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4
votes
2answers
51 views

Looking for details on historical math anecdote

My memory is very sketchy here so bear with me. A fairly prominent 19th or 20th century mathematician was captured by a military force, probably invaders. He claimed that he was just a civilian, a ...
2
votes
0answers
48 views

What are some topics of advanced number theory every young geometers should know? (soft question)

By "advanced number theory", I mean topics like arithmetic/Diophantine geometry, modular/automorphic forms and Shimura varieties. I'm interested in derived/non-commutative algebraic geometry, some ...
3
votes
2answers
40 views

How can one determine if a function should have parenthesis around their argument?

I have noticed that there are a select few functions that are acceptable if their argument is not in parenthesis. For example, here are a few functions I noted do not require an arguement: Trig or ...
3
votes
0answers
67 views

Why is recursion theory suffering from terminological bloat?

Several questions on MSE in recent months and most recently this one have made me feel that recursion theory is suffering from terminology bloat. Why have so many synonyms for "recursive" and ...
2
votes
1answer
24 views

Linear algebra MOOCs

I am a statistics student studying a module of linear algebra at the undergrad level. I was looking for MOOCs that might help me. I tried saylor which meets my syllabus but I cannot find videos for ...
3
votes
0answers
52 views

Collective name for algebraic structures

I am doing a thesis about various algebraic structures, primarely about groups, rings and modules (with maybe hint of algebras). However always having type out ALL of them constantly gets very tedious ...
0
votes
1answer
33 views

Question about Bachelor thesis and future lectures.

I just finished my exams one day ago but lectures will already reassume in less than two weeks. I currently finished my 5th semester and will therefore tackle my last semester of my bachelors. But I'm ...
1
vote
1answer
74 views

What is so special about Higman's Lemma?

Is there a motivational example of Higman's Lemma that brings out the true beauty and importance of Higman's Lemma? What is the thing that made so many people care about it? For an example, I was ...
0
votes
0answers
35 views

Is there a specific name for these methods of summation?

When calculating summation of series I use these methods ; Ex: Method One $$U_r=\frac{1}{(r-1)r(r+1)(r+2)}$$ $$U_r=\frac{1}{(r-1)r(r+1)(r+2)}\left[\frac{(r+2)-(r-1)}{3}\right]$$ Then ...
3
votes
2answers
102 views

Is category theory ambiguous? or it just is the case for beginners? [on hold]

First of all, I have to say that I'm not going to offend anyone/anything here; I just need some clarification/studying tips about category theory. I'm totally new in category theory and this happens ...
0
votes
0answers
44 views

Several options using Black-Scholes equation(s)

Could someone provide me some information about the modelling of several options at the same time by using Black-Scholes (probably coupled) equations? Any reference to papers and/or books shall be ...
0
votes
1answer
21 views

A Mapping from a Power Sets of a Vector Space to a Set of Subspaces of a Vector Space

I don't necessarily have a question on how to approach the problem. In this post, I want to get some clarification on how the problem is defining a certain function. The following question was given ...
-5
votes
0answers
46 views

Is it better to self-teach mathematics or get a tutor? [on hold]

What is the advantage of each? What is the disadvantage of each? Any personal anecdotes / experiences?
0
votes
1answer
20 views

Alternative methods to solve DLP for $GL_{3}(\mathbb{F}_2)$

Is there (or rather what is) a more elegant/efficient way to solve the DLP for $g^x=h$ in $GL_3(\mathbb{F}_2)$ where $$g=\begin{pmatrix}0 &1 & 1 \\ 1 &1 &1 \\ 1&0&1 ...
0
votes
0answers
17 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
0
votes
1answer
23 views

Proving uniqueness using $\dfrac{\partial}{\partial y}$? [on hold]

I remember in the beginning of my undergrad linear differential equations class (while or before we were introduced to linear ODE's), we proved the uniqueness of a solution to an IVP by taking the ...
2
votes
0answers
17 views

Are there useful visual representations of magmas?

