For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

learn more… | top users | synonyms

0
votes
0answers
22 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
3
votes
1answer
68 views

What is the role of fixed point theorems in modern mathematics?

About Fixed Point Theorems, Wikipedia says: Results of this kind are amongst the most generally useful in mathematics. This seems an accurate statement: indeed, there are many journals ...
-1
votes
1answer
69 views

Basic Concepts of Mathematics by Elias Zakon

Has anyone studied the book "Basic Concepts of Mathematics" by Elias Zakon? (To whom) Can you recommend it? On what level of difficulty is it (like early undergraduate for example)?
2
votes
1answer
96 views

Projects for Topology?

I am in a Topology course in undergraduate. We are in Chapter 2 right now of Patty's Foundations of Topology. We are supposed to do a project outside the book but I'm not feeling creative right now. ...
0
votes
3answers
94 views

Best way to learn pure mathematics [closed]

I'm currently enrolled in an introductory real analysis course. While I enjoy the beauty of pure mathematics, there are 2 problems I face. 1) Constructing proofs 2) Attempting to understand a proof ...
3
votes
2answers
60 views

What are the uses of cross-theoretic identifications within mathematics?

I've been thinking about the identification of objects from different mathematical theories. For example, when you do set theoretic constructions of the natural numbers and identify, e.g., 0 with the ...
2
votes
2answers
64 views

A break in symmetry between Algebraic number fields over Q and otherwise

Most of the theorems in algebraic number theory seem to generalize to arbitrary base fields apart from $\mathbb{Q}$ apart from one. The characteristic of the residue field is equal to positive prime ...
1
vote
0answers
21 views

On the existence of certain Weierstrass-type Extreme Value Theorems

It is well-known that Weierstrass Extreme Value Theorem can be generalized to lower and upper semi-continuous functions. Are there any other generalizations of this important result; and more in ...
4
votes
2answers
107 views

Does randomness exist? [closed]

I've been plagued with this question for a few years now and wanted to know what others think. Does true randomness really exist? In mathematics, a random process is based on the concept of random ...
1
vote
0answers
23 views

What is the state of art of the question that pi has every secuence on it´s decimal expansion? [duplicate]

I have heard that if pi have all disctinct sequence on it´s decimal expansion, then all the books that are not written can be found there and it is one of the most romantic stories i have ever heard ...
1
vote
0answers
74 views

P = NP, NP example problems in our daily life

For a little presentation for school, i want to try to explain the P=NP? Problem. I'm searching for examples for daily life NP-problems. (example: is making the weather forecast a NP problem?) And if ...
0
votes
0answers
39 views

Is there a name for an object with both position and velocity?

I know of "position vectors" and "velocity vectors". I'm looking for the name of an object which contains both a position vector and velocity vector, if such a name exists?
4
votes
1answer
76 views

Maths Discoveries thanks to Computer Science

Which discoveries have been made in mathematics thanks to computer science ? For example fractals have been discovered thanks to computers (correct me if im wrong) do you know any similar discoveries ...
3
votes
0answers
109 views

Are there human integrators? [closed]

Are there human "integrators", "differentiators", or "analysts"? I've heard of and seen people capable of performing seemingly complex arithmetic calculations mentally. Often this involves memorizing ...
1
vote
0answers
21 views

Usage: Holomorphic Functions

This isn't a math question, but rather a question is word usage in mathematics. Why do people say " $f$ is an isomorphism," or "$f$ is a diffeomorphism," but in complex analysis, we say that "$f$ is ...
0
votes
1answer
43 views

arclength parametrization intuition

I have a question about parametric curves. I have learnt about arc length re parametrization and I understand how do the problems , for example finding the length of the vector and integrating with ...
6
votes
1answer
89 views

Surveys: problems, conjectures, and questions in some areas of nonlinear analysis

I would like to create a "big-list" of resources (e.g., survey papers, webpages, conference proceedings, monographs, etc.) that collect and offer some context and ...
0
votes
0answers
18 views

How to intuit the axiom $p(A \mid B \cap C)p( B \mid C) = p (A \cap B \mid C)$?

