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0
votes
0answers
22 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 ...
4
votes
2answers
89 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
31 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 ...
2
votes
2answers
88 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 ...
8
votes
2answers
160 views

What is going on in this degree 8 number field that fails to be a quaternion extension of $\mathbb{Q}$?

This is a soft but very mathematically hands-on question. Hopefully it will be interesting to more than just me. Thanks in advance for your help in thinking clearly about what follows. I have been ...
0
votes
1answer
18 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 ...
0
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0answers
21 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.
-4
votes
0answers
44 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?
11
votes
2answers
91 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. ...
0
votes
1answer
18 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
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 ...
25
votes
19answers
475 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
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0answers
14 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?
1
vote
0answers
15 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 ...
14
votes
12answers
10k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
5
votes
1answer
104 views

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 - ...
5
votes
1answer
91 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 ...
0
votes
1answer
40 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 ...
18
votes
3answers
974 views

What are the applications of finite calculus

I'm reading through Concrete Mathematics [Graham, Knuth, Patashnik; 2nd edition], and in the section regarding Summation, they have a sub-section entitled "Finite and Infinite Calculus". In this ...
0
votes
1answer
63 views

Reciprocals of theta functions

I've spent the last few months with partial fraction expansions, and thought to create a function with simple poles over a lattice of zeros, like that of any of the Jacobi theta functions... but I ...
1
vote
0answers
22 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 ...
3
votes
1answer
58 views

The Mathematics of Finite State Automata

I am a final year undergraduate mathematics student preparing to undertake my BSc-HONS project, provisionally titled for the time being, "Finite State Automata and Regular Languages". Having had a ...
1
vote
1answer
79 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 ...
26
votes
9answers
8k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
0
votes
2answers
70 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
1answer
48 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 ...
6
votes
1answer
153 views

Is it worth proving every theorem you learn?

Ever since I determined mathematics - mainly set theory and number theory - was my main passion, and I began learning mathematics formally outside of the curriculum posed within secondary schools I ...
13
votes
1answer
219 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 ...
14
votes
3answers
4k views

Are one-by-one matrices equivalent to scalars?

I am a programmer, so to me $[x] \neq x$—a scalar in some sort of container is not equal to the scalar. However, I just read in a math book that for $1 \times 1$ matrices, the brackets are often ...
0
votes
0answers
15 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 ...
2
votes
2answers
40 views

Unsolved problems in graph theory

Is there a good database of unsolved problems in graph theory?
0
votes
0answers
46 views

Learning outcomes of reading textbooks [on hold]

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 ...
0
votes
1answer
60 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 ...
25
votes
6answers
5k views

Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program?

I have a computer engineering degree , and i have studied several mathematics courses like single variable and multiples variables calculus , complex variables , probability , numerical analysis ... ...
-7
votes
0answers
59 views

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

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 ...
1
vote
5answers
189 views

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

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
0answers
52 views

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

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 ...
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 ...
1
vote
0answers
83 views

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

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
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
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 ...
9
votes
3answers
314 views

Developing Mathematic Intuition

I'm an engineering student, currently working my way through the fundamental mathematics courses. I've done reasonably well so far—mostly A's and a couple of B's in Algebra, Statistics, ...
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 ...
2
votes
0answers
99 views

Number of non-isomorphic groups of square-free order $n$

$G$ is a group of order $n=p_1p_2....p_k$ then how to find the number of non-isomorphic groups of order $n$ where $p_i's$ are distinct primes I can find the number of number of non-isomorphic ...
13
votes
4answers
736 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 ...
72
votes
14answers
10k views

Can the golden ratio accurately be expressed in terms of e and $\pi$

I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the ...
-6
votes
1answer
116 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 ...
17
votes
3answers
2k views

Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus says the following: Theorem. If $f$ is the derivative of $F$ at every point on $[a,b]$, then under suitable hypotheses we have that $$\int_{a}^{b} f(t) \ dt = ...
5
votes
1answer
125 views

Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer. Thank you!