For questions that don't admit a definitive answer. Please do not ask too many of these.
27
votes
6answers
1k views
A Question about Doctoral Theses in Mathematics [closed]
This is most definitely a soft question, which I'm sure may get some negative attention, and perhaps even be voted closed. However, I genuinely would like to generate answers on this matter as it ...
3
votes
2answers
53 views
What is the relationship between “recursive” or “recursively enumerable” sets and the concept of recursion?
I understand that "recursive" sets are those that can be completely decided by an algorithm, while "recursively enumerable" sets can be listed by an algorithm (but not necessarily decided). I am ...
0
votes
0answers
11 views
Teach in an university with a master degree [migrated]
I don't know if here is the best place to ask that but I'm finishing my master degree in pure mathematics and I would like to travel and know another countries before enter into a doctorate school. In ...
0
votes
0answers
33 views
Is is possible to study mathematics PHD with another bachelor degree like Business Aministration? [migrated]
Is is possible to study mathematics PHD with another bachelor degree like Business Aministration? Have you heard of sth similar and how they do it?
Personally I am a BBA student. I found that i love ...
3
votes
2answers
103 views
Why demonstrations are important in mathematics?
Good evening, I'm studying math and would like to know how important are mathematical proofs in the world and particularly in a school of mathematics
Thanks for your help
1
vote
3answers
42 views
A simple probability reasing to predict rain fall
A friend told me the following about whether it will rain tomorrow (or not):
The probability that it will rain tomorrow is $1/2$ since it will either happen or not. But -even as a non mathematician- ...
26
votes
11answers
2k views
What is $-i$ exactly?
We all know that $i$ doesn't have any sign: it is neither positive nor negative. Then how can people use $-i$ for anything?
Also, we define $i$ a number such that $i^2 = -1$. But it can also be seen ...
0
votes
1answer
95 views
Which topics of real-analysis should be studied if you have already done calculus
Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
14
votes
1answer
212 views
Why learning modern algebraic geometry is so complicated?
Many students - myself included - have a lot of problems in learning scheme theory. I don't think that the obstacle is the extreme abstraction of the subject, on the contrary, this is really the ...
16
votes
6answers
249 views
Why is boundary information so significant? — Stokes's theorem
Why is it that there are so many instances in analysis, both real and complex, in which the values of a function on the interior of some domain are completely determined by the values which it takes ...
2
votes
1answer
50 views
About the type of numbers allowed by axioms and Nature
I have a question which has 4 different subcases or "avatars":
1) Has every "interesting" class of number been invented?
2) Has every "possible" class of number been invented?
3) Does Nature use ...
4
votes
6answers
162 views
Which topics of mathematics should I study?
I'm a first year econometrics student with a great interest in mathematics. I very much enjoy my study, but still I am interested to learn about more topics in mathematics which are not part of my ...
0
votes
0answers
23 views
Applications of Scoring Play Combinatorial Game Theory
I'm currently looking into economic applications of scoring play combinatorial game theory. Details of the theory can be found in this paper.
http://arxiv.org/abs/1202.4653
A friend of mine ...
0
votes
0answers
21 views
Preparing for Curveball Questions/Traps
Previous math education was exclusively of the form of memorize this here equation and then put the numbers in and solve according to the procedure you memorized. Now I'm trying a course where I'm ...
6
votes
0answers
71 views
Working with subsets, as opposed to elements.
Especially in algebraic contexts, we can often work with subsets, as opposed to elements. For instance, in a ring we can define
$$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$
...
4
votes
0answers
61 views
Soft question: why are there non-smooth manifolds?
Topologists are often very good at explaining the geometric intuition behind certain results and programs of research. For instance, the particular interest in 4 manifolds is often explained by ...
3
votes
2answers
97 views
Getting better at math? [duplicate]
I really want to get better at math, but I'm not sure how. I have a book with competition problems from which I could learn, but I really don't enjoy sitting there for half an hour trying to find some ...