In group theory we have Cayley graphs. Are there analogous or anyway useful visual representations of magma structures? I am unsure about how to construct a graph representing, for instance, a free ...
0
votes
1answer
45 views

Math for a computer engineering graduate course [on hold]

I'm going to take a master's course in Computer Engineering. Now I've not taken a CS course in my undergrad, hence my knowledge in some of the core areas of CS like algorithms are limited. I'm quite ...
1
vote
0answers
30 views

Is class of graphs with eigenvalue $1$ of any particular importance?

Are graphs with eigenvalue $1$ of multiplicity more than $1$, important one? Please guide me to any book or article discussing such graphs.
1
vote
1answer
157 views
+50

Is it to the students' advantage to learn the language of infinitesimals?

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
2
votes
3answers
113 views

Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
5
votes
1answer
93 views

Why isn't finite calculus more popular?

I'm reading through Concrete Math, and learning about finite calculus. I've never heard of it anywhere else, and a Google search found very few relevant sources. It seems to me an incredibly powerful ...
1
vote
0answers
23 views

What does “loss of regularity” mean?

I have seen a lot the phrase "loss of regularity" in references regarding PDE. (For instance, there are questions like "do solutions of 3D Navier-Stokes equations lose regularity or not?") Could ...
1
vote
1answer
82 views

The magic of the morphisms

Given a set $X$. Let $S\subseteq X$ and consider $(X,S)$ as a very simple mathematical structure, lets call it a spotted set. Given two spotted sets, then a morphism $\alpha ...
1
vote
1answer
50 views

How does this picture called?

Some time ago I saw this in my teacher's room. She called this picture in honor of some scientists (Lagrange,Lie or Liouville, or some other, but I don't remember). Please, name this picture. Thank ...
0
votes
0answers
14 views

How to define and make the dot product of two continuous matrix?

I was thinking recently that i always learn algebra with discret basis. But in case where the basis is continuous, how can i define a continuous matrix and when it is define how can i do the dot ...
0
votes
0answers
16 views

Can we attach a space with discrete signal?

This question refers to the link https://en.wikipedia.org/wiki/Space_(mathematics) and https://en.wikipedia.org/wiki/Discrete-time_signal. My question is how can we associate a discrete signal with a ...
25
votes
19answers
510 views

What are some surprising appearances of $e$?

I recently came across the following beautiful and seemingly out-of-the-blue appearance of $e$: $E[\xi]=e$, where $\xi$ is a random variable that is defined as follows. It's the minimum number of ...
0
votes
1answer
62 views

The role of visualization and intuition in graduate and postgraduate math and developing it

In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf musicians and follows the same to mathematics. Mathmatics today, he argues, is mostly build on abstract symbolic ...
-7
votes
0answers
59 views

Can a picture be it's own pie chart? [closed]

Wow! can vote to close or vote down , but cant say it is correct or incorrect? So this image is going around, but some how I think the visual ratio of what is in the picture is not translated 1-1 to ...
11
votes
2answers
92 views

What is the main purpose of learning about different spaces, like Hilbert, Banach, etc?

I just started to learn about functional analysis and have started to learn about various spaces, like $L^{p}$, Banach, and Hilbert spaces. However, right now my understanding is rather mechanical. ...
2
votes
2answers
44 views

Unsolved problems in graph theory

Is there a good database of unsolved problems in graph theory?
1
vote
0answers
52 views

How to wite a Statement of Purpose for a Summer Program in Representation Theory. [closed]

I want to attend a summer research program in Representation theory,$\;$for that I need to write a statement of purpose or simply a write up, so I want to know prerequisites for this course, and what ...
0
votes
2answers
72 views

Non-abelian fundamental group on a path-connected space

I am doing a self-study of algebraic topology, and am having some difficulties comprehending the idea of a non-abelian fundamental group on a path connected space. (See for example Hatcher Exercise ...
1
vote
2answers
61 views

