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3
votes
0answers
13 views

Is there a searchable database of mathematical objects that you can search by property?

For example, I could search for functions that are continuous, but that don't have differentiability, and come up with a continuous non-differentiable function. Or a smooth but non-analytical function....
0
votes
0answers
19 views

Real life illustration of the fact that rationals have measure zero

I wonder if there's any real world phenomenon that reflects the mathematical fact that $\Bbb Q^k$ has Lebesgue measure zero in $\Bbb R^k$, or put another way, the likelihood that we get a rational ...
0
votes
0answers
59 views

Phd topic in Field / Galois theory [on hold]

I just finished Masters degree in CS (Machine Learning) and I'm thinking of doing a Phd in Mathematics (I have first degree in math). I'm mainly interested in Finite Fields and Galois theory. What ...
0
votes
0answers
26 views

Calculus & Analytic Geometry VS Vector Calculus

This question may be applicable for Academia SE, however this is strictly math-oriented and requires math whizzes' opinions. I intend to go to a tech institute to get a BS majoring in Computer ...
-1
votes
1answer
58 views

Why is the notation for irrational number not mainstream? [on hold]

In everywhere you see the symbol for the set of rational number as $\mathbb{Q}$ However, to find actual symbol to denote the set of irrational number is difficult. Most people usually denote it as $\...
3
votes
0answers
41 views

How are varieties related polynomials?

My teacher says that varieties and ideals are related to each other while I tend to mix polynomials and varieties in my terminology. Could some explain how varieties are related to polynomials? And ...
0
votes
0answers
36 views

Is it possible to study Lie algebras without knowing too much of representation theory?

There's a course on Lie Groups that I'd like to take, but it seems that for various reasons it's a good idea to take Lie algebras along with it. But after having a brief look at the contents of the ...
1
vote
2answers
33 views

Can we define component of a matrix which is orthogonal to another matrix?

Given two vectors $A$ and $B$ one can easily find component of $A$ along $B$ and component of $A$ perpendicular/orthogonal to $B$ and vice versa. This is possible as we can define dot product of two ...
3
votes
3answers
63 views

Topology: is it ever good to write $x \in U \in \mathfrak{T}$

Sometimes I come across a sentence in my topology book that says, let $U$ be an open set that contains $x$ I can't help but write it down as: Let $$x \in U \in \mathfrak{T}$$ Is it good ...
2
votes
0answers
34 views

Why are sequences and functions notated differently?

Why do we usually write, e.g., $s_n$ for sequences, while functions are usually written as $f(x)$? Conceptually, aren't sequences just functions with a subset of the naturals, not of the reals, as ...
0
votes
0answers
10 views

References request: two-queue, one-server model with pre-emptive queue priority and finite buffers

Sorry of the title is a mouthful. I'm developing a queue model with the following characteristics: Two queues: One contains an infinite number of people (Queue A) while the other (Queue B) is ...
3
votes
0answers
40 views

Algebraic Geometry Project ideas related to Computer Science

I am a Computer Science Undergrad student with an interest towards Algebraic Geometry.I have just recently started and am currently reading Miles Reids' Undergraduate Algebraic Geometry(I have read ...
3
votes
1answer
109 views

Old books on calculus

I'd like to know if there are other old books of the same level of the classic and well-known books like Apostol, Courant, Spivak and Hardy.
3
votes
4answers
97 views

Is there an alternative way to represent the $\operatorname{diag}$ function?

In optimization, it is common to see the so called $\operatorname{diag}$ function Given a vector $x \in \mathbb{R}^n$, $\operatorname{diag}(x)$ = $n \times n$ diagonal matrix with components of $x$ ...
1
vote
1answer
58 views

Can someone come up with a better way to write $V = \operatorname{diag}(x_1,x_2)(Y-\mathbf{1}X^TY)$

$\newcommand{\diag}{\operatorname{diag}}$Let $X = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$, $Y= \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}$ I have a vector: $$V = \begin{bmatrix} x_1(y_1 - \...
0
votes
2answers
85 views

Why weren't “degrees” replaced with a more intuitive angle measure?