2
votes
0answers
29 views
Intuition behind criterion for an irreducible Markov chain to be transient
I have been looking over my notes for Markov chains, and I have come across the following:
Theorem: An irreducible Markov chain is transient iff for some state $i$ there exists a nonzero vector $y$ ...
-5
votes
0answers
101 views
How would you improve on what Scott Young did (MIT Challenge guy)? [closed]
I've been reading a lot about this Scott Young guy, and I've watched some of his videos. Today I found a LOT of criticism of his MIT Challenge online, some of it from MIT students. You can imagine ...
5
votes
3answers
104 views
Importance of Neatness / Organization / Speed in Math?
Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes.
How important is neatness in math?
Does having messy writing put ...
4
votes
3answers
122 views
Rationale behind truth values
I originaly asked a question on Programmers.SE to know why $0$ was consider $\text{false}$ and all the other [integral] values were considered $\text{true}$. That was a huge debate and many said it ...
4
votes
0answers
58 views
Good examples of proofs in mathematics exemplary of creative reasoning [closed]
Just what the title says. I'm not looking for any proofs that require specialized knowledge past the very fundamentals of real analysis. I'm looking for proofs for important results (don't have to be ...
3
votes
2answers
69 views
How to start learning knot theory?
Knot theory really sounds cool and I'm very interested in it. But I'm wondering what basic knowledge it is required and how I should start learning about it. Thanks
18
votes
2answers
163 views
+500
Conjectural closed-form representations of sums, products or integrals
What are some examples of infinite sums, products or definite integrals that have conjectural closed form representations that were confirmed by numerical calculations up to whatever maximum precision ...
0
votes
0answers
73 views
How should we study maths? [duplicate]
what is the best way to study maths ?
also , should we memorize the proofs of the theorems ? or just read them and understand them but not memorize ?
also , should we follow one text or more than ...
4
votes
1answer
54 views
Applications of information geometry to the natural sciences
I am contemplating undergraduate thesis topics, and am searching for a topic that combines my favorite areas of analysis, differential geometry, graph theory, and probability, and that also has ...
2
votes
1answer
66 views
Differential Geometry Video Lectures
I know there's a similar question here, however since what I found there wasn't what I was looking for I thought on creating a new question. I'm studying Differential Geometry through Spivak's book "A ...
1
vote
1answer
27 views
Special numbers in patterns and the reasons they are special
I know there are several big list questions out there (e.g. Patterns that break down at certain numbers) that touch on classifications of mathematical structures where certain numbers don't fit in, ...
3
votes
1answer
52 views
Intended Audience for N Is a Number?
Is the film N is a Number appropriate (mathematically) for a student entering high school?
9
votes
1answer
110 views
List videos of interesting courses at the doctoral level.
Many mathematics departments has provided video lessons their courses (usually one semester) that are offered in their doctoral programs in mathematics. Most often these courses total average of 26 ...
9
votes
4answers
197 views
Should $\mathbb{N}$ contain $0$? [closed]
This is a classical question, that has led to many a heated argument:
Should the symbol $\mathbb{N}$ stand for $0,1,2,3,\dots$ or $1,2,3,\dots$?
It is immediately obvious that the question is ...
0
votes
1answer
60 views
“The whole is greater than the sum of its parts” as a mathematical expression [closed]
I'm trying to come up with a coherent way to express the saying "The whole is greater than the sum of its parts" using mathematical constructs. The second half of the statement (greater than the sum ...
2
votes
3answers
57 views
PDEs in biology
I am student who mostly heard lectures on partial differential equations and homogenization. But I really like the idea of working in biology or with biologists - but (with my lack of overview) it ...
4
votes
3answers
81 views
Statistics Workshop for High School Students
We are going to hold an introductory workshop about the statistics. The participants will be students who have just finished their 8th or 9th grade. The workshop consists of 10 two-hour sessions. The ...
