For questions that don't admit a definitive answer. Please do not ask too many of these.
2
votes
4answers
193 views
How does linear algebra help with computer science
I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult ...
7
votes
2answers
102 views
What is the relationship between completeness and local compactness?
On the one hand, $\mathbb{Q}$ is neither complete (as a metric space) nor locally compact (as a topological space). On the other hand, $\mathbb{R}$ is both complete and locally compact.
My question ...
8
votes
4answers
270 views
A Math book with an inspiring ethos?
I was for some time curious about William Feller's probability tract (first volume); luckily, I could lay my hands on it recently and I find it of super qualities. Its provides a complete exposition ...
4
votes
2answers
122 views
Wolves and chicks puzzle
This problem is from the handheld video game, Professor Layton and the Curious Village.
I think the solution is very cool, but more than that, I want to know how to show that the minimum number of ...
7
votes
1answer
186 views
How to start a math blog?
I'd like to start a blog where i can write mathematics related notes. The intended audience is mainly myself, but i don't mind it being available for public viewing. I'd like to keep setting up, ...
1
vote
1answer
86 views
Drawing lattices
I would like to be able to draw the lattices of subgroups of certain groups. I thought it would be easy when I already know the structure, but I've never done it before, and it turns out it's harder ...
4
votes
1answer
62 views
Geometric explanations of approximations of $\pi$
Does any fast modern algorithm for approximating $\pi$ have a geometric interpretation as $\int \sqrt{1 - x^2}$ does?
3
votes
1answer
121 views
What would be surprising facts in various areas of mathematics?
This might be too broad question - but what would be the things that you consider as surpising facts and discoveries in various areas of mathematics?
If this seems too broad, it is fine to stick ...
30
votes
6answers
912 views
Why do we negate the imaginary part when conjugating?
For $z=x+iy \in \mathbb C$ we all know the definition for the "conjugate" of $z$, $\bar{z}=x-iy$. Geometrically this is the reflection of $z$ across the $y$ axis.
My question is: couldn't we have ...
0
votes
4answers
105 views
How to verify method used to solve integral was actually the fastest?
Is there any way to verify if the method I chose to integrate (by hand) was indeed fastest, or if there exists some better technique? Can a computer tell me or show me what the fastest method was, ...
1
vote
1answer
164 views
What's the best way to measure mathematical ability?
Very soft question I admit, but it's something that's been bothering me for a while.
I've been thinking that being self taught has the problem of accreditation. You can't evaluate a mathematician ...
6
votes
1answer
216 views
Is there a rigorous theory of context, whereby sets can gain additional structure within a context?
Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
11
votes
2answers
110 views
H0w have group theory and fractal geometry been combined?
Has there been a significant tie made between group theory and fractal geometry? What are some ways that they have been tied together?
I've been inspired to ask this question by this image of a free ...
2
votes
1answer
139 views
Why is a full circle 360° degrees? [duplicate]
What's the reason we agreed to setting the number of degrees of a full circle to 360? Does that make any more sense than 100, 1000 or any other number? Is there any logic involved in that particular ...
1
vote
0answers
58 views
Properties of Non-Diagonally Dominant Matrix
I have a question about properties of matrices which are or are not diagonally dominant.
So I understand that a diagonally dominant Hermitian matrix with non negative diagonal entries is positive ...
0
votes
0answers
27 views
Likely related elements
I have lists of pair like so :
KHLM1800, (a,b,c)
KHLM1900, (a,b,d)
KHLM1840, (a,b,c,d)
KHLM1845, (a,b,c)
TCMB9001, (a,c)
.
.
.
Naively it looks like KHLM ...
3
votes
0answers
70 views
$M_n=2^n-1$ Mersenne numbers in mathematics
Did the Mersenne numbers turn out to be interesting in other fields of mathematics besides the Numbers Theory?
In other words, the function $M(n)=M_n$
where
$$M_n=2^n-1$$
or the recursive realtion
...
37
votes
13answers
3k views
Is there such a thing as proof by example (not counter example)
Is there such a logical thing as proof by example?
I know many times when I am working with algebraic manipulations, I do quick tests to see if I remembered the formula right.
This works and is ...
7
votes
2answers
232 views
Connection between algebraic geometry and high school geometry.
if there is one thing that going to math competitions has taught me it is that I suck at high school olympiad level geometry. However I often find solace in the fact that not a lot of mathematicians ...
1
vote
0answers
45 views
Who could find an elementary proof of prime number theorem? [closed]
What kind of abilities should one have to find an elementary proof of prime number theorem?
If Erdos and Selberg were not mathematicians - it's definitely a big loss for us, but let's suppose so - ...
4
votes
1answer
44 views
Literature request - Classification of periodic holomorphic functions
For a seminar, I received the assignment to present the classification of periodic holomorphic/meromorphic functions. I have access to a limited amout of resources that I receive from my lecturer - ...
3
votes
0answers
52 views
Why is the Euclidean metric called the prime at infinity?
I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the ...
0
votes
4answers
159 views
will computers replace (most) mathematicians? [closed]
We already have computers doing proofs and assisting mathematicians with generating proofs. I would expect that their presence will only grow larger with time as the algorithms become more practical.
...
1
vote
3answers
194 views
What are the best websites for learning math? [closed]
What I known:
this site
mathoverflow
khanacademy
Are there any other website for learning math? Which one do you think is the best?
5
votes
4answers
91 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 ...
4
votes
1answer
79 views
The complement of a torus is a torus.
