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.

learn more… | top users | synonyms

104
votes
44answers
12k 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 ...
3
votes
0answers
55 views

Real Analysis book with pictures and ideas of proofs

I am taking real analysis course in my graduate class of Maths. My classes will start in 3 months. I have studied real analysis but not very rigorously. Whenever I see theorem I have no idea on how ...
10
votes
0answers
91 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
2
votes
0answers
24 views

Good starting point for learning noncommutative geometry?

Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical ...
11
votes
1answer
135 views

Has the age at which we teach Mathematics changed over the last two centuries?

My experience of learning Advanced Trigonometry and Calculus is that it was done to 17 and 18 year olds (School Curriculum in Australia). I assumed that it was similar in the UK, US and Europe. In ...
19
votes
5answers
1k views

Is 1+1 =2 a theorem?

A theorem is defined to be a mathematical statement that is proven to be true. The statement $1+1=2$ has definitely been proven in the history of mankind (Russel and Whitehead had once proven it in ...
0
votes
3answers
26 views

Looking for good intro book on differential equations

I am looking for a good book to study ordinary differential equations. My background is that I have successfully completed calculus 1 through 3. So this included derivatives and integrals, ...
0
votes
1answer
30 views

How to evaluate a squared sum?

I need (the name of) the formula to evaluate $(x_1 + x_2 + ... + x_n ) ^2$ . I know the question is not very interesting, but I am stuck and WolframAlpha also doesn't get my input. Thanks in advance
20
votes
1answer
2k views

What are some strong algebraic number theory PhD programs?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
0
votes
0answers
49 views

Which version of MIT Single Variable Calculus should one take? [on hold]

MIT offers nine versions of the single variable calculus course. five with course number 18.01..., and four versions under the course number heading "Supplemental." 1) Which do you recommend to ...
-4
votes
0answers
45 views
2
votes
2answers
88 views

Why are quadrants defined the way they are?

I was thinking about planes and things, and suddenly wondered why quadrants are defined the way they are, the first on the top-right, and so on. I wonder if this gives us any benefit, or if any ...
34
votes
2answers
970 views

What is this pattern called?

Back-Story I became interested in the patterns in multiplication tables for different base number systems a while ago. Specifically, the pattern made by the last digit of each number in the ...
4
votes
1answer
93 views

Where is Cauchy's wrong proof?

Allegedly, Cauchy mistakingly "proved" that pointwise convergence of continuous functions is continuous. I saw this somewhere in a book, and it is also in wikipedia: Uniform convergence. In his ...
1
vote
5answers
57 views

Is a pattern proof?

Let's say I want a formula that takes any number and makes it into 170, and I come up with a formula that I think does it. If I plug 1 into it, 2 into it, 3 into it, etc. up to a pretty large number ...
2
votes
0answers
37 views

Textbook +reference book in complex analysis

Which book can be used as an introductory textbook in complex analysis? I have some choices (more suggestions are welcomed) Marsden & Hoffman J.B. Conway Ahlfors Palka Lang Stein & ...
0
votes
1answer
30 views

Which discrete mathematics book do you think is better between Epp's and Rosen's for a clueless self-learner?

I am a programmer, and I want to become a machine learning researcher and a good software engineer. I dabbled with calculus, linear algebra, and real analysis for a few months when I was enrolled in a ...
1
vote
0answers
27 views

Referencing a Theorem in a Paper?

I'm making the final edits for a paper and I have a question more about the etiquette. I want to use a theorem from another paper and its obvious I have to cite it, but do I need to prove it too? I ...
0
votes
0answers
25 views

What are some genuine ways to define the derivative of a fractal?

Seeing the success of applying measure theory to generalize integration to fractals, I wonder whether or not there is a method to generalize the derivative to a fractal. Most courses start off fractal ...
2
votes
0answers
53 views

What is the point of basis vectors?

Why do we even bother with basis vectors? Why don't we just notate an element $x$ of an $n$-dimensional vector space $V$ as an ordered set $(x_1,x_2,...,x_n)$ and go from there?
2
votes
1answer
468 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
9
votes
2answers
471 views

How to introduce type theory to newcomer

I want to introduce (dependent) type theory to some friends having background in mathematical logic and set theory. To make this introduction easy I would like to give an informal presentation that ...
4
votes
3answers
220 views

OCR: some App to calculate the derivative on a line graph with iPhone/iPad?

Problem I have a set of points like the ones shown on the right hand side of the image. So for each 'Ships Head' there is a corresponding value for 'Deviation'. In this example we can treat west ...
3
votes
1answer
89 views

How is arithmetic overflow avoided by using the Dawson function over the erfi function?

I came across the term arithmetic overflow while reading up on the IEEE754 yesterday, and read up its definition and related terms as well. Today, while reading about the error function and its cousin ...
5
votes
1answer
144 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
8
votes
2answers
87 views

How would you explain a quadratic field to a beginner?

