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2
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2answers
31 views

$X$ be a non-empty subset of irrational numbers such that sum of any two elements of $X$ is rational ; then is there any upper bound for $|X|$?

Let $X$ be a non-empty subset of irrational numbers such that sum of any two elements of $X$ is rational ; then is there any possible upper bound for the cardinality of $X$ ? Can $X$ be infinite ?( I ...
1
vote
1answer
26 views

Is there a rearrangement theorem for conditionally convergent improper integrals?

The famous Riemann rearrangement theorem states that for a conditionally convergent real number series, we can rearrange the order of summation to make it converge to any prescribed number in the ...
1
vote
0answers
20 views

Determine if fitted line is actually one line

I am trying to fit multiple lines through many data points in 3d space. My working method is sequential RANSAC, which now is fast enough and fits some lines, but produces some lines that don't fit one ...
3
votes
3answers
97 views

What applications does abstract algebra and algebraic geometry have in computer science and programming? [closed]

I love math and programming. Abstract Algebra and algebraic geometry seems very pleasant to me. But I also would like to improve my skills as a programmer, but I would love to do so in the fiels that ...
27
votes
9answers
2k views

Is formal truth in mathematical logic a generalization of everyday, intuitive truth?

I'm trying to wrap my head around the relationship between truth in formal logic, as the value a formal expression can take on, as opposed to commonplace notions of truth. Personal background: When I ...
5
votes
1answer
90 views

Was there a golden age of industrial mathematics that is now over?

I read "The Man Who Loved Only Numbers," a great book about Paul Erdős, last summer. The book describes Ronald Graham, a super interesting character who worked on discrete math and graph theory at AT&...
0
votes
0answers
26 views

A problem with my computer in WolframAlpha

I wonder if the problem I have on my computer with a calculation with WolframAlpha, also occurs on other computers. The situation is that asking for integer solutions of the equation $$x^2+y^2=5(xy-1)...
2
votes
1answer
108 views

Application of calculus in real life

I'm no mathematician, so bear with simplicity of what I'm asking. My calculus course(post-Soviet country, a while ago) was utter trash. I've recently decided to approach the topic for self eduction. ...
1
vote
0answers
35 views

Reference Quest: Measure Theoretic and Functional Analytic Intro to Stochastic Processes

Does anyone have any recommendations for a good book which introduces and cleanly and rigorously explains the measure theory and functional analysis implicit in and relevant to stochastic processes, ...
1
vote
0answers
42 views

Discretizations of Differential, Geometric and Topological Notions

I have noticed a recurring theme in Graph Theory / Theoretical Computer Science (abbreviated GT and TCS throughout this post) in that notions typically belonging to differential calculus / geometry / ...
2
votes
3answers
84 views

What is the 'meaning' of nowhere dense set?

In some books, nowhere dense set is defined to be $int(\bar A)=\emptyset$ but meanwhile is defined to be $int(A)=\emptyset$ in some books(e.g. Munkres). So what is the 'meaning' (i.e motivation, ...
0
votes
0answers
16 views

What would be form of Lagrange's linear PDE?

For Lagrange's linear PDE of type $\xi(x,t,u)\frac{\partial u}{\partial x}+\tau(x,t,u)\frac{\partial u}{\partial t}=\eta(x,t,u)$ one would write characteristics equations as: $\frac{dx}{\xi(x,t,u)}...
3
votes
0answers
70 views

Are all statements about math inherently formal? Can one do math without formal logic? [duplicate]

Are all people who do mathematics applying (whether they know it or not) formal logic? Does every statement someone may make about math, at its core, a formal statement in mathematical logic? (I'm ...
18
votes
9answers
2k views

Where do I start learning Higher Mathematics? [closed]

I am 17 years old and I would like to begin learning Mathematics. I am only familiar with Algebra and a bit of Geometry. Do I need to learn Calculus next, or should I try linear algebra? I find myself ...
1
vote
0answers
34 views

Book on Random Group Theory

I'm looking for a book on random group theory. I haven't had any luck in finding books specifically on this topic.
1
vote
1answer
45 views

Different Mathematics

Hey I am a high school student who is very interested in the philosophy of mathematics. I was watching this talk by Stephen Wolfram about whether or not mathematics is invented or discovered. In it he ...
0
votes
2answers
191 views

