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-7
votes
1answer
131 views

Remarkable mathematics in the The Simpsons television show [on hold]

Notice: See this meta post that is currently addressing issues about this question post along with many of the most upvoted questions on MSE that are now closed thanks to unilateral moderator actions. ...
1
vote
0answers
27 views

What is the relationship between the circle, the oval, and the angle of tilt of a glass of water? [on hold]

Do to limited clean glass ware options this morning when I woke up with heart burn, I dropped 2 tablets of Alka-Seltzer into a 1/3 full of water Pokemon glass. The fizz-fizz effect was ...
0
votes
0answers
12 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 ...
2
votes
1answer
31 views

Why Square Brackets for Expectation [duplicate]

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 ...
2
votes
1answer
31 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
242 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
16 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
41 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 ...
3
votes
1answer
56 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 ...
4
votes
0answers
62 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?
3
votes
0answers
44 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
73 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 ...
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.
4
votes
1answer
264 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 ...
5
votes
3answers
82 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 ...
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
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
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 ...
1
vote
2answers
60 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 ...
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 ...
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 ...
5
votes
0answers
84 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 ...
-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 ...
2
votes
1answer
28 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
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: ...
9
votes
2answers
178 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 ...
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. ...
1
vote
0answers
33 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 ...
-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
122 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 ...
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 = ...
2
votes
5answers
233 views

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

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. ...
12
votes
2answers
527 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 [closed]

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?
0
votes
1answer
62 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
1
vote
1answer
52 views

Is Mathematics a branch of “Natural Science”? [closed]

Actually, I was seeking for top universities, which has mathematics depart, in Pakistan and I found one, namely Quaid-i-Azam University. Which is known for its Education in "Natural Science". Then I ...
6
votes
1answer
139 views

Does this curiousity have any meaning?

If $\pi$ is calculated to the $360$-th digit after the decimal point, the last digits are $360$ : ...
-16
votes
0answers
69 views

Please help? Because I need help? [closed]

Why does math have numbers????
0
votes
1answer
26 views

The difference between a matrix valued random variable and an $n \times p$ matrix of data

So I am totally new to the field of random matrices, but I was not sure about how they are applied. According to Wikipedia, a random matrix is "a matrix-valued random variable—that is, a matrix some ...
4
votes
1answer
75 views

Is general topology essential for applied mathematicians?

I am a second year undergraduate college student interested in applied math program. I hear a lot that general topology(e.g. the first half of Munkres' book Topology) is very useful, but is it really ...
13
votes
5answers
189 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 ...
7
votes
4answers
643 views

What is the motivation for complex conjugation?

I have been dealing with complex numbers for few years now. But when I've tried to think about the motivation behind complex conjugation, I was not sure. Let me write what I am working with. For a ...
1
vote
3answers
37 views

What book is good in studying beginning optimization?

Recently, I heard some talks about Optimization. And I am beginning to love that field. I want to study beginning optimization, what book can you recommend for me? Also what tips can you give to a ...
1
vote
1answer
66 views

Understanding cofibration sequence

Recently I'm studing some basic homotopy theory. An important brick of the exact sequence of cofibration is the following sequence: $$X \stackrel{f}{\longrightarrow} Y \stackrel{i}{\longrightarrow} C ...
4
votes
2answers
68 views

Modeling curves in nature?

On my windowpane, I've traced the contour of a distant line of hills as they appear to an observer sitting in the sill. This short curve can of course be viewed as a continuous and single-valued ...
9
votes
3answers
151 views

What do groups and rings “look like”?

Taking undergraduate physics courses, I had to deal with Euclidean vectors often. In classes like Calc III, the concept was also there. I'm not sure if this is why, but I've always had a more ...