For questions that don't admit a definitive answer. Please do not ask too many of these.
27
votes
3answers
360 views
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 ...
48
votes
10answers
8k views
Results that came out of nowhere.
Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups. ...
5
votes
17answers
2k views
Can we get just $3$ from $\pi$? [closed]
Today, a friend and I solved a question and one point came up where we were discussing whether we should write $(-1)^{n-1}$ or $(-1)^{n+1}$ and quickly we remembered that it was the same thing (for ...
3
votes
1answer
62 views
Why is Cauchy's integral formula always written with the function as the subject?
Why is Cauchy's integral formula always written as $$f(w)=\frac1{2\pi i}\int_L\frac{f(z)}{z-w}dz$$ instead of as $$\int_L\frac{f(z)}{z-w}dz=2\pi i f(w)$$? Isn't the latter form how it's typically ...
0
votes
2answers
98 views
Application of maths in economics
What are the branches of maths where we can see undoubtful connections with economics? Where can we use mathematical methods or models and apply them to analyze economic concepts?
4
votes
2answers
144 views
Going back to the basics?
I'm currently in my second year of college majoring in comp sci and I haven't really taken any math courses yet except pre-calc. In high school, I thought of myself as a pretty good math student and ...
30
votes
7answers
2k views
How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?
I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by ...
1
vote
1answer
62 views
Name for three-valued sign $+, -, 0$
Is there an accepted term (an adjective or prefix) like strict, trichotomous, strong or definite sign to indicate the three-valued sign whose values are $+$, $-$, and $0$?
Are there words reserved ...
0
votes
1answer
125 views
Need algorithm to take “max” of scores, but with “quality” weighting
I have an application where I get a small number of scores from medical tests (the same test repeated a few times) and I need to combine them. Normally the highest score would "win" in this ...
3
votes
7answers
138 views
Guides/tutorials to learn abstract algebra?
I recently read up a bit on symmetry groups and was interested by how they apply to even the Rubik's cube. I'm also intrigued by how group theory helps prove that "polynomials of degree $\gt4$ are not ...
2
votes
0answers
101 views
Hamlet to be or not to be in Primes?
It is conjectured that, if you read $\pi$ long enough you'll find Hamlet. Since other numbers, like the Copeland-Erdös constant are known to be normal in base 10, it should be true at least there. I ...
1
vote
0answers
34 views
What are some definite integration techniques?
Are there any definite integration techniques which I could learn (calc AB student)? I mean techniques which don't require you to find the anti derivative. Thanks!
29
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 ...
28
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 ...
11
votes
2answers
246 views
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 ...
3
votes
2answers
59 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 ...
106
votes
20answers
7k views
Is mathematics one big tautology?
Is mathematics one big tautology? Let me put the question in clearer terms:
Mathematics is a deductive system: it works by starting with arbitrary axioms, and deriving therefrom "new" properties ...
13
votes
5answers
340 views
What does it mean for a set to exist?
Is there a precise meaning of the word 'exist', what does it mean for a set to exist?
And what does it mean for a set to 'not exist' ?
And what is a set, what is the precise definition of a set?
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 ...
3
votes
2answers
106 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
20
votes
1answer
2k views
Grad school with low undergrad GPA
I'm hoping to apply to grad schools this fall. I think I'm a reasonably good candidate, one aspect aside -- I have around a 2.5 undergraduate GPA in-major and failed several math classes in college.
...
33
votes
1answer
428 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 ...
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 ...
53
votes
9answers
2k views
How do I sell out with abstract algebra?
My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
1
vote
3answers
43 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- ...
2
votes
1answer
71 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 ...
0
votes
1answer
98 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 ...
2
votes
1answer
51 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 ...
14
votes
1answer
220 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 ...
3
votes
2answers
161 views
Good reference texts for introduction to partial differential equation?
As the title, are there any good reference texts for introduction to partial differential equation?
0
votes
0answers
24 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 ...
16
votes
6answers
252 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 ...
4
votes
6answers
182 views
Which topics of mathematics should I study? [closed]
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
1answer
29 views
Standard notation for the the collection of all *minimal* elements of the set of all upper bounds?
Let $(P,\leq)$ denote a poset and suppose $X \subseteq P$. Then the minimum element of the set of all upper bounds of $X$ can be denoted $\operatorname{sup} X$, or $\bigvee X$. Is there a similar ...
6
votes
0answers
74 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
$$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$
...
0
votes
0answers
25 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 ...
4
votes
0answers
67 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
99 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
30 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
3answers
108 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 ...
15
votes
5answers
488 views
Elementary results from Algebraic Number Theory
The purpose of this question is to motivate me to study algebraic number theory.
Let me explain. My motivation for studying number theory is to learn about beautiful results with simple, accessible ...
4
votes
3answers
132 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 ...
10
votes
7answers
604 views
What's the hard part of zero?
A lot of textbooks said it was hard for human to accept zero when it was first introduced.
How could it be? It seems to me as natural as positive integer which represent there is no elements at all.
4
votes
0answers
61 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
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 ...
9
votes
4answers
199 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 ...
5
votes
1answer
57 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 ...
9
votes
6answers
257 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
3answers
83 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 ...