Memorizing Formulas for Differentiation

Once upon a time, I memorized the following formula out of laziness. Let $k(x)=\frac{f(x)^{g(x)}h(x)+i(x)}{j(x)}$. Then $k'(x)$ is as follows. ...
1
vote
0answers
84 views

Do math experts personally care that much about how mathematics is interpreted philosophically? (Platonism vs. formalism, for example) [closed]

Just wondering about how professional mathematicians feel about philosophically about mathematics: whether philosophy of math matters to them, what their personal views are, etc. I had a few teachers ...
1
vote
5answers
191 views

Why are the symbols of operations written on the left or right of the objects to which they apply? [closed]

I was wondering why operations, actions and other stuff in mathematics are always defined "on the right" or "on the left". Is that a reflex of our (western) way of writing? For example, japanese is ...
1
vote
1answer
35 views

Is there a measure which allows me to tell how closely something is to an ellipse?

Roundness is the measure of how closely the shape of an object approaches that of a circle. I am trying to find a similar measure which shows how closely is something to an ellipse. Is there any ...
3
votes
1answer
44 views

What Sort of Discovery Warrants Writing a Paper

I am a high school student who is deeply passionate about mathematics and I have written many different mathematical proofs. I was wondering what sort of discovery warrants writing a mathematical ...
0
votes
0answers
52 views

Learning outcomes of reading textbooks [closed]

So I've densely mined this site for the scholarly materials I need most. And have prudently written many of them down, so I can sort them if I see fit. But, are the books always the preferred method ...
-6
votes
1answer
119 views

Why do we teach Calculus in High School instead of, say, programming? [closed]

I was wondering "Why do we teach Calculus in High School instead of programming?" 'Calculus' only goes up to about partial derivatives, then its called different things like real analysis and other ...
0
votes
0answers
42 views

Record-holding mathematical proofs [closed]

Which mathematical theorems admit proofs that are extreme in some sense? Here is what I have in mind: The classification theorem for finite simple groups is the longest proof mathematics has seen. ...
13
votes
4answers
745 views

How to define “being inside of something” in the context of topology?

I'm a Psychologist and Neuroscientist with interest in math and I just started reading about Topology. I have to say it's not easy to grasp the concepts without a practical example, so I'm trying to ...
0
votes
0answers
12 views

Biorthogonal (discrete wavelet) noise bases?

I am slightly interested in discrete wavelet transforms (DWT), but so far I have mostly used already-derived and existing well-known wavelets, such as Daubechies, Cohen-Daubechies-Faveau, Symlets and ...
-2
votes
0answers
62 views

Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read? [closed]

I've noticed that many books that are difficult to read are considered some of the best. Why does hard to read indicate that it is rigorous? For example: Rudin, Apostol, Lang, Hungerford, Ahlfors, ...
2
votes
0answers
38 views

Why is a projective variety 'the best kind'?

In Hartshorne's AG, he discusses the classification of curves by birational equivalence class says 'based on the idea that a nonsingular projective variety is the best kind..'. What exactly makes a ...
1
vote
0answers
20 views

Infinite series, continued fractions, nested radicals and such - is there a general recursive algorithm theory?

The nature of infinity and irrational numbers (among other things) always gave me trouble. But recently I learned to think about infinite sequences in terms of recursive algorithms and their time ...
0
votes
0answers
32 views

Translation of a book

I am an undergrad studend, my professor told me that a good work I can do is to translate a book on universal algebra (subject which I like a lot) in my language. I'm asking if this kind of work is ...
0
votes
0answers
42 views

how to mathematically represent a matrix of vectors?

My problem is the following: I have a dataset in particular have $4$ dimensions, for didactic reasons I need to represent this dataset as a $m\times n$ matrix array such that the ($i$-th, $j$-th) ...
5
votes
1answer
1k views

Which is the most powerful language, set theory or category theory? [closed]

As far as I know, mathematics is written based on a language which can be for example set theory or category theory. My concern is about the power of these languages. How can we realize which language ...