What are some of the Hardest Unsolved Mathematics Problems? [closed]

At the moment, are there any major unsolved mathematical problems yet to be solved, and do they have any prize associated with the solving of them? Furthermore, is there any particular reason that ...
1
vote
2answers
41 views

Difference between two math signs

I've a question about two math different math signs: What is the difference between $\approx$ and $\cong$?
0
votes
0answers
43 views

Simplifying calculation

My education system won't allow me to use calculator even though within complex number. Luckily, we use multiple choice (which I can do approximation) I am no human calculator, and if I count, it ...
7
votes
2answers
161 views

Gödel's ontological proof and “modal collapses”

Recent findings on Gödel's ontological argument allowed to ultimately establish a couple of things: Gödel's original axiomata are inconsistent Scott's variation instead is consistent Scott's axioms ...
1
vote
2answers
71 views

Thinking math critically [closed]

First, I'm from Indonesia and trying to take SBMPTN (kindal GRE or SAT test) I have trouble in math. Which my teacher says that math is about creativity. But here's the main question How do I ...
7
votes
2answers
165 views

How did the name “The Calculus” come about, was there a reason or just good marketing?

This is a historical and lighthearted question about etymology. The area of mathematics that deals with limiting processes over real numbers (Real Analysis) or real vector spaces, or even complex ...
1
vote
0answers
46 views

How to learn time series by myself

I would like to learn time series by myself. Could anyone introduce a beginner/introduction book to me so I could have a basic idea of that. Also, is there any background requirement for that class? ...
0
votes
2answers
26 views

Soft Question: Taking Multivariable Calculus vs. Introduction to Proofs Class [closed]

Would taking multivariable calculus be boring in comparison to an introduction to proofs class for someone good at Calc. I and II? The multivariable calculus class would not cover topics like Green's ...
2
votes
1answer
43 views

Difference between Backward and Forward differences

In numerical methods we are all familiar with finite difference table where one can identify backward and forward difference within same table e.g. given any entry in finite difference table, one can ...
1
vote
1answer
38 views

Documentary on number theory

Can anyone suggest documentaries on Number theory ? Looking to show it to high school and undergrads Thanks
1
vote
1answer
70 views

Collected works of Mathematicians

The collected work of any mathematician is, in my opinion, more than collection of his works. Since it is edited (collected) by some people which have passed through many papers of the mathematician, ...
4
votes
0answers
66 views

Concrete Mathematics: Not taught how to solve problems.

I've read and studied the first 3 paragraphs from Concrete Mathematics and now I've made the first couple of problems. When I got to the actual homework problems I was lost because I tried to solve ...
2
votes
2answers
513 views

What is the average prime numbers we've found till now?

When you count from 0 to 100 you have 25% prime numbers. Till now the largest prime consists of $2^{74,207,281}-1$ numbers. But is known what the average is till now? With average I just mean the ...
0
votes
1answer
87 views

How to do complicated problem without messy mind?

I have trouble when doing complicated problem, when I look at a problem with so much information. (e.g. deal with some concrete example such as proving a 'ugly' space is homeomorphic to another 'ugly' ...
1
vote
0answers
25 views

Applications of the Axiom of Regularity to non-set-theoretical Mathematics [duplicate]

In the beginning of my mathematics studies at university, we have learnt that nearly all of ordinary mathematics not dealing with proper classes can be formalized within ZFC, which is a famous ...
1
vote
1answer
23 views

Language used in projective linear group

In lectures and text on topic of projective linear group, I hear and see the word "factor out" or "quotient out" thrown around a lot. What is the word supposed to mean? If this is vague, I can ...
2
votes
0answers
41 views

Is this an accurate layman's description of the Anti Foundation Axiom

I'm writing an article that covers as one of its topics hypersets/non-well founded sets. In order to do so I have to describe what the anti-foundation axiom (AFA) is my description is currently as ...
0
votes
1answer
20 views

Multidimensional Cantor diagonal argument for ordering infinite sets [duplicate]

Cantor diagonal argument is a powerful proof technique. It has been used for a lot of proofs. For instance, it has been used to prove that $|\mathbb{N}| < |\mathbb{R}|$. What can we say about the ...
2
votes
2answers
64 views

How to access the world's specialised knowledge? [closed]

This is a question that relates to almost all domains, I just happen to be passionate about maths. In my early teens, I used to believe that the path through all stages of standard education would ...
5
votes
1answer
292 views

Soft Question: Why does the Axiom of Choice lead to the weirdest constructions?