$\bf History$ It is speculated that the seemingly arbitrary number $360$ used to indicate a full revolution in degrees was chosen because the Babylonians counted in base $60$ and $60 \times 6 = 360$. ...
2
votes
2answers
50 views

Finding counterexamples in elementary set theory.

I had the following two problems: Find a counterexample for $f_*(A \cap B) \supseteq f_*(A) \cap f_*(B)$ and $ f_*(A-B) \subseteq f_*(A) -f_*(B).$ Where $f_*(X)$ is the image of $X$ under $f$ for ...
8
votes
4answers
109 views

Are there any tricks to remembering proofs of mathematical theorems?

Is there a way to quickly and thoroughly remember theorems? For example, proofs of the mean value theorem, or Rolle's theorem. Having to remember all of them off by heart has been quite tedious. ...
3
votes
3answers
73 views

Is there a mathematical reason why rotation in the counterclockwise direction positive and clockwise rotation negative?

This inquiry has recently come to me in my study of trigonometry and the unit circle. It was said right from the very start that counterclockwise rotation were positive while clockwise rotations are ...
2
votes
2answers
261 views

Algebraic structure on any infinite set

Given any algebraic object $X$, say group, ring, integral domain, etc., and a special subset $I$ of $X$ namely normal subgroup, ideal etc., it is always possible to put a structure on $X/I$ induced ...
1
vote
0answers
37 views

What is the intutition behind the negative exponential ? in linear logic?

The positive exponential ! has a very satisfying interpretation in terms of the standard resource interpretation of linear logic. Given a resource $a$, we know that $!a$ means an infinite supply of $a$...
4
votes
1answer
38 views

Is it possible to express an integral equation inside of a convolution

Given $$u(t) = \int_0^t y(\tau) d\tau$$ Consider a convolution type of integral $$W = \int_0^t\lambda^{t-\tau}y(\tau) d\tau$$ $\lambda$ a positive real number Is it possible to write $W = f(u(...
3
votes
1answer
55 views

Unsure on which sources to choose related to Calculus

I tried to get into Spivak's Calculus only to find that I've never been taught the type of Math presented there. First chapters talk about the properties of numbers, then mathematical induction, ...
1
vote
2answers
201 views

Is there a reason for the existence of prime numbers? [on hold]

Is there a reason for the existence of prime numbers, or is there a reason that some numbers are prime numbers, but others are not? Does the number theory have any answers or at least ideas about ...
-3
votes
1answer
22 views

Is it possible a (3x3) matrix (3x1) vector multiplication represent by quaternions?

Nowadays I am studying rotation using quaternion. I understand, that rotation can formulated a several way. In matrix notation: $$ \vec{v}^{new} = \bar{\bar{R}}^{new}_{old}\cdot\vec{v}^{old} $$ where $...
0
votes
1answer
18 views

Is convexity the most general dividing line between “easy” and “hard” optimization problems.

Just got started with Boyd's Convex Optimization. It's great stuff and I see how it directly subsumes the all-important linear programming class of models. However, it seems that if a problem is non-...
0
votes
3answers
171 views

Are there important situations where we study false statements as if they were true?

I know of two situations resulting from asserting that a false mathematical statement is true (by this we assume that the statement has been made to be a mathematical axiom and that it must be true ...
2
votes
0answers
40 views

Big Rudin directly after baby rudin?

I'm a high school student who went through Rudin's Principles of Mathematical analysis a while ago in its entirety, except for the last two chapters. I bought Real and Complex Analysis too, and ...
3
votes
0answers
60 views

Are there any modern mathematicians whose research interest is in “Probability Theory”?

