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14
votes
2answers
129 views

Is it Possible to Construct all Proofs in Complex Analysis using Brownian Motion?

(First, I am very aware of the fact that Brownian motion is actually probably more difficult to understand than at least basic complex analysis, so the pedagogical merits of such an approach would be ...
2
votes
0answers
48 views

'Math teaching in india is robotic,make it creative'-Manjul bhargava. Then how to make it creative? [closed]

Manjul Bhargava once said "Math teaching in India is robotic,make it creative."My question is then what is the true way to study math?I am postgraduate student from India.In our institute normally ...
1
vote
2answers
33 views

A generalization of working problem.

Question: If X finishes for 4 hours a project and Y for 6 hours a project than how long it takes if they work together in same project? These questions for two people are pretty simple, just product ...
1
vote
0answers
18 views

Dimensionality of a function

When people refer to the "$x$-dimensional" case of a function or relation, how is the dimensionality determined? For example, let's say I have the functions $f(x,t)$ and $g(x, t)$. I could refer to ...
6
votes
4answers
478 views

What should “The Fundamental Theorem of Linear Algebra” assert? [closed]

Unlike some other basic fields of mathematics, linear algebra does not seem to have a universally agreed-upon fundamental theorem. This I imagine might be because the subject usually admits a lot of ...
0
votes
1answer
21 views

Representation of indeterminate forms?

I am learning about l'Hospitals rule (side note - interesting history behind it in that it should really be called Bernoulli's rule) and indeterminate forms such as $\frac{0}{0}$ , ...
2
votes
2answers
87 views

How do you understand calculus ideas? [closed]

I have dyscalculia, so I'm wondering how most people process math ideas. I can only solve problems by memorizing what to do after being shown step-by-step how to solve similar problems. None of the ...
0
votes
1answer
56 views

Soft Question: Do most mathematicians agree that the function is “the most important concept in all of mathematics”?

Spivak (Calculus, 3e, p. 39) writes: Undoubtedly the most important concept in all of mathematics is that of a function---in almost every branch of modern mathematics functions turn out to be ...
3
votes
1answer
118 views

Is there some kind of deep relationship between substitution and recursion?

Define $\mathbb{N}$ as the initial object in the following category: Objects. Sets $X$ equipped with a function $S : X \rightarrow X$ and an element $0:X$. Morphisms. Functions that preserves ...
1
vote
1answer
26 views

What is the Difference Between a Version and a Modification of a Stochastic Process?

Under what circumstances would one say that: The stochastic process $X$ is a version of the stochastic process $Y$? Background: See here for a related but slightly different question on ...
6
votes
3answers
474 views

What does “the average continuous function is nowhere monotonic” mean?

I plan on asking my professor what he meant by "average continuous function," but as it is possible that this is a concept as vague as the statement, I was hoping to get some interesting ...
0
votes
0answers
29 views

Is Engelking and Sieklucki's “Topology: A Geometric Approach” a Good Introduction to Algebraic Topology?

I only found this book incidentally while looking at Engelking's more well-known "General Topology". I posted a link here. ...
2
votes
2answers
30 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
23 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
84 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 ...
25
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
86 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 ...
0
votes
0answers
25 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 ...
2
votes
1answer
99 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
33 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, ...
0
votes
0answers
25 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
78 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
13 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: ...
0
votes
0answers
49 views

What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
3
votes
0answers
67 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? ...
17
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
31 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
41 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
99 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
1answer
148 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
164 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
45 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
34 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
68 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
59 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
508 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
83 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
24 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
39 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
19 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
62 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 ...
4
votes
1answer
275 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
21 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 ...