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13
votes
7answers
712 views

How should one picture a topology/ topological space?

I can form a mental image of sets with structures like metrics or norms. But if I try to picture a topology/ topological space I fail every time. The information provided in Wikipedia confuses me ...
6
votes
1answer
47 views

How to geometrically interpret intertia of primes in field extensions?

I am trying to understand the intuition of thinking about number theoretic ideas in terms of geometric ones. For example, ramification is something that happens when a "covering" space of a Riemann ...
4
votes
1answer
63 views

“On Numbers and Games” or “Winning Ways for Your Mathematical Plays”?

I'm really interested in John Conway's work on games and I want to spend my winter reading something of his but I'm not sure between "On Numbers and Games" or "Winning Ways for Your Mathematical ...
10
votes
1answer
256 views

How to begin self study of Mathematics?

I'm aware that this question has been asked several times, but I have specific questions hence why I'm asking again. I began to appreciate the beauty of mathematics when I glossed over the ...
3
votes
1answer
72 views

Mathematical importance of the golden ratio [duplicate]

I know the golden ratio is the limit of the ratios of consecutive Fibonacci numbers and that it appears when studying many related combinatorial objects (such as the sequences of zeros and ones with ...
4
votes
1answer
107 views

What background is needed to study quantum game theory?

Currently I am learning ( a beginner ) about Bell inequalities and device independent outlook on quantum mechanics. I come across some papers using these concept in quantum game theory. Most of the ...
5
votes
2answers
125 views

A shirt with the imprint of a formula.

Before I began to study mathematics, a friend of mine bought me a shirt with the imprint of a formula. I did not know what these characters were and had no desire to think about it. Yesterday, I ...
1
vote
4answers
191 views

Applications of algebraic topology?

Terribly sorry if this has been asked, but I'm not about to search 382 pages of technical questions in the field. I am trying to develop a very basic understanding of what algebraic topology is ...
2
votes
1answer
66 views

How far can I get with graph theory?

I am an undergraduate who had recently finished his $2$nd year. I was wondering how far can I get with Graph Theory this summer. I am studying from Bondy & Murty's book. I already finished ...
1
vote
0answers
28 views

Can we do better than zero padding of FFT?

My background is in signal processing and never took any course related to functional analysis or even advanced algebra. But I have a strong conviction (may be wrong) that we may be do better then ...
1
vote
1answer
52 views

Advice Rudin PMA

I'm currently working through Rudin's Principles of Mathematical Analysis. My background consists of mainly working through most of Apostol's Caluculus Vol. 1, Velleman's How to Prove it, Lang's ...
0
votes
2answers
51 views

Difference between topology and sigma-algebra axioms.

One distinct difference between axioms of topology and sigma algebra is the asymmetry between union and intersection; meaning topology is closed under finite intersections sigma-algebra closed under ...
1
vote
2answers
63 views

Integration by parts done fast

Even though I've been through countless instances where I needed to use integration by parts, to this day, I still derive it from the chain rule, identify my 'parts' and apply the formula. At some ...
1
vote
1answer
26 views

Limit(s) of a Sequence from the decimal expansion of $\pi$

I found a statement in a book concerning the decimal expansion of $\pi$ that I do not really understand. The statement is my problem number 2, where problem number 1 really looks like a reference ...
6
votes
2answers
172 views

What does “rigorous proof” mean?

I have heard several times that some mathematician has given another and more rigorous for an established theorem, but I don't know what does it really mean and what differences makes it to be more ...
2
votes
1answer
135 views

Coordinate Geometry and Trigonometry book recommendation for GRE Math Subject Test

I am currently a math major at university and I plan to take GRE Math Subject Test in future (most probably next year). Can you please suggest any good book for revising and brushing up Coordinate ...
2
votes
2answers
133 views

Why is ${n\choose k}$ is always a product of the primes of $n$ for all $n>k$? [closed]

Let $n, k$ be two positive integers such that $n>k$. Why is ${n\choose k}$ always divisible by a prime dividing $n$ (or even a product of such primes)? Please help me understand why. I cannot seem ...
5
votes
4answers
420 views

Is there any published research on the value of finding new proofs for old theorems?

