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

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3
votes
3answers
95 views

Surprising applications of topology

Today in class we got to see how to use the Brouwer Fixed Point theorem for $D^2$ to prove that a $3 \times 3$ matrix $M$ with positive real entries has an eigenvector with a positive eigenvalue. The ...
0
votes
0answers
12 views

Red-Black tree - “Insert-Delete”

I am looking at red-black trees. Unfortunately in my lecture notes, the operations "Insert" and "Delete" are not well explained. Could you explain to me steps that we have to do for these two ...
1
vote
0answers
28 views

Combinatorics project ideas for high school students

It's that time again! Last year I asked for high school project ideas in the area of algebraic geometry, this year it's combinatorics (you can include graph theory and combinatorial game theory if you ...
0
votes
1answer
39 views

Universe as a finite 3-manifold without boundary

My question is soft and imprecise, as I know very little differential topology. Nevertheless, I hope it makes some $\epsilon>0$ of sense. Assume the Universe is a 3-manifold without boundary, ...
0
votes
0answers
21 views

What is your “go-to” method/style to prove convergence or divergence?

I was wondering if you guys have some sort of "one seize fits all" method or approach that you always use or go through when proving convergence or divergence of a series/sequence.
0
votes
0answers
29 views

Taking Putnam as a freshman.

Currently, in 11th grade, I've always thong about participating exams like the Putnam. I have however, sent the problems, and they seem, to be grueling hard!! I have access to problem solving ...
1
vote
0answers
30 views

What abstract structures allows us to describe “nets that converge toward each other”?

Topological spaces are equipped with a bare minimum of structure to allow for a formalization of the statement "the net $a$ converges to the point $x$." Actually this isn't strictly true, but its true ...
3
votes
1answer
93 views

How important is the own talent for research of your PhD supervisor?

Currently I am in the process of finding a PhD. Some potential supervisors are more didactical than others, some are nicer and warmer than others, and some are more famous mathematicians than others. ...
7
votes
1answer
266 views

The Purpose of Master Thesis

I am posting this question in the aftermath of the earlier posting in this link. Here are what I would like to know more about master and PhD thesis: (1) I understand that schools' math departments ...
-1
votes
1answer
62 views

Best schools for commutative algebra [on hold]

I will be applying to graduate programs this fall and I was curious which schools have the best commutative algebra groups. I know berkeley and michigan are up there, but what are others?
0
votes
0answers
20 views

which number satisfy the given relation in graph [on hold]

I am unable to find the relation in the graph?
0
votes
0answers
14 views

Different notation for Jacobi symbol

Is there a different, sort of established, notation for the Legendre / Jacobi / Kronecker symbol $\left(\frac{a}{b}\right)$? If yes, where is it used (in which texts)? I'm asking, because I ...
1
vote
0answers
24 views

Is Problem Solving Strategies by Engel sufficient?

Is a book like, Problem Solving Strategies by Arthur Engel sufficient for the Putnam Exam or should I consult something else? I asked a similar question asking for recommendation, no one discussed ...
0
votes
1answer
60 views

Book recommendation for Putnam/Olympiads

I have been concentrating on olympiad questions, and PUTNAM exams, Putnam is my main focus. Can you suggest a book from one of these: Problem Solving Strategies By Arthur Engel Putnam and Beyond by ...
1
vote
0answers
24 views

Understanding the Jacobian past calculus

What's taught in calculus: In the calculus of multiple variables I learned that the Jacobian $$\textbf ...
0
votes
0answers
13 views

Role of functional equations in current panorama of pure mathematics

It seems that currently functional equations are greatly explored as a research field. I would like to know what is the importance and role of such a field in the panorama of the current development ...
2
votes
0answers
46 views

What computations would advance math knowledge a lot?

