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1
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1answer
40 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
48 views

Are these Putnam ranges actually accurate? [closed]

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
119 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
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0answers
49 views

Advance mathematics but not basic mathematics? [closed]

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
39 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
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1answer
34 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 - ...
1
vote
1answer
34 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 ...
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
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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
19 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
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0answers
66 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
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0answers
29 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
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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
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0answers
67 views

Removed due to revision [closed]

I need to revise a few things before reuploading.
0
votes
1answer
56 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
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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
48 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
74 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
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2answers
73 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 ...
6
votes
1answer
77 views

Theorems discovered without observation

Can you name me a few theorems that were discovered without first observing some special cases? In other words, by brute logic: Starting from the known and logically deducing the unknown? EDIT: As an ...
6
votes
0answers
61 views

Why is topological group not a popular topic?

In Japan, there are many universities with a formal course about topological group using the classic by Pontryagin. Yet topological group is not studied in a formal course in many other countries, ...
6
votes
0answers
142 views

Do hom-sets really live in the category Set?

In familiar introductory books on category theory, one of the first examples of a category given is Set. And what category is that? Typically no explanation is given at this stage. But of course ...
3
votes
1answer
74 views

Intuitive Approach to de Rham Cohomology

The intuition behind homology may be summarized in a sentence: to find objects without boundary which are not the boundary of an object. This has geometric meaning and explains the algebraic boundary ...
1
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2answers
68 views

Graph Theory Software with simple GUI

To the best of my knowledge I cannot find, on this site, any graph theory program resources. I am looking for a program where I can draw nodes and edges and most importantly drag and drop vertices ...
2
votes
2answers
118 views

What are some things that mathematics students know, but others don't

Someone asked it on Quora and I answered to my best. What other things I can add to it, as it is well received there and carries nice information to non-mathematics people. Here is my answer ...
0
votes
1answer
49 views

Have Information Theoretic results been used in other branches of mathematics?

consider this a soft-question. Information Theory is fairly young branch of mathematics (60 years). I am interested in question, whether there have been any information theoretic results that had ...
0
votes
1answer
48 views

Math Competition (Math Olympiad)

In the future, I will take part in a Maths Olympiad Here's my question: This questions is mainly regarding The Math Theory involved. (not mainly problem solving). What basic concepts ( Mathematics ...
0
votes
4answers
182 views

Why do transcendental numbers exist?

(This is a revision of the below question, which was not clear. If I have used incorrect terminology, please offer corrections.) Given the sets A and B, B contains transcendental elements relative to ...
1
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0answers
42 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
5
votes
0answers
64 views

Examples of categorical adjunctions in analysis and differential geometry?

In a lot of introductory texts on category theory, it seems like the majority of examples come from algebraic topology, algebra, and logic. Are there any good examples of adjunctions in analysis and ...
3
votes
1answer
41 views

Geometrical or Physical significance (interpretation) of the inner-product $\langle A,B \rangle := Trace (AB^t)$ over $M_n(\mathbb R)$

$\langle A,B \rangle := Trace (AB^t)$ is an inner product over the vector space $M_n(\mathbb R)$ of all real matrices of size $n$ , I would like to know whether this inner-product has any Geometrical ...
1
vote
1answer
39 views

Characteristic of a ring: intuitive explanation

I know the following definition of characteristic of a ring: it is the smallest positive $n$ such that $$\underbrace{a+\cdots+a}_{n \text{ summands}} = 0$$ for every element a of the ring, if $n$ ...
2
votes
1answer
107 views

An endless loop in a program that search for mathematical theorems and proofs − a milestone? [closed]

I don't know if there exist computer programs working on its own, trying to find and prove theorems, delivering proofs and go on searching for new theorems. But if (when) there are such programs, ...
0
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0answers
59 views

New proofs of the Fundamental Theorem of Calculus

Apart from the standard one, are there any other proofs of the Fundamental Theorem of Calculus which have been published recently?
2
votes
1answer
81 views

How to remember all the proofs in mathematics

I have a problem where I forget the proof of a theorem after some time without reworking it out. However, my teacher said that he was able to prove a theorem even without reworking it out for a long ...
1
vote
1answer
50 views

Is Tetris a packing or covering problem?

I am looking for some information about packing and covering problems. Some texts mention Tetris without further elaboration. Now, I am wondering if Tetris is a kind of packing or covering problem. ...
3
votes
0answers
66 views

(Soft Question) How active an area of research is Non-Commutative Geometry? [closed]

I am currently an undergraduate, but I am considering applying for a phd in algebraic geometry or a related field. I am quite interested in the link between non-commutative geometry and theoretical ...
0
votes
3answers
128 views

The obivious “why”-questions [on hold]

Whenever someone is introduced to a mathematical concept but doesn't stuck to it long enough there are always this "why"-questions. Why is $8+2=2+8$ etc. The answer to that is obvious I think for the ...
2
votes
2answers
66 views

British “S-Level” Mathematics Books

The British S-level exams (not to be confused with A-levels or O-levels) were said to be challenging exams that were used to select who got a place at the University of Oxford or Cambridge. Is anyone ...
0
votes
0answers
34 views

Is there a name for functions “opposite in nature” to orthogonal functions?

Suppose a function $f_n(x)$ is orthogonal over some domain $[a,b]$, then we have $$\left|\int_a^b f_n(x)f_m(x)dx\right| \left\{\begin{array}\\>0\text{ if }n=m\\ =0\text{ if }n\neq ...
14
votes
5answers
600 views

OK at Applied Math but Fail Pure Math?

Summary. Name Applied Math as AM, and Pure Math as PM. I want to succeed in PM but what am I doing wrongly? Am I too dumb, or is my brain unfit, for PM? Should I just stick to AM? Here, I read the ...
2
votes
2answers
305 views

An example of a great explanation or freely accessible article on a math concept

Question: Give an example of a great explanation or freely accessible article on a math concept (suitable at the undergraduate or lower level), and explain why you think it is great. Possible ...
2
votes
4answers
87 views

Book recommendation for Measure Theory

What book would you recommend me to read about measure theory and especially the following: Measure and outer meansure, Borel sets, the outer Lebesgue measure. The Cantor set. Properties of ...
88
votes
41answers
11k views

What's your favorite proof accessible to a general audience? [on hold]

What math statement with proof do you find most beautiful and elegant, where such is accessible to a general audience, meaning you could state, prove, and explain it to a general audience in ...
5
votes
1answer
193 views

What's the “real” reason a finite map has finite fibers?

This is a soft question. I have encountered two very different proofs of what seems like "basically the same theorem," and I want to understand how they relate and "what the real explanation is." ...
-4
votes
0answers
44 views

Why can't infinity be a number? [duplicate]

Why can't infinity be a number? All reasons why it can't that I come up with, require that it already isn't one. Yes you are right, by definition $\infty$ is larger than all numbers, take $\infty ...
2
votes
3answers
67 views

Examples of orthogonal/orthonormal functions which are not finite degree polynomials?

I've been reading "Fourier Series & Orthogonal Polynomials" by Dunham Jackson. Great introductory read for anyone interested by the way! My question is, what are other examples of Orthogonal ...
1
vote
1answer
43 views

Why is “random” in the definition of discrete random variable?

We defined discrete random variable as follows: Suppose $S$ is a countable sample space. Then a function $X:S\to R$ is called a discrete random variable. The lecturer made a note that the "random" ...