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

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2answers
60 views

Proving “if and only if” statements

I have the following proposition: $m - n = p - q$ if and only if $m + q = n + p$. From what I understand, $A = B$ if and only if $C = D$ means two statements: if $A = B$, then $C = D$ and ...
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3answers
323 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 ...
47
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6answers
2k views

What to answer when people ask what I do in mathematics

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 ...
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0answers
53 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 ...
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1answer
695 views

Most efficient way to learn mathematics [closed]

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 ...
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1answer
212 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
80 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 ...
8
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2answers
131 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 ...
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3answers
399 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 ...
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0answers
167 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 ...
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0answers
88 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
104 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
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1answer
87 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
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3answers
96 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 (...
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1answer
77 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
99 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 (Göttingen)...
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1answer
265 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 ...
3
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2answers
314 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 ...
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2answers
119 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 (...
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4answers
1k 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
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1answer
111 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
45 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
81 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
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1answer
134 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 ...
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1answer
116 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.
1
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1answer
79 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 ...
6
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1answer
158 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
38 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
85 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
85 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
76 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
173 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
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2answers
144 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. ...
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2answers
170 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 ...
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4answers
191 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 $$\ln(2)\sum_{k=-\infty}^{\infty}\frac{...
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2answers
139 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 ...
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1answer
97 views

what does it actually take to become a mathematician

Does one have to be an amazing problem solver to become a mathematician or its the passion and dedication? Can every mathematician solve the IMO problems? What is required to solve IMO ...
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2answers
35 views

Pythagoras triples

Regarding the parametrization of the pythagora's triples: $x=p^2-q^2$ $y=2pq$ $z=p^2+q^2$ When $x=0, p^2=q^2$. Given that $\gcd(p, q)=1$, is there a contradiction? Why(not)?
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4answers
128 views

problems in mathematics

Where can i find long and interesting problems related to analysis (or to mathematics in general) in order to prepare for the Phd qualifying exams (outside of usa) i don't want research problems, but ...
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1answer
29 views

How to write an equation for a fixed range scale

I'm writing a report and I need to use an equation to represent a relationship in the Methodology section. Here's how it works: Everything in between 3 and 8 is between 0% and 100% Everything below ...
0
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1answer
41 views

How (the graphic of) a $\mathcal C^1$ but not $\mathcal C^2$ function looks like

We know examples of functions (obviously we are in the context of real valued functions) which are continous but not derivable; the simplest is $x\mapsto|x|$. In particular we have a precise graphic ...
2
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0answers
120 views

A book like Michael Spivaks Calculus, for multivariate Calculus.

Is there a book like Michael Spivaks Calculus, that is for Multivariate Calculus? That is a "real analysis" multivariate calculus book?
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0answers
105 views

Decorating eggs

I came across this question as I have been helping someone decorate styrofoam eggs by gluing wrapping paper onto it. The question is quite simple but I found myself stumped. Given an egg what is the ...
2
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0answers
50 views

Set theory, motivating factors [duplicate]

Set theory seems to pop up in many different fields of mathematics. As someone with a CS degree, I've only encountered very basic set theory; dealing with non-specific sets, and their intersections, ...
4
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1answer
116 views

Opportunities for Mathematicians to Work in Biological/Disease Areas

Yesterday, I was reading some of the question Can I Use My Powers for Good? and it got me thinking. It's quite an old question (3 years), so I don't want to resurrect it and also my own question's ...
3
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1answer
63 views

Spaces vs. Structures

Examples of spaces I've come across include vector spaces, inner-product spaces, and metric spaces. Examples of structures I've met include rings, fields, and groups. I have always understood spaces ...
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4answers
1k views

Can Number Theory be visualized?

So I was thinking about a hard euclidean geometry problem, when it hit me just how much more difficult it would become without the aid of a diagram. This got me thinking: Wouldn't it be great if we ...
2
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0answers
62 views

(Concrete) mathematical aspects of programming

It is often said that progamming is mathematics as it "makes use" of "discrete mathematics". However, I would like to ask a more concrete question: what are the concepts of a programming ...
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0answers
54 views

Benefits of combinatorial reasoning?

What I usually do instead of counting something, I form a polynomial whose coefficients count it and go from there. If you had to convince someone why they should learn combinatorial reasoning what ...
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0answers
90 views

Solution for an ODE given only at discrete points

The problem I have: For each $n \in \mathbb N$ I have $$\begin{align} x_0^n & \in \mathbb R \\ h_n & \in \mathbb R \\ x_k^n & = x_0^n + k \cdot h_n \text{ for } k \in \{0,1,\ldots n\} \\ ...