There have been many conjectures in history of mathematics that some of them after passing long journey have resulted in lengthy and high-level-math proofs. Perelman's proof on the Poincare's ...
1
vote
0answers
16 views

Prequisites for a PDE course (Strauss)

This question is quite general. In four days I will enroll in a PDE course which will use Strauss as the textbook. However, today when I checked the course description I found that 'multivariable ...
5
votes
0answers
62 views

What are some arguments/counterarguments for Zeilberger's “proof certificates”?

Here is the quote I wish to ask about: "I speculate that similar developments will occur elsewhere in mathematics, and will 'trivialize' large parts of mathematics, by reducing mathematical ...
34
votes
2answers
421 views

Sign Language and Deaf Mathematicians

Something I've often wondered (and I suppose this goes for all kinds of technical terminology, not just that of mathematics) is what kind of sign language exists for practising professional ...
3
votes
2answers
70 views

Is a simple derivation for a formula publishable?

I'm a high school student and recently discovered an interesting method of deriving the definition for $\arcsin z$ for the complex domain using integration. I typed it up for fun in LaTex and am ...
3
votes
0answers
30 views

It is possible to talk about the degree of a transcendental equation?

When we deal with algebraic equations involving polynomial and so on we know what the degree of the equation is and this tells us how many solutions we'll find (at least in complex numbers). But this ...
1
vote
0answers
45 views

What is the connection between game theory and (modal) logic?

I'm interested in dynamic epistemic logic lately (reasoning about information and change in multi-agent systems). I also like game theory. I'm looking for some good resources about the connection ...
19
votes
8answers
2k views

How do authors make their problems/exercises for their math books? [closed]

I want to be a math professor one day, but I'm wondering how to make my own original problems to give them to my students. I think that it is a responsibility of the professor to create original and ...
2
votes
2answers
66 views

suggest an elementary text in analysis

I have just completed my undergraduate course in mathematics but I don't feel better in analysis, there is a mugup of books in my book collection But don't know what to choose who will help me to ...
0
votes
2answers
48 views

How to do multiplication (capital pi) in WolframAlpha?

How do i ask this in WolframAlpha: $$\prod_{i=0}^{i=10} \sin{(i)}$$ I used $\text{product}(...)$ and $\text{multiply}(...)$ or even $\text{multiplication}(...)$ but they don't seem to work. I am ...
0
votes
2answers
40 views

Differential Equations vs Analysis I [closed]

I just got done taking Multivariable Calc and I have room for either Differential Equations or Analysis I for the next summer session. These 15 week courses are condensed into 7 weeks, which one would ...
3
votes
1answer
78 views

Soft Question about International Graduate Schools [closed]

Hello members of this site! I hope this question isn't too bothersome, but I need to ask some professionals who know what they're doing. Furthermore, I know that this is supposed to be a more ...
3
votes
1answer
48 views

unintuitive meaning to Bayes theorem

The equality $\frac{\mathbb{P}(Y\mid X)}{\mathbb{P}(Y)}=\frac{\mathbb{P}(X\mid Y)}{\mathbb{P}(X)}$ means that in a supermarket analysis, knowing that a customer bought milk ($X$) multiplies the ...
0
votes
1answer
23 views

Book reference for introduction to Normed Spaces

I wanted a book reference for the study of normed spaces and linear operators. Im still not into functional analysis, but I wanted a reference of an introductory book as to start reading. What would ...
0
votes
0answers
20 views

Books about Gamma, Polygamma and other related functions

I'd like to know the most possible things about Gamma function, Polygamma functions, their derivatives and logarithms and other generalizations. But searching on the internet is too annoying for such ...
2
votes
1answer
62 views

About the topology textbook.

I'm trying to study topology. I got two books, one written by croom and another one written by munkres Which one do you think is better for the beginner? I would appreciate any help.
14
votes
2answers
147 views

Bellard's exotic formula for $\pi$

In his webpage, Fabrice Bellard mentions an exotic formula for $\pi$ as follows $$\pi = \frac{1}{740025}\left(\sum_{n = 1}^{\infty}\dfrac{3P(n)}{{\displaystyle \binom{7n}{2n}2^{n - 1}}} - ...
1
vote
1answer
92 views

What is a good book to learn all of precalculus?