2
votes
0answers
31 views
Request for translation from Russian: 'Bayesian Sufficiency' from a paper by Kolmogorov
The following seminal paper by the great Kolmogorov introduced the important statistical concept of Bayesian Sufficiency.
Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi ...
12
votes
5answers
675 views
Do we really need polynomials (In contrast to polynomial functions)?
In the following I'm going to call
a polynomial expression an element of a suitable algebraic structure (for example a ring, since it has an addition and a multiplication)
that has the form ...
20
votes
4answers
502 views
Why do we study prime ideals?
I hope this isn't an inappropriate question here!
I'd like to ask the following (perhaps slightly ill-posed) question: why do we study prime ideals in general (commutative or non-commutative) rings? ...
2
votes
0answers
77 views
Imagining four or higher dimensions and the difference to imagining three dimensions
I’m very interested in how people envision four or higher dimensions.
And I’m especially interested in how geometers and topologists who actually work in four dimensions do.
Now I know of the video ...
2
votes
2answers
30 views
Repeating u-substitution
A question about the integration technique of u-substitution:
Is it allowed to apply u-substitution over and over again, to reduce the integral to a more manageable form?
0
votes
0answers
45 views
Improving my Mathematics [duplicate]
This isn't a regular maths question.
So I'm currently in my first year at Uni doing a Mathematics major. I would like to know what things I can do to help me improve in Mathematics? I would say I am ...
10
votes
2answers
198 views
+50
Math blogs, pros and cons for writers?
I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics.
But now I am more interested in the writers' perspective, and I ...
0
votes
2answers
89 views
Why do we name equations more in applied math?
In pure math, equations aren't often named. For instance, we might define that $f$ is a (real) polynomial function iff there exists a finite sequence of real numbers $a_i$ such that $$f(x)=a_0 + a_1 x ...
0
votes
0answers
36 views
Intuition on matrix multiplication and algorithms
Yesterday, I was watching Strang's lectures on Matrix multiplication. He mentioned five different ways of looking at the multiplication A x B = C.
Classic way (row of A x column of B).
Column (of B) ...
9
votes
6answers
230 views
Should every group be a monoid, or should no group be a monoid?
Question: What is more convenient/useful? Writing mathematics as if every group is a monoid, or as if these two classes are disjoint?
Additional discussion. Define a monoid as follows.
Defn 1. A ...
4
votes
1answer
60 views
Can we use proper classes in this way, to define a new infinity larger than |Ord|?
I believe there is a way to do this that makes sense, and I explain it below. I would like to know if I did some obvious mistake, or if the idea doesn't make sense for some reason I didn't figure it ...
7
votes
4answers
154 views
Connection between number theory and abstract algebra
I haven't taken abstract algebra yet but I was curious on what connections do number theory and abstract algebra share? Do the proofs of things like Fermat`s little theorem, the law of quadratic ...
32
votes
1answer
415 views
Unexpected approximations which have led to important mathematical discoveries
One often finds at MSE approximate numerology questions like
Prove $\log_{\frac{1}{4}} \frac{8}{7}> \log_{\frac{1}{5}} \frac{5}{4}$,
Prove $(\dfrac{2}{5})^{\frac{2}{5}}<\ln{2}$,
Comparing ...
9
votes
1answer
75 views
Examples of Diophantine equations with a large finite number of solutions
I wonder, if there are examples of Diophantine equations (or systems of such equations) with integer coefficients fitting on a few lines that have been proven to have a finite, but really huge number ...
30
votes
3answers
654 views
What are examples of unexpected algebraic numbers of high degree occured in some math problems?
Recently I asked a question about a possible transcendence of the number ...
20
votes
4answers
376 views
Is $\mathbb{N}$ impossible to pin down?
I don't know if this is appropriate for math.stackexchange, or whether philosophy.stackexchange would have been a better bet, but I'll post it here because the content is somewhat technical.
In ZFC, ...
