For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

learn more… | top users | synonyms

1
vote
1answer
19 views

What is a prime ideal?

I am having some trouble understanding the concept of a prime ideal in ring theory. I have researched what a prime ideal is and the simplest answer I got was this: An ideal $P$ of a commutative ...
2
votes
0answers
40 views

Status of Ultimate L

I have not heard much from Ultimate L development. What is happening now? The last time I heard from it was like 5 years ago, and I haven't heard much since then. Apparently, Hugh Woodin moved from ...
4
votes
1answer
51 views

Recommendation for books on topology (light reads) [on hold]

Are there any books on topology which can be read without having to do any exercises and look up definitions every second line? Something to read while relaxing, and not meant to replace a textbook ...
2
votes
0answers
46 views

Where are multisets used in mathematics? [duplicate]

Outside of factorization (integers into primes, polynomials into irreducibles) where else are multisets naturally useful in mathematics? [edit] Deleting. If anybody wants me to stop, please say so ...
0
votes
0answers
41 views

Should you create a dictionary when learning mathematics? [on hold]

Usually when I need to look up a term, I just consult the internet. But recently I found myself in an unfortunate situation where I was camping high up in the mountains and needed to look up the ...
8
votes
1answer
69 views

What is the importance of modules in algebraic geometry?

I have been trying to teach myself the basics of algebraic geometry. I understand the basic premise, how we define geometry spaces (algebraic sets and schemes) in terms of commutative rings. And I ...
1
vote
0answers
31 views

Book similar to Milnor's book [on hold]

I just finished to read "Topology from the differentiable viewpoint" of Milnor, and for me this was the perfect mathematic book : short, clear with really beautiful results proved at the end. (I'm ...
1
vote
0answers
22 views

Stochastic process, Fourier transform and $L^2$

Consider a time domain signal received at a sensor $x(t)$ over some time $t$, and we have performed Fourier transform on $x(t)$ to obtain $X(w)$. While performing Fourier Transform to find the ...
-1
votes
2answers
69 views

Is this mathematics journal reputable? [on hold]

A little background, I have written and had the necessary people revise my first paper that will not be supported directly by an institution (meaning I'm pretty much on my own) and am curious as to ...
0
votes
0answers
32 views

Positive definite function and covariance matrix.

I tend to view positive definite function as a function of elements of positive definite matrix. A reference is: https://en.wikipedia.org/wiki/Positive-definite_function My question in essence: is ...
2
votes
0answers
37 views

How do I make sure that I've learned and mastered a part of the Visual Complex Analysis book?

So I'm reading Visual Complex Analysis by Tristan Needham. It's a beautiful book that's not very hard to understand at all; however, I just don't know if I have sufficiently learned what I'm supposed ...
1
vote
0answers
27 views

Analytical approach of representation theory

I'm doing M.Sc. in mathematics. I want to do my M.Sc. thesis on Representation theory in analytic approach. So I start reading the book Representations of Finite and Compact Groups by Barry Simon. ...
1
vote
1answer
53 views

Number Theory or Abstract Algebra first? [on hold]

I have the option of choosing Number Theory or Abstract Algebra as a course. However, I can only choose 1 of them! Which is preferable to undertake first? I am somewhat used to rigorous mathematics, ...
0
votes
0answers
10 views

On statistical analysis and sudden changes in data

Here we see the value of Euro against the United States Dollar, provided by BBC approximately 10.00 GMT on the 6th of June, 2015. On the 5th Greece had a referendum, and it's outcome of "No" to ...
0
votes
0answers
43 views

Inner Product Properties And Applications

In every calculus or analysis class we are told that the concept of inner product is very important, and that its applications are vast, diverse, and extremely useful. I don't think there is a single ...
2
votes
1answer
24 views

Example of Non-separable stochastic process.

