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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2answers
59 views

Self-studying differential forms and tensors

I am interested in understanding the generalized Stokes' Theorem. From my understanding, this theorem involves differential forms and exterior algebra, and tensors (to some extent). I'm not ...
1
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0answers
57 views

What are some really cool problems that involve “least squares and Eigenvalue problems”?

I am required to find a research topic in this domain, so I'm really interested in finding out what kind of problems are covered in this domain, and how others are using these techniques to solve ...
4
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6answers
134 views

Notable examples of “impossible” results ruled out by earlier barrier or no-go theorems or widespread beliefs

there is a certain style of type of proof in mathematics something like a "barrier theorem" but which also relates to widespread mathematical beliefs/ "conventional wisdom". an example would be the ...
3
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0answers
356 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
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0answers
32 views

How a proof like this should be written?

I'm studying with Apostol's Calculus I, and it has required me to carry out some proofs, which I'd never done before (which has turned out to be pretty neat, by the way). When proving a statement ...
2
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2answers
55 views

Banach Spaces which are not $L^p$

Most of the times, when I think of Banach Spaces I think of $L^p$ spaces. I would like to know if there is any Banach space which can not be written as $L^p$ space. Please also indicate any ...
2
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0answers
89 views

What is the legacy of Bourbaki?

As I was preparing a short lecture (for amateurs) on the mathematics of the '900, I realized that this year marks the 70-th anniversary of the founding of the Bourbaki group. I remember that Bourbaki ...
4
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0answers
70 views

Asperger's and math [closed]

I am 19, recently diagnosed with Asperger's syndrome. Question to anyone here who has AS: Has your AS helped you or held you back while learning math? If so, in what ways?
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1answer
80 views

What's With The Diagonal Morphism?

Given a morphism $X \to Y$ of schemes, we can construct a diagonal morphism $\delta: X \to X \times_Y X$ via the universal property of the fiber product applied to the identity map $X \to X$. ...
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1answer
43 views

Beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?

Calculus textbooks often have us calculate indefinite integrals as exercises. However, beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?
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0answers
20 views

Book for computational classes

Recently I started reading about computational classes in quantum mechanics. I just have basic experience in theory of computation. ( I am reading sipsers currently ). The papers I am reading keep on ...
1
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1answer
82 views

Starting mathematical education late

Degreeless autodidacts are doubtless viewed with at best suspicion, having countless holes in their mathematical knowledge, questionable methods, whose lack of academic qualifications understandably ...
4
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1answer
39 views

Why do we have to classify semisimple Lie algebras?

Almost all Lie algebras textbooks deal with the classification of semisimple Lie algebras. Why is it so important?
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2answers
103 views

What is the difference between 'thus', 'hence' and 'therefore'? [closed]

When explaining and writing proofs for certain things in my notes I find myself using these words interchangeably however I'm left to wonder if there is a certain protocol to follow when using them? ...
1
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3answers
106 views

Higly axiomatic geometry book recomendation

Recently I have started dipping my toes in mathematical waters besides calculus,and with varying success I have started learning bit of something about "everything". But I have one issue,namely I can ...
41
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6answers
1k views

What to answer when people ask what I do in mathematics [closed]

This is not really a math question, but I think that every mathematician and student in math (specially pure) struggles with this at some point. Inevitably at some point when we're talking with ...
2
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0answers
41 views

Lost Chevalley Manuscript

In the end notes of chapter 9 in Mac Lane's "Categories for the Working Mathematician", he mentions a lost Chevalley manuscript A systematic treatment of all possible properties of limits was ...
6
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0answers
162 views

Most efficient way to learn mathematics

So there's a lot of advice on how to learn mathematics most efficiently, and it mostly revolves around doing problems, asking questions, and considering all possible generalizations. However, I was ...
6
votes
1answer
137 views

math.stackexchange has so many good mathematicians, were you all good at maths since school? [closed]

I'm afraid this question will be kicked out but I have to ask this. Were you all mathematicians brilliant and had good maths brain since you were kid? I was very bad in maths when I was in grade 8 ...
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2answers
66 views

What do you suggest I do to prepare? Thanks In advance!

Firstly, I'm in the military stationed overseas and I don't have access to a calculus class except online. My query is whether you think Calculus is something that can be studied by someone who has ...
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2answers
94 views

Why isn't the use category theory for graph transformation more prominent?

On the surface, it would seem that category theory would be a very natural and useful mathematical tool to address the subject of graph transformation. Yet, early indications from online searches seem ...
16
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3answers
280 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
1
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0answers
79 views

Textbooks: Spivak vs Lang vs Adams

Alright everybody, this is a fairly simple one. Obviously, Spivak's been mentioned very often on this forum, but I was wondering. A good friend of mine has decided to major in maths too. Now, the ...
4
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0answers
45 views

Books/“resources” for national math competitions.

I have started participating in math competitions an year ago. My target is to reach as far as I can in the future (USAMO and even IMO). I know that succeeding in these competitions requires a lot of ...
3
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1answer
69 views

Should I drop a class which I may not be ready for in order to pursue more time for personal study [closed]

This is my first time asking for advice on here, but I have seen some great advice given here. I am a first year student in a graduate program and I am currently enrolled in a course on advanced ...
2
votes
1answer
67 views

Shall I include my inventions in book or first publish them in some journal?

Dear and respected all. Today I am not going to post any problem right now but would like to get suggestion on the following matter. I do not know what step shall I take. I need your valuable ...
2
votes
3answers
56 views

Undergraduate summer activities in the US or Europe?