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
3
votes
0answers
59 views

Monads in monoids

This question is almost a duplicate of this one, but not quite. There the person asked about examples and intuition, I am asking about terminology and applications, and I am addressing my question ...
-2
votes
0answers
88 views

Looking for a constant from complex analysis, ( and maybe other interesting constants) [closed]

Looking for a constant that is in complex analysis, it is about ratio of two types of sets in complex analysis. I have tried googling, wikipedia to no avail. I think I read about a constant ratios of ...
2
votes
0answers
94 views

“admissible” maps from context

I have been reading Massey's Algebraic Topology and on page 158 came across the following "semi-mystical principle" which he says guides much mathematical research: Whenever we wish to gain ...
0
votes
0answers
53 views

Confusion about Saibians article about primes

Here : https://sites.google.com/site/largenumbers/home/1-5/2 Saibian claims that it was proven that infinite many twin primes exist. Did I miss something ? Isn't the twin-prime-conjecture open ?...
-1
votes
1answer
35 views

How can i best learn advanced calculus over two months? [closed]

I am currently a second semester physics student at a german University and have set the goal of learning a lot of advanced calculus over the semester break for myself. I am motivated to do this, ...
-2
votes
1answer
32 views

Redundant proof in Math paper

Recently, I read a published math paper and I found that in the excessive argument in the proof of one of its theorem. In fact, in my opinion, the redundant part is not even correct, because it ...
5
votes
1answer
157 views

Corollaries of the Yoneda Lemma in Analysis?

I am looking for some simple examples of how the Yoneda Lemma can be applied in analysis and probability theory and related fields. A simple candidate example that I can think of and somewhat ...
4
votes
4answers
211 views

Is any real-valued function in physics somehow continuous?

Consider the following well-known function: $$ \operatorname{sinc}(x) = \begin{cases} \sin(x)/x & \text{for } x \ne 0 \\ 1 & \text{for } x =0 \end{cases} $$ In physics, the sinc function has ...
1
vote
0answers
58 views

What is the Star of David theorem?

I came across a MathWorld entry for the Star of David Theorem, but it doesn't provide much context. I have never heard of this before, can somebody explain its significance and any applications it ...
0
votes
0answers
49 views

Next book in in learning Analytic Number Theory

I have just finished the book "Tom M. Apostol - Introduction to Analytic Number Theory". My aim is to reach to graduate level to do research, especially on Rationality/Irrationality and Algebraic/...
-1
votes
2answers
59 views

Is every finite category identifiable with a directed multigraph? (and vice versa?) [duplicate]

What seems implicit in this talk on youtube, is the claim that every directed multigraph (with loops) can be identified with a finite category and vice versa, if we consider the paths of the directed ...
6
votes
1answer
171 views

How to know if you are “tough enough” to study Algebraic Topology [closed]

I am graduating with a BA this summer and I am very interested in topology. I admit it, I never went that deep into topology and all I know is about point-set topology (metric spaces etc.) but from ...
-3
votes
0answers
56 views

Is it weird that I barely got a “C” in pre-calc but have nearly a perfect score in Calc I? [closed]

I'll admit that I absolutely hated pre-calc. I mean HATED it. The geometry (I really hate all things in elementary geometry, especially the ugly notation), the memorization of all the trig identities ...
3
votes
3answers
88 views

Is a pure mathematics degree worth it from a financial standpoint? [closed]

I know this isn't a math question but this has been on my mind for quite some time. I am a second year university student who is planning on getting a degree in pure mathematics. I really enjoy the ...
11
votes
1answer
139 views

Lonely theorems [on hold]

What are some instances of theorems which are especially unique in mathematics, i.e. for which there are not many other theorems of a similar character? An example I have in mind is Pick's theorem, ...
-2
votes
1answer
20 views

Maximum data storage in a paper sheet? which theory should I look for?

I'd love to study a problem: How much information can be stored in a blank paper sheet. with those considerations: "store in a sheet" means writte letters or numbers or equations, with a pen and a ...
20
votes
4answers
830 views

How do I tell if I am able to go to graduate school in math? [closed]

This is my first question on this site, and this question may sound disturbing. My apologies, but I truly need some advice on this. I am a sophomore math major at a fairly good math department (top ...
2
votes
0answers
77 views

Can Local Martingales be characterized only using their FV process and BM?

See Theorem 1 here. Theorem 1 Any continuous local martingale $X$ with $X_0 = 0$ is a continuous time-change of standard Brownian motion (possibly under enlargement of the probability space). ...