I need a no-fluff book with great exposition on precalculus. It should cover up intermediate algebra, trigonometry and anything else needed to get a strong preparation for Spivak's Calculus. It ...
0
votes
1answer
96 views

Applications of $p_{n+2}+p_{n+1} \le p_1p_2…p_n , \forall n >2$?

Let $p_n$ denote the $n$-th prime number ; I know that $p_{n+2}+p_{n+1} \le p_1p_2...p_n , \forall n >2$ . I am looking for some applications of it , for example I know one application of it ...
5
votes
1answer
159 views

Algebraic geometry papers for beginners

What are some papers/books suitable for a beginning graduate student interested in algebraic geometry? I have taken commutative algebra and a classical algebraic geometry class, but I have no other ...
2
votes
1answer
78 views

What is a good book to learn all of prealgebra?

I am an old man trying to learn mathematics, starting off with prealgebra and need a good comprehensive book for it. The book should NOT contain annoying images like in most American textbooks or ...
41
votes
15answers
4k views

What are “instantaneous” rates of change, really?

This is driving me crazy, I'm literally losing sleep over it, please help me resolve this confusion. Here's how I see it (please read the following if you can, because I address a lot of arguments ...
0
votes
0answers
32 views

Prerequisite for algebraic topology?

I'm a math undergraduate and taking undergraduate algebraic topology next semester. I didn't take topology and algebra but studied little of them. I studied some part of group theory for algebra and ...
3
votes
3answers
57 views

Equation of a … 3D object???

(Stupid question...) Well we can represent a point as something like $P(a,b,c)$ We can represent a line as $\dfrac{x-a}{p}=\dfrac{x-b}{q}=\dfrac{x-c}{r}$ We can also represent a plane as ...
0
votes
0answers
11 views

Precise statement of Gersho's conjecture

Here is the Gersho's conjecture from his paper "Asymptotically optiaml block qunatization" "For $N$ sufficiently large the optimal(distortion-minimizing) quantizer for a random vector uniformly ...
2
votes
0answers
37 views

Geometric Interpretation of Determinant of Transpose

Below are two well-known statements regarding the determinant function: When $A$ is a square matrix, $\det(A)$ is the signed volume of the parallelepiped whose edges are columns of $A$. When $A$ is ...
4
votes
1answer
76 views

Introductions to Ehresmann connections and Chern-Simons forms

I am looking for introductory texts on Ehresmann connections and Chern-Simons forms. I seek detailed, hands-on presentation. Please, recommend sources that employ a differential forms approach rather ...
0
votes
0answers
28 views

What exactly is Applied Analysis

I hope this question is not irrelavant for this site, and if so I would like to apologize in advance. I have seen the applied analysis as a research field in some applied mathematics programs and ...
0
votes
1answer
65 views

How to download the Latex file of an article from arXiv.org?

It is a non-mathematical question . Mathstackexchange is a not a right place to ask this question but I don't have any other choice. Any help will be appreciated. $\bf{Question:}$ How to download ...
3
votes
1answer
53 views

How did the ancient Greeks discover formulas for volume and surface area?

How did the ancient Greeks discover formulas for volume and surface area of different objects, e.g. of a sphere? They did not know about integrals, so there must another way?
3
votes
0answers
52 views

Topological issues in large deviation principle

Let $X$ be a topological space, let $B_X$ be its Borel $\sigma$-algebra, and let $B$ be the completion of $B_X$. We say that the family of probability measures $\mu_\epsilon$ defined on $(X,B)$ ...
3
votes
0answers
32 views

Minimum Knowledges to precisely calculate PDEs (integral equations)

Basically all I want to do is to calculate (or prove) precisely equations such as $$ \frac{1}{n\alpha(n)r^{n-1}}\int_{\partial B(x,r)} u(y) dS(y) = \frac{1}{n\alpha(n)} \int_{\partial B(x,r)} ...
1
vote
0answers
24 views

How to find an optimal solution for a missing player in a double-elimination tournament

Say that you have a double elimination tournament consisting of four teams with 2 players. Each of those teams of partners could be: (A,B), (C,D), (E,F), and (G,H), where A is B's partner, C is D's ...