Suppose we where given a super computer that would be capable of computing anything, but only for one day. We could for instance compute many of the Ramsey numbers. What would be some computations ...
0
votes
0answers
27 views

Mathematically compare two sets of oscillatory data

I need to compare two sets of oscillatory data from a biological process. The data is quite noisy. Both sets have a similar frequency spectrum. I wonder what is the appropriate mathematical tool to ...
0
votes
0answers
43 views

What is umbral calculus, really? [duplicate]

I've seen this page on umbral calculus as well as wikipedia and and another question asked on this website (What's umbral calculus about?), but I still cannot realize what really umbral calculus ...
0
votes
1answer
16 views

Motivation for the binary entropy function

What is the motivation for the definition of the binary entropy function $H(x) = -p\log_2(p) - (1-p)\log_2(1-p)$? I understand that we want the entropy to be zero at $p = 0$ and $p = 1$ (no ...
0
votes
1answer
36 views

Study of systems of Linear Differential Equations?

Is there any area of mathematics that deals with and formalizes systems of Linear DEs, akin to how Linear Algebra deals with systems of linear equations? Does it provide any insightful results?
0
votes
0answers
19 views

Modeling predator/prey pursuit behavior?

I want to program a model of predator/prey pursuit behavior on a 2D topographical map (not predator/prey diff. eq. model!), primarily for fun, but I'd love to know if there's any literature or ...
1
vote
0answers
26 views

Solutions $n^2 = -1 \mod (p_n-1)$

Consider the equation $n^2 = -1 \mod (p_n-1)(*)$ where $p_n > n$ and $f(n) = p_n$ is the largest prime that satisfies the equation. $f(n)$ gives $p_n$ assuming there is a solution to the equation ...
0
votes
0answers
26 views

Naive explanation of the key concept of Teichmuller theory

I heard that Teichmuller theory has a great array of applications, is an active field of research, and has great relevance to other branches of mathematics. However, I have not the necessary ...
3
votes
1answer
102 views

New primality test, now what (publishing and proof)? [on hold]

Over my research, I found a new relatively simple way to calculate whenever a number is prime or not. What's exciting is that it runs in $O(\log^2 n)$ running time (where $n$ is the number of digits ...
1
vote
0answers
87 views

How do you remember “Mathematics” [on hold]

Sorry for a bad title/a silly question. How do you remember various theorems/techniques in mathematics especially advanced topics where there is no exercise or topics on what you have not done formal ...
1
vote
1answer
26 views

Significance and physical meaning of diagonalization of linear maps and bilinear forms, eigenvalues and eigenvectors

In linear algebra, I have studied the diagonalization of a linear map and of a bilinear form; and also the concepts of eigenvalues and eigenvectors. However, the importance of diagonalizing a linear ...
1
vote
1answer
37 views

Completely self-contained (and as elementary as possible) introduction to Teichmuller Theory

Can you recommend a completely self-contained and elementary (as much as it can be) introduction to Teichmuller Theory?
-2
votes
0answers
44 views

Are these Putnam ranges actually accurate? [on hold]

From Putnam 2013 Score cutoffs, statistics You see that fifth-place is $88/120$. Is that actually accurate? many people score from 20-40 points, so then I would assume fifth place at least to be much ...
7
votes
3answers
117 views

Moscow State Oral Exam

I have heard that during the 1960s, prospective students had to take an 'Oral Maths' exam (alongside written maths, physics and Russian literature). I having trouble imagining what type of exam this ...
1
vote
0answers
49 views

Advance mathematics but not basic mathematics? [on hold]

Here is the issue, As a high school student I have explored several area of mathematics, complex analysis, real-analysis, number theory, but now I cant seem to do simple SAT questions!? A simple ...
1
vote
0answers
36 views

For a given integer $n>1$ , for which type of rings $R$ is it true that $(xy-yx)^n=0 , \forall x,y \in R \implies R$ is commutative?

For a given integer $n>1$ , for which type of rings $R$ is it true that $(xy-yx)^n=0 , \forall x,y \in R \implies R$ is commutative ? (It is obvious indeed that if $R$ is an integral domain or a ...
1
vote
1answer
32 views

How should I think when combining multiple inequalities?

