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-2
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0answers
46 views

Why Syracuse's problem so difficult to solve?

I'm really astonished that Syracuse's problem is very difficult to solve ! How it is possible, here the sequence : $U_{n+1}=\frac{U_n}{2}$ if $U_n$ is an even number and $U_{n+1}=3\times U_n+1 $ ...
5
votes
2answers
79 views

Is Keno a fair game?

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with probability, which perhaps yields the shortest, simplest proofs, but other ...
59
votes
34answers
6k views

Easy math proofs or visual examples to make high school students enthusiastic about math [closed]

I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or ...
0
votes
0answers
21 views

What does this statement mean exactly?

I would like some clarification about the following from Fejes Toth's paper "A stability criterion to the moment theorem" The setup is: For each positive integer $n$, let $r(H_n)$ and $R(H_n)$ ...
5
votes
0answers
56 views

How do you avoid getting rusty at applied math after univeristy [closed]

As a new postdoc working in a bio-math interface discipline, I often wish I had more formal math training than my math minor many years back. Compared to others who came from more of a ...
4
votes
0answers
66 views

Manifold in Milnors Morse Theory

While reading "Morse Theory" by Milnor, I noticed that certain arguments would not work, if the considered manifolds have nonempty boundary. Example: Proof of 3.5 I could not find the definition ...
3
votes
0answers
32 views

Where to study type theory?

I want to learn more about (homotopy) type theory, constructive mathematics and univalent foundations. To my knowledge, there are only few faculties with large type theory groups. In Europe, most of ...
0
votes
0answers
34 views

GRE Math Subject Test ,Please Check my Plan

I am to give test in october. I have planned to use Schaum series 3000 solved problems in calculus and 3000 solved problems in Linear Algebra for that .Also i will use Herstein for group theory .Since ...
2
votes
1answer
114 views

Is it feasible for a sophomore in high school (15 years old) to learn complex analysis? [closed]

I've been reading up on complex analysis and it seems an incredibly fascinating subject to me and one I'd like to learn more about. However, most of the books I've come across are for graduates, which ...
1
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1answer
33 views

Complex integration: normally on a closed contour?

I have been studying complex integration for a few months now, and it seems my textbook mostly considers integration on closed contours. Is there no interest in integration on non-closed contours ?
3
votes
1answer
27 views

Skill plateau, overpracticing, and alternative practice methods

It's the summer holiday for me right now and I've been spending a lot of time doing math problems. I've done a bunch of Olympiad questions and the like recently, and I feel like I've hit a plateau ...
4
votes
4answers
84 views

Mathematical philosophical questions about the general theory of stochastic processes.

After 6 months spent on what is termed the "general theory" of stochastic processes and after having worked out many nuances of the field, I realized that: The general theory is beautiful ...
14
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4answers
203 views

How to write $\aleph$ by hand

So far, I've only seen the symbol $\aleph$ in its printed form and am wondering how this symbol could be written by hand on paper or on a board (in mathematical contexts, of course). Whenever I try to ...
4
votes
1answer
58 views

Difference between ,say, “At least 8” and “8 or more”

Are they not the same the thing? Just to be on the safe side I wanted to verify this with others. Sorry for the stupid question.
8
votes
1answer
104 views

Is there a “Coalgebra - Cogeometry” duality? Good opposite of a category of coalgebras?

So the category of affine schemes is dual to the category of commutative rings, Stone spaces are dual to Boolean algebras, localizable measurable spaces are dual to commutative Von Neumann algebras, ...
1
vote
1answer
122 views

What would be the “action” in functional analysis?

I am reading Simmons' "Topology and Modern Analysis". He keeps bringing up the idea of studying the set of all structure preserving mappings to obtain info regarding the structure of a certain normed ...
0
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2answers
275 views

Am I too old to reach to the point of a ground-breaking research and achieve it? [duplicate]

I am sorry if I am posting this question here; I thought that since I am looking for historical evidences of successful people in mathematics, so may not this question be an opinion-based one. And ...
4
votes
2answers
90 views

Is theoretical Linear Algebra still an active field of research?

Numerical Linear Algebra seems to be a very active area right now, but is there any work still being done on the purely theoretical side? To put it another way...is it possible for someone to write a ...
13
votes
2answers
394 views

Why we use the word 'compact' for compact spaces?

Considering the definition of compactness in either Analysis or Topology books, or its equivalent definitions (i.e. [It] is compact $\Longleftrightarrow\dots$), I couldn't understand why ...
4
votes
2answers
1k views

Why can only those younger than 40 years old win the Fields Medal?

There are some prizes in Mathematics nowadays that may be considered probably as hard to win, like the Abel Prize, but they were established quite recently. Looking back to a few years ago, the Fields ...
3
votes
0answers
51 views

Intuition behind generic point of a scheme?

I've been reading a little about algebraic geometry and how there seems to have existed this notion of "generic point" on a variety which wasn't carefully defined at first. But often times, ...
26
votes
7answers
5k views

Are older mathematics textbooks still “valid”?

Being interested in learning rigorous calculus (as opposed to the content taught in AP Calculus and intro calculus courses in university), some textbooks mentioned quite often on the internet include ...
1
vote
1answer
33 views

When the group of isometries of a norm determines the norm?

$\newcommand{\<}{\langle} \newcommand{\>}{\rangle} $ Let $V$ be a finite-dimensional normed space. Assume that $G=\text{ISO}(||\cdot ||_1) = \text{ISO}(||\cdot ||_2)$. When can we conclude that ...
0
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0answers
78 views

Undestranding Basic Game Theory

Lately I'm studying game theory for an exam. I'm having troubles in understanding some theorems since notes I'm studying on are very brief and concise about sense of definition. In this question I'll ...
0
votes
1answer
25 views

Good resources on chemical graph theory

Are there some good resources on chemical graph theory, mainly some covering even the recent results (past 2000)? Tnaks in advance for any help.
8
votes
3answers
334 views

Need Suggestions for beginner who is in transition period from computational calculus to rigorous proofy Analysis

I have completed basic calculus 1,2,3 courses, Linear Algebra, etc. I have not, however, got into rigorous Analysis yet, which I am planning to do now. I have three books in mind. They are : Terence ...
1
vote
2answers
71 views

Next book in learning General Topology

I have just finished the book "C Adams & R Franzosa - Introduction to Topology. Pure and Applied". My aim is to reach to the level of the book "G E Bredon - Topology and Geometry". Bredon's book ...
13
votes
7answers
678 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
44 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
46 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 ...
8
votes
1answer
163 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
65 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
103 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 ...
1
vote
0answers
60 views

Why is combinatorics not a part of the Tripos? [migrated]

I do not officially study mathematics, so I always rely on what's on the internet. Specifically, I follow the schedules of the Tripos – the math program at Cambridge, supposedly one of the most ...
5
votes
2answers
111 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
171 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
58 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
22 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
42 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
36 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
58 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
25 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
115 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
89 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
128 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
390 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
15 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
60 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 ...
4
votes
0answers
52 views

Experiencing a breakdown [closed]

I have been experiencing some sort of a "breakdown" recently. My brain isn't as fresh as it used to be, and I get very tired after say one hour or two of doing math. Moreover, I became very slow and ...
34
votes
1answer
361 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 ...