I a currently a college freshman and I would like to do something math-related in the summer. I will have taken all of the basic courses except for analysis and set theory by the end of the summer ...
0
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1answer
40 views

Defining the exponential and logarithm functions

As the title says, I'm wondering what is the "correct" (or maybe "most logically consistent") way to define the logarithm and exponential functions, $\ln(x)$ and $e^x$. It seems that in every course ...
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0answers
64 views

Introduction to algebraic number theory

How do you get started in algebraic number theory? I am an undergraduate going through a Bachelor in Applied Computer Science and I just finished my first course in Algebra. My university ...
2
votes
1answer
153 views

Software for drawing braid-related graphs

I am looking for a (preferably free) software that can draw braid-related graphs, such as and (Quoted from A Study of Braids By Kunio Murasugi, B. Kurpita) I have seen this question, but the ...
2
votes
1answer
81 views

Self-Studying Measure Theory and Integration

As the title says, I'm interested in reading about measure theory and integration theory on my own time, and was hoping for book recommendations, prerequisites, and things like that. As for my ...
1
vote
2answers
64 views

Suggestion For Books From experts on number theory

Regarding My Background I have covered stuff like 1.Single Variable Calculus 2.Multivariable Calculus (Multiple Integration,Vector Calculus etc) (Thomas Finney) 3.Basic Linear Algebra Course ...
1
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4answers
146 views

Euclid: What is the difference between a 'surface' and a plane 'surface'?

I've begun to study Euclid's Elements and i've a few questions regarding the difference between a surface and plane surface. A surface is said to be "that which has length and breadth only", it then ...
7
votes
1answer
67 views

What do you do when you are completely lost during a proof?

We've all been in the sort of situation where your professor is doing a proof/derivation, and the whole thing goes completely over your head (if you don't know what I meant, I envy you). And when they ...
2
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0answers
33 views

Derived Category in terms of Torsion Theory?

It is known that there's a bijection between hereditary torsion theories on, and localizations of, a fixed abelian category. Is this bijection natural? How/why not? How can I think of the derived ...
3
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0answers
67 views

Affine space terminology

I am wondering about the terminology "affine space" in algebraic geometry. As I understand it, given a basis field $k$, the affine space $\mathbb{A}^n$ is simply the space of n-tuples $k^n.$ I know ...
2
votes
1answer
121 views

To find all odd integers $n>1$ such that $2n \choose r$ , where $1 \le r \le n$ , is odd only for $r=2$

For which odd integers $n>1$ is it true that $2n \choose r$ where $1 \le r \le n$ is odd only for $r=2$ ? I know that $2n \choose 2$ is odd if $n$ is odd but I want to find those odd $n$ for which ...
0
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1answer
64 views

what is required for a person to do well on imo

What kind of skill is required to solve IMO or Putnam sort of problems. Does one have to be a genius or just learn some tricks.
0
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1answer
56 views

How should I study Topology

My semester includes a course in General Topology which includes: 1.Topological spaces 2.Continuous Functions 3.Connectedness 4.Compactness 5.Separation Axioms 6.Product Spaces 7.Complete ...
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0answers
44 views

Exponential fields as structures with three binary operations.

The exponential rings and fields are usually studied as structures with two binary operations $(+,\cdot)$ and one unary operation $\exp(x)$ defined on a set $K$. Why not consider the exponential as a ...
0
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1answer
34 views

Avoiding getting 0 equals 0 in geometry?

In geometry problems, I aways set up various equations and then when I find something that is the same in two equations, I isolate it and set the remaining parts equal. E.g. if I have $a^2x+b^2=c$ and ...
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0answers
24 views

About non-zero divisors and related queries concerning endomorphism rings

Let $G$ be an abelian group. Then $\operatorname{End}(G)$, the set of all homomorphisms from $G$ to $G$, is a ring under addition defined as pointwise addition of functions and $.$ defined as ...
1
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0answers
73 views

Stirling's approximation via elementary methods

I was trying to think how I'd prove the asymptotic formula $n! \sim \sqrt{2\pi n} n^n e^{-n}$ to a student who could think like a mathematician but lacked a background in Taylor series, Riemann sums ...
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2answers
80 views

$1,2,\cdots,n$ or $1,\cdots,n$?

In mathematical writing, when should one write "$1,2,\cdots,n$" and when should one write "$1,\cdots,n$"? It seems to me that writing $1,2,\cdots,n$ is actually wrong if $n=1$ is allowed. When ...
4
votes
1answer
63 views

Does performance in math competitions accurately reflect natural aptitude in mathematics? [closed]

Many great and respected mathematicians have won accolades in math (ex: IMO), does that necessarily mean that these competitions reflect one's potential to be a great mathematician?
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0answers
54 views

Any online Legendre polynomial calculator?

Do you know if there is any online calculator to calculate Legendre polynomial's coefficients? And combined with a graphing utility would also be desirable. Thank you for your time and help.
4
votes
2answers
97 views

What is the algorithm hiding beneath the complexity in this paper?

So, I am a computer scientist (at least, I'm working to become one..) and I asked a question on here concerning some mathematics behind the Mandelbrot set. A reply I recieved pointed me to this paper. ...
0
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2answers
62 views

Elementary algebra book for review/revision

What books are there that cover elementary algebra, but are not bloated with pedagogically padding?. I searched in this website and the web in general, but the books I could find about elementary ...
4
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3answers
157 views

Do you know any almost identities?

Recently, I've read an article about almost identities and was fascinated. Especially astonishing to me were for example $\frac{5\varphi e}{7\pi}=1.0000097$ and ...
2
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2answers
107 views

Is there a math website to study math from a mathematician point of view (ie proof oriented?)

I´m a student of the University of Puebla, Mexico, and I think that we lack of exigence there so I want to study math on internet to improve my education. I have already looked sites like edX, but I ...