I encountered the axiom $p(A \mid B \cap C)p( B \mid C) = p (A \cap B \mid C)$ as a variant of the axioms $p(A \mid B) = p(A \cap B \mid B)$ and $p(A \mid B)p(B \mid C) = p(A \mid C)$ for $A \subseteq ...
2
votes
0answers
24 views

Nilpotent groups in geometry.

I have read sometimes conclusions pertaining nilpotent groups in geometrical settings. Particularly I read that Fukaya and Yamaguchi proved that if $M_i$ is a sequence of Riemanian manifolds ...
3
votes
1answer
49 views

Example of equivalence relation where reflexivity/symmetry is not trivial

For basically any equivalence relation that I've encountered in my mathematical studies, the only problematic part (if at all) was proving transitivity. Is there a "real-world" (i.e. appearing in some ...
7
votes
1answer
101 views

What came first, the $\forall$ or the $\exists$? [closed]

I imagine that these symbols originated in one of the following ways: "I will declare a symbol for "for all." I will just use the letter "A" flipped upside-down. Yes, let $\forall$ represent "for ...
3
votes
3answers
183 views

Can I skip computational advanced calculus and work on Spivak's 'Calculus on Manifolds'?

I have completed Velleman's book, 'How to prove it'. I have also worked through Apostol Vol.1. I have messed about with many rigorous single variable calculus textbooks, e.g.,Apostol, Spivak, Courant, ...
2
votes
1answer
50 views

Ackermann Function - Book recommendation

What books would you recommend me for the topic "Ackermann Function" ?? I will have a presentation at the end of the semester for this topic and I would get some information...
0
votes
3answers
73 views

Formal notation for representing decimal numbers

What is the formal mathematical notation for representing a decimal number using variables as it's digits? I am honestly surprised that this has not been asked yet on MSE. Let me clarify a ...
1
vote
1answer
85 views

Is Contest-Math Worth It? [closed]

I am very interested in Contest-based mathematics. The questions such as the ones that come up in the AMC, or AIME, USAMO and most specifically Putnam are very interesting. It is very different ...
1
vote
1answer
85 views

Is a derivation a proof?

Is there a difference between "derivation" and "proof"? I imagine a derivation is a type of proof but that proofs are perhaps more general. Although then again, I suppose every proof should be ...
3
votes
1answer
68 views

Soft clarification on Gödel's incompleteness theorems

I've read an article, and I would like to ask the author for clarification, but I couldn't find contact details. Link: http://www.mathpages.com/home/kmath347/kmath347.htm Oddly enough, some ...
3
votes
0answers
83 views

Undergraduate research program (REU) with focus on nonlinear analysis (accessible to European students)

Is there an undergraduate summer research program (REU) -- to which also European students can apply -- which usually has projects (i.e., specialized faculty) on nonlinear analysis (i.e., ...
1
vote
1answer
112 views

In balancing effort and advancement in what concerns learning

What's new besides showing modern advancements in modern mathematics as well as eloquently written notes also contains some good advice to young people like me in this room (career advice:!). in ...
0
votes
0answers
15 views

Difference of radian and degree measure.

I had noticed that in studying trigonometric functions some fields of Math favors the radian measure such as calculus and analytic trigonometry, while others favor degree measure for instance in ...
4
votes
3answers
252 views

Logic in Philosophy vs. Mathematical Logic

At my university, students majoring in philosophy take a course called "Logic in Philosophy" and there is also a course offered in the Math Department called "Mathematical Logic". There are also ...
0
votes
1answer
54 views

Understanding derivatives in simple terms

Im am trying to understand the idea of derivatives and how they relate to the real world. I understand if i have function, in pkysics first derivative is the velocity, and the second derivative is ...
0
votes
2answers
39 views

Is it wrong to “imagine” a one when thinking about exponentiation? (e.g. $3^2 = 1 \times 3 \times 3$)

This might be a bit of a basic question, but I'm going through Khan Academy to refresh my math skills in order to pursue a self-study of higher mathematics, so I'm really focused on the "why" of the ...
3
votes
5answers
120 views