I hope this is not too off-topic / soft for math.stackexchange. My basic question is: why does the Axiom of Choice allow for some of the weirdest constructions in math? I'll make a list of the weird ...
0
votes
0answers
22 views

What is a probable form of Fermat's triplet?

The mathematical community is now aware beyond reasonable doubt that Fermat's Last Theorem was accurate. However, I cannot help asking, if there were any non trivial Fermat's triplet: -What would ...
56
votes
8answers
8k views

How to debug math?

May seem strange as I'm good in programming, but I just started diving into math. ATM I'm learning combinatorics at Khan Academy, and here's an example of a question that I struggled with (that's not ...
1
vote
1answer
26 views

Investigation Problem to challenge mathematical reasoning

I am a sophomore in college and currently enrolled in a Upper Division Problem Solving class. I was assigned a final project in which I need to come up with some sort of mathematical investigation ...
2
votes
2answers
24 views

Soft question about Lie Groups and 3D rotation

Let $R(\phi, \boldsymbol{n})$ be a member of Lie Group SO(3). According to Wikipedia If $R(\phi, \boldsymbol{n})$ denotes a counter-clockwise 3D rotation through an angle $\phi$ about the axis ...
5
votes
4answers
103 views

Should we or should we not take $1$ as a prime number? [duplicate]

I think I know that there were times in the past when it was convenient to look at a number $1$ as a prime number, and, as far as I can remember, even then it was dependent on who we ask is it prime ...
0
votes
1answer
29 views

Computing the “Mean Value” of a Point Sample From an Arbitrary Manifold

A friend of mine noticed that taking the "mean" of two points on the circle isn't as easy as just computing the arithmetic mean of their arguments: If one point has argument $-3.13$ radians and one ...
2
votes
0answers
27 views

Tricky divergent binomial expansions?

The binomial expansion of $(a+b)^n$, where $n\notin\mathbb{N}$, is given as $$(a+b)^n=a^n+\frac{n}{1!}a^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^2+\cdots$$ In some situations, we can find the result of a ...
2
votes
0answers
52 views

What is the purpose of homomorphisms?

I know that a mapping $\phi:A\to B$ is a homomorphism provided that $$\phi(A*B)=\phi(A)\times\phi(B)$$ where $*$ and $\times$ are two operators on the algebraic structures $A$ and $B$ respectively. In ...
0
votes
0answers
18 views

Video Lectures on Multi variable Calculus in n dimensions

I am teaching myself multi variable calculus from various resources on the internet. I have completed the famous 18.02 offered at MIT. This is an introductory course on Multi variable Calculus and is ...
2
votes
0answers
61 views

What should I have learnt as an undergraduate? [closed]

I am getting my bachelor's degree this summer, and I feel like I don't know as much as I should in several fields in math (geometry, functional analysis, measure theory, abstract and linear algebra, ...
8
votes
1answer
413 views

What is the current state of formalized mathematics?

Russell and Whitehead famously tried to actually create and use a formal system to explicitly develop formal mathematics in their work, "Principia Mathematica." Much more recently, with the aid of ...
2
votes
2answers
85 views

About the Words “recursion” and “recursive”

According to Wikipedia, Recursion is the process of repeating items in a self-similar way. On the other hand, the word "recursive" is an adjective and is often used as a synonym of "computable" when ...
3
votes
3answers
49 views

Does the PNT establish a connection between primes and the logarithm?

The prime number theorem states that $$\pi(x) \sim \frac x {\ln(x)}$$ Morally, this seems to suggest that there is a fundamental connection between primes and the natural logarithm. But since we're ...
3
votes
1answer
118 views

Vladimir Blinovsky's Union-Closed Sets Conjecture Proof

Recently, Vladimir Blinovsky published an article (http://arxiv.org/pdf/1507.01270v6.pdf) claiming that he proved the union-closed sets conjecture (https://en.wikipedia.org/wiki/Union-...