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0
votes
0answers
9 views

What subjects properly belong in operations research as their “owning” discipline?

Warning: This is a soft question, hence I would make it a wiki-community post if I could. Operations Research involves a broad swath of disciplines, ranging from probability and statistics/stochastic ...
12
votes
10answers
996 views

Problems that are largely believed to be true, but are unresolved

Are there unsolved problems in math that are large believed to be true, but for reasons other then statistical justification? It seems that Goldbach should be true, but this is based on heuristic ...
2
votes
1answer
26 views

Why Square Brackets for Expectation

I've often seen $\mathbb{E}[X]$ instead of $\mathbb{E}(X)$, but it seems variance is almost always $Var(X)$. E.g., Wikipedia for Expected Value and Variance. Is there a good mathematical reason for ...
8
votes
0answers
217 views
+200

Overview of nonlinear analysis, differential equations (ODE and PDE), dynamical systems, and mathematical physics, and their relationships

The fields of (i) nonlinear analysis, (ii) ODE and PDE, (iii) dynamical systems, and (iv) mathematical physics (e.g., electromagnetism, general relativity, gravitation, etc,...) are very huge, ...
1
vote
0answers
22 views

n points can be equidistant from each other only in dimensions $\ge n-1$?

2 points are from equal distance to each other in dimensions 1,2,3,... 3 points can be equidistant from each other in 2,3,... dimensions 4 points can be equidistant from each other only in ...
5
votes
4answers
227 views

How to not feel bad for doing math? [on hold]

I have a MsC and want to take a PhD in algebraic topology. Probably very few people in the world will have any interest of my thesis. They will pay me for doing my hobby. Its the only job I can think ...
0
votes
0answers
15 views

On (known) applications of fixed point theorems to some conjectures in elementary number theory

Let $\sigma$ be the classical sum-of-divisors function. Call an integer $n$ almost perfect if $\sigma(n)=2n-1$. The only known examples are $n=2^k$ for $k \geq 0$. Let $I(n)=\sigma(n)/n$ be the ...
0
votes
1answer
36 views

Learning math by analyzing/proving theorems?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
4
votes
5answers
161 views

Which are the operations used in mathematics? [on hold]

Everyone knows +,-,x,:,^. But I would really like to know which other operations exist, and what they do.
3
votes
1answer
52 views

Why are there so many conjectures in number theory and comparatively less in others?

My question is that : Why are there so many conjectures in elementary number theory and comparatively less in others? This is particularly weird because every topic in maths should have its equal ...
9
votes
2answers
169 views

Why is it so difficult to find beginner books in Algebraic Geometry?

I don't understand why it is so difficult to find a really beginner book in Algebraic Geometry. Let's take for example Fulton's algebraic curves: An introduction to Algebraic Geometry. I've already ...
4
votes
0answers
55 views

Why do so many mathematicians study and work on quantum field theory? [on hold]

Quantum field theory sounds a lot like physics, why are there a lot of mathematicians working in this area?
2
votes
0answers
30 views

Matrix Calculus

My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion ...
1
vote
0answers
15 views

How to visualize orientation of 3d objects

The way I visualize orientations of $1$- and $2$-dimensional objects is by an ant walking along a path. For a $1$d object (like a line/ line segment/ etc), just place the ant on the line and confine ...
3
votes
2answers
69 views

Why are radians used in calculus. [duplicate]

Ok, please ignore my silliness. So, why do we use radians in calculus and why is it considered more scientific than degrees. And how did mathematicians know or prove that radians would work for all ...
178
votes
64answers
40k views

'Obvious' theorems that are actually false

It's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true". Now, I know a fair few examples of things that are obviously true and that can be proved ...
5
votes
3answers
81 views

examples of non-abstract rings?

In group theory, it helped me a lot to use symmetry groups of geometrical objects like a triangle to understand the more abstract concepts. Are there rings with a similar low level of abstractness? I ...
4
votes
1answer
260 views

What branch of Mathematics does the study of Algebraic/Transcendental Numbers lie in?

I've always been fascinated by polynomials, ever since first learning them in high school. I absolutely adore the notion of 'playing around with the coefficients' and watching what happens to the ...
6
votes
8answers
2k views

How should I self-study calculus? [duplicate]

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic ...
16
votes
6answers
6k views

What books are recommended for learning calculus on my own? [duplicate]

I recently graduated with a degree in bachelor of science with a focus interactive and multimedia design. I had to opportunity to take 1 C++ course and 1 HTML course. I was also only required to take ...
1
vote
0answers
28 views

Inverse functions multivalued or not?

The square root of $y$ is usually defined as the positive solution $x$ to $y=x^2$, so the negative variant is not considered. In the same way, the inverse cosinus and sinus give the solution on ...
1
vote
2answers
39 views

How to improve visualization skills (Graphing)

Okay, so my problem is, that I have difficulty visualizing graphs of functions. For example, if we have to calculate the area bounded by multiple curves, I face difficulty in visualizing that how the ...
0
votes
0answers
18 views

Relationships Between Moduli Space and Objects They Parametrize

My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the geometry of the objects that the space parametrizes. As an ...
1
vote
2answers
59 views

How to avoid rote learning and perform deep learning?

I saw this question on brillant's facebook and I didn't even thought of/figure out to use difference of squares to solve this question. All the while, I have been a C student for Maths and barely ...
-1
votes
0answers
87 views

Greek School Exams-Calculus problem [on hold]

This problem was posed yesterday - along with 3 others of lesser difficulty - on the Greek national exams for the 3rd grade of Lyceum. This is the final class that determines University success. The ...
2
votes
2answers
52 views

Why does unary minus operator sometimes take precedence over exponentiation, and sometimes it doesn't?