How would you explain a quadratic field to a beginner? Eg. how did the subject first start? All the modern stuff they use to explain it makes it really confusing how one should think about it in more ...
74
votes
15answers
7k views

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of ...
-1
votes
1answer
146 views

Who are the big names in Mathematics nowadays? [on hold]

The questions I pose are: Who are the big names in mathematics now? What branch do they study, what big problems are they looking at? I know of Wiles and Perelman (and I don't even know if those are ...
-1
votes
0answers
49 views

Why do some mathematics professors teach more/less courses than others? [migrated]

Not sure if this belongs on the Academia site, but since I'm a math major and the question is based solely on my observation of mathematics professors, I figured this site would be best. At my ...
5
votes
1answer
553 views

Why is unique ergodicity important or interesting?

I have a very simple motivational question: why do we care if a measure-preserving transformation is uniquely ergodic or not? I can appreciate that being ergodic means that a system can't really be ...
2
votes
1answer
42 views

Blow-up toric varieties.

I have to take a talk of an hour and I have to talk about blow-up of toric varieties. Can you suggest me some interesting examples that I can present? How can I find a good reference for the theory ...
6
votes
9answers
1k views

what is the definition of Mathematics ? [on hold]

we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically but the question is, what is mathematics ? how can we ...
2
votes
2answers
312 views

How come mathematics is applicable to the real world?

Before the dam breaks, namely, the one that holds the waters of accusations, I want to specify that the question I'm asking is a "reference-request", and therefore does have an answer. Often in ...
5
votes
1answer
66 views

Could the real numbers have been invented without the natural numbers

The real numbers are constructed from the rational numbers which are constructed from the integers which, in turn, are constructed from the natural numbers. But if we had no notion of the natural ...
21
votes
0answers
236 views

When are two proofs “the same”?

Often, we find different proofs for certain theorems that, on the surface, seem to be very different but actually use the same fundamental ideas. For example, the topological proof of the infinitude ...
3
votes
0answers
33 views

Generalizing convexity of sets

Let $X$ be a subset of some Euclidean space. We say that $X$ is convex if for any two points $p$, $q$ in $X$, the line segment joining $p$ and $q$ is also in $X$. But what if we loosen this definition ...
3
votes
0answers
38 views

What is the densest, most opaque way of saying two odd numbers add up to an even number? [on hold]

Here's what I've come up with: In $\mathbb Z$, any pairwise sum of elements in the $\langle 2 \rangle + 1$ coset is in $\langle 2 \rangle$. But there's got to be a way to make this even briefer, ...
9
votes
4answers
206 views

Algebraically, What Does $\Bbb R$ get us?

In terms of the basic algebraic operations -- addition, negation, multiplication, division, and exponentiation -- is there any gain moving from $\Bbb Q$ to $\Bbb R$? Say we start with $\Bbb N$: ...
0
votes
3answers
35 views

Proving limits via episilon-delta definition vs. algebraic manipulation.

In real analysis textbooks, limits are proved using the epsilon-delta definition directly. However, at some point, limits start being solved using algebraic manipulation. For example: $$\lim_{x \to ...
2
votes
1answer
81 views

Amazing integrals and how is solved it [closed]

There a lot of integrals, however many people solved it in different ways, we can find interesting integrals in Table of Integrals, Series, and Products. I wonder What is the most exciting integral ...
3
votes
3answers
127 views

What is it like to understand complicated/advanced mathematics?

Whenever I see very complex equations, they look, in a way, beautiful even though I don't understand them. This was directly taken from another question: "- Definition 1 - Given an open subset ...
1
vote
1answer
25 views

SDE Modeling: Ito vs. Stratonovich

In my SDE class last semester there were some hints that sometimes an SDE model makes more sense in the Ito sense, and sometimes in the Stratonovich sense. This was explained very briefly and vaguely. ...
0
votes
2answers
20 views

Given the solution to some differential equation, is the original equation necessarily unique?

For example, if I have the fundamental solution set $\{x^2\}$, such that $y(x)=Cx^2$ is the solution to some unknown differential equation, is it guaranteed that only one such equation exists with ...
1
vote
2answers
21 views

Confusion about division in rates.

I would really appreciate help with this because it's been driving me insane for a while now... I understand what "per" means in "$x$ kilometers per $y$ hours". What I don't understand is how to make ...
182
votes
88answers
15k views

Surprising identities / equations

What are some surprising equations / identities that you have seen, which you would not have expected? This could be complex numbers, trigonometric identities, combinatorial results, algebraic ...
76
votes
7answers
40k views
21
votes
9answers
1k views

Very good linear algebra book.

I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), ...
-2
votes
2answers
43 views

Do you have any good iOS app suggestions for taking notes? [closed]

Thanks for stopping by my thread. I'm an engineering student with an avid interest in Maths. I hope to do some kind of research in Maths someday. I really enjoy Maths and am doing a lot of reading so ...
34
votes
10answers
2k views

How do mathematicians find formulas? [on hold]

How do mathematicians find formulas? For instance, the area of a triangle is $$\mathrm{area}=\frac{\mathrm{base}\times \mathrm{height}}{2}.\tag{1}$$ When I study maths, the book I am using tells ...
3
votes
3answers
295 views

Textbook Recommendation: Topological Dynamics

I need to take credits satisfying a topology requirement, and can structure it myself. My field of study is dynamical systems, can someone recommend a textbook that handles differential ...