Problem book on general topology [duplicate]

Can one please suggest some problem book on general topology? I have Munkres but exercises are easy, that's why I want a book which consists of slightly non trivial or interesting problems. Also you ...
9
votes
1answer
113 views

Mathematical Research seems daunting [closed]

Suppose you are a research mathematician. I imagine your problems are generally unlike the problems of fellow scientists in the physical sciences, because you deal with proofs, and proofs demand ...
1
vote
2answers
41 views

what is the difference between these two type of convergence and why people saying that that one of them is stronger than the another?

what is the difference between these two type of convergence and why people saying that that one of them is stronger than the another? In another word,how come point-wise convergence is weaker than ...
3
votes
0answers
39 views

Advice on methods to capture lecture board and add notes [closed]

I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and ...
1
vote
0answers
51 views

What really is inductive reasoning?

I am looking for concrete information on "induction" in the old sense of the word. Now it is used to refer to proof by "mathematical induction"; however, I am aware that it also means inductive ...
0
votes
0answers
16 views

Are free group&product the hardest free object&product to construct? And why?

The free objects I know are free group and free module. It is weird that even though the structure of module is more complex than that of group, the construction of free group is much harder than that ...
8
votes
2answers
155 views

How do I explain Complex Analysis to my grandma?

After I got selected to the university, one day I visited my grandma. She asked me what my favorite subject was. I said, "My favorite subject is Complex Analysis". Then she said "what is this, Complex ...
1
vote
1answer
25 views

Advantages of solvability, nilpotency and semisimplicity of Lie algebras?

After pondering on the notion of solvability, nilpotency and semi-simplicity of linear Lie algebras for days (I have been reading Humphreys' Introduction to Lie algebra lately), I remember a professor ...
4
votes
0answers
68 views

Solving a question by using special products (Students debate to Teacher)

So today,we got back our exam papers,and we found a question marked wrongly and teacher said that it is wrong.We all students do NOT believe this.So here is what happened. Before reading the next ...
11
votes
2answers
282 views

Open/publicly available textbooks worth their salt

I've been reading a bit about "open textbooks", i.e. textbooks made available for easy, online access. These can be nice for those without access to a great library, or who might not be willing to ...
0
votes
0answers
17 views

Asymmetric correlation and graphs - Some ideas?

Imagine to have $n$ identical "systems" arranged on a graph, where each vertex corresponds to a "system". An edge between two vertex $v$ and $w$ is weighted by a real number $a_{v,w} = a_{w,v}$ (it ...
2
votes
1answer
80 views

PDEs in industry [closed]

Doing my undergrad now and having mostly focused on PDEs and Analysis, I wanted to do a internship in the summer. However, I have not studies any applied maths or coding. Where can I actually use my ...
6
votes
2answers
133 views

On the philosophy of Category Theory

I have been told by my professor that Category Theory is not just a language but is a shift in the way we think. As an example he pointed out that in category theory we do not worry about the objects ...
0
votes
1answer
25 views

Are these equivalent definitions of a quotient group?

After grappling with the concept of a quotient group I have come across two different definitions of a quotient group. The first which is used in Algebra Chapter 0 uses an equivalence relation $\sim$ ...
0
votes
2answers
88 views

What is the difference between the geometric and trigonometric definition of an angle?

I vaguely remember reading that there is a difference between the geometric definition of an angle and the trigonometric definition of an angle. I've tried to search everywhere I can think of but I ...
3
votes
2answers
47 views

Homeomorphism from $(-1,1)$ to $\mathbb R$

I know that $f: (-1,1) \to \mathbb R$ defined by $f(x)=\tan \Big(\dfrac{\pi}2x \Big)$ is a homeomorphism . I am looking for some other homeomorphism between $(-1,1)$ and $\mathbb R$ which is not in ...
0
votes
1answer
59 views

Difference between Double and triple integral?

Hi all I am going to be starting multivariable calc and I am trying to read up but I can't seem to quite grasp this exactly yet. What are the differences between double and triple integrals? I am ...