This question is related to the link: http://www.encyclopediaofmath.org/index.php/Separable_process The link provided a basic definition of separable Stochastic process. I felt all the process under ...
4
votes
1answer
96 views

Differential topology versus differential geometry

I have just finished my undergraduate studies. During last two semesters I've taken two subjects dealing with manifolds: Analysis on manifolds, containing: definition of manifold, tangent space (as ...
7
votes
0answers
47 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
0
votes
0answers
41 views

How to effectively learn from and use Ramanujan's notebooks? [duplicate]

I will come back and elaborate on the question if necessary (I must be off for a while...). But I'll try being specific. I have all four of Ramanujan's notebooks, with their respective Errata ...
1
vote
1answer
23 views

Difference between stochastic process and chaotic system [on hold]

Can anyone please point out some difference and similarity between stochastic system and chaotic system?
-1
votes
0answers
41 views

Research areas lying at the confluence of Analysis and Geometry [on hold]

I wanted to get expert opinion on what are the areas of active research lying at the confluence of Analysis and Geometry. Two areas that I have heard about are : (1)Geometric Analysis and ...
1
vote
1answer
64 views

How to master the Calculus? [on hold]

I believe its a broad topic to ask a question about but the strange fact is I'm not confident at it. I do know the formulas and I've also done quite a few sums but I'm never confident that I can do a ...
0
votes
0answers
16 views

Question about “non-question” types of exchanges. [migrated]

Sorry if posting this question in the wrong forum, it is more of a meta-question. What if I have something interesting to discus or get feedback on, but am not able to formulate a question about it? ...
1
vote
3answers
63 views

History of convolution

Let $f, g\in L^{1}(\mathbb R),$ we may define the convolution of $f$ and $g$ as follows: $f\ast g(x)= \int_{\mathbb R} f(x-y)g(y) dy, (x\in \mathbb R).$ It is well known that it can be defined on ...
2
votes
0answers
38 views

Calculus on Spaces other than $R$

I was thinking that all that the real numbers (and the complex numbers similarly) need for calculus to work is for them to be a field and a complete metric space, and probably have the usual field ...
7
votes
1answer
53 views

Topological space $\nRightarrow$ Metric space $\nRightarrow$ Normed space $\nRightarrow$ Inner product space (Examples)

If I have an inner product space, the hierarchy goes: Inner product space $\Rightarrow$ normed space $\Rightarrow$ metric space $\Rightarrow$ topological space. The reverse, however, is not always ...
3
votes
1answer
85 views

Difference between proof-based calculus and analysis?

When I asked a teacher at school what the difference between calculus and analysis he said that calculus is essentially analysis without proofs. So where does proof-based calculus lie? Is it somewhere ...
8
votes
1answer
141 views

Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis

I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without ...
3
votes
1answer
54 views

A negative third derivative implies a positive first derivative at a point.

Let $f$ be three times differentiable on $\mathbb{R}$ with $f(0)=f(1)$, and for all $x\in[0,1]$, $f'''(x)<0$. Prove that $f'(\frac{1}{2})>0$ I actually have a proof of this question using ...
2
votes
0answers
20 views

Mixed vs Equal Characteristic Local Rings

This is more of a vague, intuitive type of question, so perhaps there isn't anything too concrete anyone can offer. I am trying to get a sense of precisely why working with local rings of equal ...
35
votes
6answers
2k views

Is there something between summation and integration?

Let's take a general function $f(x)$, we can do a summation like: $$\sum_{k=m}^n f(k)$$ And we can do an integration like: $$\int_a^bf(k)dk$$ The basic difference between the two operation is that ...
1
vote
1answer
38 views

Is there a way to generate groups, rings, fields, etc.? [closed]

There are ways to generate a list of numbers $a_1, a_2,...a,n$ such that no $a_i,a_j$ share any factors, mainly by letting $a_{n+1}=a_n^2-a_n+1$ with $a_0>1$, my question is: is there a way to ...
3
votes
1answer
109 views

What motivates the definition of a ring in abstract algebra? [closed]

I've read a lot of questions about rings but I still don't know why they are useful/ I'm sure they are, but I don't know why. Are their properties somehow used in proofs or as foundations for ...
0
votes
0answers
20 views

Order of 'Strength' of inequalities

There have been times when we solve an inequality and we get the reverse sign of inequality. The reason is quite simple- we did not choose a strong inequality. So my question is- Is there an order of ...
2
votes
2answers
390 views