When reading/writing papers, I have always find it not obvious when two or more inequalities are combined. For example, taken from my current research $$\text{Pr}(X \le ab) \le -a (1-p)^{-N} (1 - ...
-4
votes
4answers
166 views

How much bigger is 1 than 0? [closed]

Bear with me -- nonsense to ensue. How much bigger is one than zero? The obvious answer is one. One is one bigger than zero. The backstory: Greg Fishel on WRAL said something along the lines of ...
1
vote
1answer
33 views

Physically, what meaning have Taylor series which have their lower order terms equal to zero, but their higher order terms non zero?

Usually, when using a Taylor series to describe a function (which may itself be a model of some physical phenomenon), we often throw out the higher order terms, as they are quite small relative to the ...
-6
votes
1answer
83 views

useful exact sequences [closed]

There are some exact-sequences or long-exact-sequences that are great help in proving to prove some surprising theorem, or have some interesting applications. What's your favorite exact ...
0
votes
0answers
24 views

Collection of solved problems in linear algebra [duplicate]

Apart from Schaum's 3000 Solved Problems in Linear Algebra, what are some good collections of worked problems in linear algebra?
1
vote
0answers
55 views

Did psychologists really publish experimental support for $R_{3,3}=6$ [closed]

A friend of mine told me that psychologist or sociologists once published a result in which they noticed that in larger groups of children there always seemed to be three children who where all ...
0
votes
0answers
18 views

Give a suitable way to study Fourier Transforms:

Give a suitable way to study Fourier Transforms. In the website called the fourier transform, gives somewhat good approach to meet it. But, I need to clarify onething. I am doing my pure papers ...
1
vote
0answers
61 views

Do all mathematical fields require an algebra?

My understanding is that "algebra" refers to a specific field in mathematics. Here is Wikipedia's introduction: Algebra is one of the broad parts of mathematics, together with number theory, ...
2
votes
0answers
28 views

Why are equilibria so important?

In studying nonlinear systems of differential equations, unlike linear systems, it turns out that we are more interested in equilibrium points rather than general solutions themselves. I mean, look ...
9
votes
9answers
1k views

examples of functions with vertical asymptotes in real life

As a math teacher, I tend to get the class involved by finding real-life applications of the math- with functions and vertical asymptotes I am having trouble finding simple enough (rational) functions ...
1
vote
0answers
63 views

Removed due to revision [closed]

I need to revise a few things before reuploading.
0
votes
1answer
48 views

Euler's complete works

If Euler's works are still being published then what is this?: http://eulerarchive.maa.org/pages/E786.html Is it only some of his works? I thought "complete works" meant literally all. Thanks
0
votes
0answers
90 views

Question about the foundation of mathematics [duplicate]

I have studied mathematical logic and set theory as an undergraduate. I studied mathematical logic (propositional and predicate logics) before set theory. When I studied mathematical logic, I was a ...
1
vote
0answers
22 views

Proper usage for term, addend, factor, multiplicand, expression, formula

The definitions and usage of the following words seem to vary, depending on the source text: term addend factor multiplicand expression formula The words are being used in the context of ...
0
votes
1answer
47 views

Choosing a Project Topic.

I am a undergraduate student and recently i have been assigned to project (one of courses). But i have to choose my own topic. I want to work in the field of ...
1
vote
0answers
72 views

Grothendieck's obituary. Anybody know the background behind this story?

"In a subsequent letter to Leila Schneps, Grothendieck said he would be prepared to share his research into physics with her if she could answer one question: “What is a metre?" " Source: ...
0
votes
0answers
12 views

I can't login math exchange using firefox or MS IE [migrated]

I'm using Windows 7. Just uninstalled Google Chrome and installed firefox, but now I can't login. After Login it seems I logged in already: but when it automatically directed to the math exchange ...
1
vote
2answers
67 views

Building up mathematics from nothing / becoming a math hobbyist

I just did this Google search and the first hit was along the lines of what I was looking for, which is a set of statements, each one building on the ones before it that start from nothing and go on ...