Take $S^3$ to be the three-sphere, that is, $S^3=\lbrace (x_1,x_2,x_3,x_4):x_1^2+x_2^2+x_3^2+x_4^4=1\rbrace$. Using the stereographic projection, $S^3=\mathbb{R}^3\cup \lbrace \infty \rbrace.$ Can ...
4
votes
3answers
75 views
Interesting theorems/facts about identification spaces
I am now studying algebraic topology (still at the beginning). I am now studying identification spaces, adjunction spaces,... As I still don't know how these concepts are going to be used, I think I ...
5
votes
8answers
194 views
Final year project ideas - complex analysis
For my final year, I have to do a project for a module. I want to investigate something in the complex analysis area. I've only covered the basics of analysis, like Cauchy's IT/IF, residue theorem ...
3
votes
1answer
40 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 ...
2
votes
2answers
63 views
Pre-test preparation
I'm currently an undergrad in maths and I wanted to know how those who have completed their degrees handled their test preparation. That is, how did you study and how did you manage the anxiety if ...
12
votes
3answers
542 views
Pure Mathematics Vs Applied Mathematics Job Prospects
I need and request some advice on selecting the area for my research.
In particular, I want to know the about job prospects of Applied Mathematics Versus Pure Mathematics in Academia. I understand ...
2
votes
1answer
95 views
Providing a sketch for a proof before proceeding through the actual proof. [closed]
Question is pretty straightforward. My mathematics is sloppy, and I recognize my inaptitude in that my proofs are more or less too intuitive. My diagnosis dictates
the fact that I attack a problem ...
-2
votes
1answer
91 views
Proving By Subsets [closed]
I am currently trying to learn about conducting proofs by using subsets. In my textbook, there is an example on this very matter; however, the seem to do something that is in contradiction with what ...
1
vote
1answer
91 views
Does π depends on the norm? [duplicate]
If we take the definition of π in the form:
π is the ratio of a circle's circumference to its diameter.
There implicitly assumed that the norm is Euclidian:
\begin{equation}
...
5
votes
0answers
63 views
How to understand convex duality intuitively
Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric ...
3
votes
1answer
182 views
Is there an intuitive non-mathematical way to show $\sum_n 1/n=\infty$?
I want to show some school students about the sum of the harmonic series diverging and I need some nice interpretation for this. I'll preferably love to have a figure.
Thanks in advance!
0
votes
0answers
53 views
Does a good mathematics researcher need to be good at illustrative problem solving?
I have this nagging question for long: a good researcher identifies interesting problems and works out new and solid ways to solve them. But is it necessary that he be good in solving illustrative ...
7
votes
3answers
133 views
Math under time constraints
I'm currently an undergrad math student and I have been wondering if being able to perform well under time constraints requires a deeper knowledge of the material than performing under no time ...
12
votes
4answers
299 views
Alternative set theories
This is a (soft!) question for students of set theory and their teachers.
OK: ZFC is the canonical set theory we all know and love. But what other, alternative set theories, should a serious student ...
1
vote
3answers
76 views
teaching concept of “subspace” to linear algebra students
I'm currently a T.A. for an introductory combined linear algebra & differential equations course geared toward engineering students. One major problem I've run across is that most of my students, ...
7
votes
1answer
90 views
Independence results that cannot be established by forcing.
I read the Wikipedia article on Absoluteness recently and found mention of Shoenfield’s Absoluteness Theorem, which states that if $ \phi $ is any $ \Sigma^{1}_{2} $- or $ \Pi^{1}_{2} $-sentence of ...
0
votes
0answers
19 views
What is the real-world intuition of a data set that exhibits a gamma distribution with shape>1?
From the special case of the exponential distribution (shape=1), we know that the interpretation of scale has to do with the rate of the success, but how can I interpret the shape? Does it mean that ...
1
vote
0answers
37 views
What kind of math knowledge do I need to understand this paper?
I would like to know what I should know to understand this IMF paper. What kind of optimization is used to maximize the utility function on page 9 (number 1) subject to constraints (2) and (3)? Thank ...
2
votes
1answer
56 views
When asked to find all solutions to a differential equation, what's left implicit?
Suppose the following problem were to appear in an introductory textbook on differential equations.
Find all solutions to $y'=y$.
What's left implicit in such a statement? My interpretation of ...
6
votes
2answers
119 views
Currently, what is the largest publicly known prime number such that all prime numbers less than it are known?
So recently, an absurdly large prime number was found, but a lot of prime numbers less than it are still not known. I am wondering up to where we know all the primes.
I put "currently publicly known" ...
6
votes
1answer
163 views
How long does it take to write a math paper? [closed]
I am currently working on an applied mathematics paper (with my supervisor, I am a student) that is long overdue: supposed to take 4-5 months but I have been working on it for 6.5 months.
I was ...
5
votes
0answers
72 views
Proof vs Practice
I've been brushing up on a lot of basic arithmetic, algebra, and logic as I work towards a review of calculus (and beyond), and I keep noticing that in order to fully understand many principles in the ...
1
vote
1answer
67 views
Definition of spinor
In most physics books, spinors are sometimes defined in an adhoc way. From my understanding, a spinor transforms under the spin group. But I'd like to know the precise detail of the definition. Can ...
0
votes
1answer
60 views
Geology with maths
Can anyone suggest me topics that connect maths with geology or geography or anything related to earth? Thank you. ...
1
vote
0answers
89 views
A puzzle of vertices
In a book of geometry of the school there is the next puzzle:
place the next nine triangles to form only one such that the vertices that join have the same symbol.
I solved it through an naïve ...