Changing from Positive to Negative

I may mess up a little bit...Sorry for that! When we want a summation to go negative in case of odd numbers and positive otherwise , we use: $$\sum\limits_{i=1}^{12} \color{red}{{(-1)}^i} 2x^3 $$ ...
3
votes
1answer
59 views

Reference Book for Calculus

I've made this post as detailed as I can so as to give you a fair idea of my level. Calculus (particularly Integration) is my passion and frankly I spend all my free time learning as much of it as I ...
1
vote
3answers
77 views

Can we generalize Aleph numbers to non integer values? [duplicate]

I'm really new to those kind of arguments so don't call me mad but I was wondering if there is a way to define an infinite set which cardinality is an Aleph-number like: $\aleph_{\frac 12}$. I have a ...
3
votes
0answers
37 views

Classical geometry vs. p-adic geometry

I am interested in learning more about $p$-adic analysis and some of the geometric theories that are commonly used. However, it seems that many of the tools there are developed from analogous ...
1
vote
1answer
40 views

What is Skorohod's Represntation Theorem Saying?

From Wikipedia: Let $\mu_n, n \in N$ be a sequence of probability measures on a metric space S; suppose that $\mu_n$ converges weakly to some probability measure $\mu$ on S as $n \to \infty$. ...
9
votes
1answer
105 views

What are some easier books for studying martingale?

What are some easier books for studying martingale? They are defined to be comprehensive but easier than Roger and William's martingale book. For example, to study Q and F martingales? It should ...
3
votes
0answers
71 views

When can we use Differentiation under the Integral sign?

Let me elaborate, 'Feynman's' trick ranks up in the top ten on most people's list, right behind contour integration, for best ways to evaluate definite integrals. However, unlike contour integration ...
3
votes
4answers
117 views

Why memorize trig identities?

I want to be a mathematician or computer scientist. I'm going to be a junior in high school, and I skipped precalc/trig to go straight to AP Calc since I've studied a lot of analysis and stuff on my ...
4
votes
6answers
419 views

Elementary number theory - prerequisites

Since summer comes with a lot of spare time, I've decided to select a mathematical subject I want to learn as much as possible about over the next three months. That being said, number theory really ...
0
votes
0answers
40 views

Is there any practical use of this algorithm?

Example The exact solution of a DE $\frac{dp}{dv}=-1.4\frac{p}{v} $ with initial condition $(P_1,V_1)=(1,1)$ can be obtain by solving the integral ...
1
vote
2answers
126 views

Is Fermat's Last theorem equivalent to $1 + 1 = 2$? [on hold]

I got into a debate with someone concerning whether FLT is equivalent to $1 + 1 =2$. He said common sense tells us it isn't equivalent. However, I disagreed. Since both are provable statements, they ...
2
votes
1answer
42 views

Desk Reference Question: Linear Algebra and its Applications by Lay or Strang? Or Handbook of Linear Algebra?

I would like a good working desk reference for linear algebra for someone in applied mathematics (no proving abstract theorems). I saw the Handbook of Linear Algebra as well, but I am concerned it may ...
0
votes
0answers
31 views

Does anybody know a good introduction to homology?

Essentially what the title says. I need something that will give me a decent introduction into homology theory. I don't need too deep of an understanding, just enough to get through a paper I'm ...
3
votes
0answers
44 views

Examples of calculus on “strange” spaces

I am interested in examples of calculus on "strange" spaces. For example, you can take the derivative of a regular expression[1][2]. Also the concept extends past regular languages, to more general ...
1
vote
1answer
45 views

Uses of stalks of sheaves and germs

I am trying to understand the motivation behind defining stalks of sheaves, but I suppose my complex geometry is a little weak. I know they are meant to represent germs of holomorphic functions at a ...
0
votes
0answers
19 views

Convex functionals, min-max of linear functionals, etc

I was reading in this book on the well-known Courant-Fischer min-max Theorem, which states that if $\lambda_1(A)\geq \lambda_2(A)\geq \lambda_n(A)$ are the $n$ eigenvalues of a $n\times n$ Hermitian ...