How should I evaluate 2*-2^3? Which one of these two is the correct one? 2*((-2)^3) 2*(-(2^3)) I was wondering what was ...
5
votes
0answers
81 views

Review on Riemannian Geometry

I'm currently reading through Griffiths and Harris Principles of Algebraic Geometry, and the only subject in the foundational material section that I am not completely comfortable with is riemannian ...
50
votes
17answers
27k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
2
votes
1answer
27 views

What are the most important corollaries/consequences and applications of certain algorithms in elementary number theory? [on hold]

What are the most important corollaries/consequences and applications of Division Algorithm, Euclidean Algorithm and Fundamental Theorem of Arithmetic? I've been studying Elementary Number Theory for ...
-2
votes
0answers
38 views

What mathematician you would have liked to know? [on hold]

I know this is a classic forum question but, to be honest, I would like know your opinions... yours opinions, the opinions of the people that participate in mathexchange. I will ask to the moderators ...
1
vote
0answers
54 views

Source for (somewhat) Informal Mathematics of All Levels [on hold]

I've been around this site for a couple years now, but never formally made an account until now. I recently stumbled upon a new mathematics blog, and I wanted to know if it is a legitimate resource. ...
2
votes
0answers
17 views

Applications of module's length

I'm studying some theory about module's length and want to know motivation for this definition. I know that it's useful for intersection theory, but i know only one example from intersection theory: ...
1
vote
0answers
31 views

Algebraic surfaces in the language of scheme

Are there materials(lecture notes, books...) that deal with algebraic surfaces in the language of schemes? I am not good at/familiar with the analytic way, and also prefer the scheme-theoretic ...
14
votes
3answers
797 views

Transcendental number

While reading on Wikipedia about transcendental numbers, i asked myself: Why is it so hard and difficult to prove that $e +\pi, \pi - e, \pi e, \frac{\pi}{e}$ etc. are transcendental numbers? ...
14
votes
4answers
524 views

Categorical introduction to Algebra and Topology

I am self-studying Mathematics in my free time. At the moment I am reading books on Algebra and on Category theory. More exactly, I started working through the book $\textit{Algebra}$ by Serge Lang. I ...
106
votes
44answers
12k views

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

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 ...
29
votes
8answers
1k views

Is university math all about proofs? [on hold]

Do mathematicians do anything else beside writing proofs? It seems like all the "upper-division" math here are about proving something rather than solving for something i.e. instead solving for $x^2 = ...
-3
votes
0answers
29 views

Technological problems in mathematics [on hold]

Although this is a very soft question, what are some technological problems or advancements that could be made to make higher mathematics easier and doable on a, for say, a tablet? Putting mathematics ...
4
votes
1answer
121 views

What is mathematical structure?

When we have an isomorphism, between 2 groups or vector spaces let us say, then it is said to be structure preserving. An isomorphism exists when there is at least one mutually invertible morphism ...
1
vote
0answers
43 views

Integration of a symmetric function

I have a bit of confusion about the following situation. Let's assume that we have a symmetric function $f(x,y)$ where it has the property $f(x,y) = f(y,x)$ for all $x$ and $y$. $x$ and $y$ have the ...
1
vote
0answers
27 views

Induction graph theory - dealing with reducing the problem

I have a general question regarding induction in graph theory. Often I am required to use induction in order to prove a theorm. I have seen a lot of cases in which the reduction of the problem was ...
9
votes
2answers
166 views

Visual Proofs of Series Summations

I'd like to put together a compilation of visually geometric proofs of series summations. I have three famous 2D examples to clarify what I mean below, but other "visually geometric" proofs of an ...
2
votes
5answers
231 views

Is there an object in reality that is proven to be uncountable? [on hold]

I've always wanted to come up with a fairly concrete example of an object or realistic set that could be uncountable. Most of the sets I can think about, even the hugest ones, are always countable. ...
390
votes
25answers
76k views

How to study math to really understand it and have a healthy lifestyle with free time?

Here's my problem. I'm studying math and when I really work hard, I think I understand things very good, but that comes at a big cost: in the last few years, I've had practically zero physical ...
0
votes
0answers
70 views

Undergraduate Research review. [closed]

I am (an undergrad student) looking for online forum, group (or something like that) to discuss/review my ideas. Any suggestion ?? Where I can discuss my ideas?
12
votes
2answers
525 views

How to avoid stupid mistakes in calculus exams without checking the whole process?

Few days ago I failed my Calculus exams. And again it was mostly due to simple mistakes such as forgetting about minus in front of fraction, switching y coordinates of two points etc. The assignments ...
0
votes
0answers
31 views

Is group theory a generalization of number theory [on hold]

The applications of group theory are abound. Many mathematical objects are examined by associating groups to them and studying the properties of the corresponding groups. But number theory and Graph ...
1
vote
1answer
32 views

Exceptions in functions

I have recently started studying functions(topics such as periodicity, odd/even, into/onto, etc.). I was wondering if there are any strange exceptions to the general rule that is taught?
75
votes
22answers
1k views

Open mathematical questions for which we really, really have no idea what the answer is

There is no shortage of open problems in mathematics. While a formal proof for any of them remains elusive, with the "yes/no" questions among them mathematicians are typically not working in both ...
13
votes
5answers
185 views

Is 'Algebraic Number Theory' the study of the theory of algebraic numbers, or is it the study of the theory of numbers from an algebraic viewpoint?

Is Algebraic Number Theory the study of the theory of algebraic numbers? Or is it the study of the theory of numbers from an algebraic viewpoint? Or is it both? I know I can just find a wiki article ...