# Tagged Questions

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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### 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 ...
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 ...
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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### 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 ...
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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### 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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### 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 ...
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 ...
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 ...
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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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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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### 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)...
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 ...
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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### 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 (...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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.
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### 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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### 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 ...
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### 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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### 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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### $1,2,\cdots,n$ 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 ...
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### 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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### 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.
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### 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. ...