme, but I copy the ...
3
votes
0answers
60 views
A few questions about nonabelian cohomology of finite groups.
I apologize in advance if these questions are broad or basic. I tried to read about them at the Wikipedia, but everything is written in the language of category theory, in which I have had no formal ...
3
votes
2answers
193 views
Why are only the first four alternating groups are non-simple?
I know asking for intuition in math is a generally flawed approach, but can anyone give any reason why only the first four alternating groups are non-simple?
1
vote
2answers
123 views
What is a intuitive proof of multivariable changing of variables formula (jacobian) without using mapping and/or measure theory?
What is a intuitive proof of multivariable changing of variables formula (jacobian) without using mapping and/or measure theory?
I was thinking that textbooks make the proofs over complicate.
If ...
