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Questions tagged [soft-question]

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.

0
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0answers
8 views

Connecting information entropy to the prime number theorem for compression of numbers?

Prime number theorem states how often primes occur (approx. how densely they are distributed). The Shannon theorem of information entropy gives us a lower bound of how much data is at least required ...
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1answer
23 views

Summation of the series using definite integral:

I am self learning Real Analysis from Elementary Analysis: The Theory of Calculus by Kenneth A. Ross Today on this website, I learned this new technique to find the summation of series using ...
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2answers
51 views

academic career in stochastic processes [on hold]

I am second year bachelor math student. I made a decision to devote myself to the study of probability and stochastic processes. Right now I know calculus, little bit of analysis (Abbott), some linear ...
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1answer
17 views

About the definition of orbifolds

I am new to orbifolds. By reading the definition (classical ones, not in terms of stacks or groupoids), I am wondering why only finite group action is allowed in the definition of local charts. I am ...
1
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1answer
30 views

Redunduncy of Pasch's Axiom of Hilbert's Foundations of Geometry

I am baffled by Hilbert's Foundation of Geometry's Axioms because the relations are not defined. They are only described, not defined. For example, the notions of 'betweeness' or 'congruency' are any ...
2
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1answer
21 views

A Question About The Addition And Multiplication Principles In Permutations And Combinations

I am learning permutations and combinations in school, and there is something confusing me about the addition and multiplication principle. There is a specific situation where I'm not sure if I should ...
0
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0answers
24 views

A naive question about operator and partition

I'm at the beginning of an University Class about Mathematical Methods for Physicians. During the last lesson, the theater introduced the operators and, to clarify the concept, said, "operator ...
2
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0answers
33 views

Is there a notion like “graded linear independence”?

I am looking for a suitable notion to discribe the following property for $\{f_i\}$. Let $R=k[x_1,\ldots,x_n]$, $\{f_i\}$ is a set a some homogenous polynomials of degree $2$ (or more general, of ...
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0answers
59 views
+50

How to think about a solution of a Backward Stochastic Differential Equation

Given a drift coefficent $g$ and a finial value $\xi$ one can consider a BSDE which we denote $e_{\xi}(g)$. A solution for such an equation is a pair adapted pair $(Y,Z)$ such that $Y_{t}=\xi + \int_{...
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4answers
1k views

How To Tell When Order Matters Or Not

I have encountered a problem involving combinatorics: My solution to it was $(4\cdot3\cdot2)+(5\cdot3\cdot4)+(6\cdot5\cdot4)$. The textbooks solution to it, however, was I would understand the ...
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0answers
13 views

What does Hilbert's second axiom of connection mean? [duplicate]

Here are the first 2 axioms of connection from Hilbert's Book: I, 1. Two distinct points $A$ and $B$ always completely determine a straight line $a$. We write $AB = a$ or $BA = a$. Instead ...
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1answer
56 views

Question about the rigor of Cantor's diagonalization proof

Diagonalization proceeds from a list of real numbers to another real number (D) that's not on that list (because D's nth digit differs from that of the nth number on the list). But this argument only ...
2
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2answers
43 views

In what area of math are “events” studied?

I was browsing mathematics articles on Wikipedia when I stumbled across this page: https://en.wikipedia.org/wiki/Event_structure. I had never heard of this before, and searching on google didn't seem ...
3
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0answers
128 views

Proving a Mathematical hypothesis using Physics

We know that mathematical models of physics phenomenas needs to becomes more and more sophisticated as our observations become more precise and comprehensive by utilizing more advanced instruments ...
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0answers
64 views

Rudin vs Zorich. [on hold]

I am looking for a real analysis text for self study. I have thoroughly studied Spivak's Calculus and Abbot's Understanding Analysis and covered the first few chapters from Rudin and done the ...
0
votes
1answer
52 views

Is Baby Rudin Outdated?

I don't mean for this to sound like blasphemy, but I've heard this before. One of my analysis professors said something along the lines of "Baby Rudin is great if you need to learn how to write proofs....
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1answer
41 views

Modified conjugate gradient methods for densely optimized calculations?

Sometimes when solving very sparse equation systems $$Ax = b$$ with conjugate gradient using computers, if $A$ is a very sparse matrix, it can be difficult to utilize the hardware computational power ...
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0answers
49 views

Non-infinitesimal differential operators, do they exist?

I already know they do exist in signal processing, I have built many myself. It is a whole art to do so in any discipline that handles noisy data. But is it possible to find out which ...
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1answer
123 views

Concerning Michael Atiyah Prove of RH [closed]

A recent paper by Michael Atiyah claiming to have prove the Riemann Hypothesis. Have professional mathematicians approve of the claim?
2
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1answer
53 views

Who for the first time defined abelian categories?

Who for the first time defined additive categories? Who for the first time defined abelian categories? I am guessing it should be in an algebraic geometric paper, but who and when? Any reference will ...
3
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0answers
41 views

Is problem solving a inborn skill or a skill which takes lots of hard work and lots of paper?

I asked this because I find myself in situations which trouble me deeply. I solve a deep interesting problem, I learn a new concept, its good but a single question which I'm not able to do, leaves me ...
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0answers
24 views

Class of functions being continously logarithmically differentiable?

In analysis, one often talks about functions which are $C^1$,$C^2$,..., $C^\infty$ et.c. Does there exist some similar concept for how many times something is logarithmic continuously differentiable? ...
3
votes
1answer
56 views

Counterexamples in Group Theory and Linear Algebra

I am studying Group Theory from Basic Algebra(Nathan Jacobson) and Linear Algebra by Hoffman and Kunze. The exercises in both the books are interesting. However when I try to solve question papers of ...
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1answer
28 views

Are there equivalents of fields, groups and whatnot with hyper operations?

I was curious as multiplication is really just a shorthand addition, so whats so special about it? Could we generalise to all hyper operations? Does there exist algebraic structures with these ...
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0answers
11 views

Name for generalization of affine functions on a Lie group

Consider a Lie group $(G,\circ)$. I'm interested in particular in finite-dimensional matrix Lie groups. The next best thing to an affine (often called "linear") function on this Lie group is $$ q\...
2
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2answers
85 views

Being successful in mathematics depends on hard work or intelligence? [closed]

I really need to ask this question. Perhaps my question is against the rules of the MSE. I am an IMO participant. I only joined once and I only managed to solve $2$ questions. ($14+1$ points). I've ...
6
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1answer
61 views

Roadmap to Iwasawa Theory

I haven’t found any posts on this, so I figured I would ask. Beyond learning basic algebra (rings, groups, fields) and complex analysis, what must one study if they want to start learning a good ...
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0answers
15 views

Clifford Algebras vs. Complex Numbers [closed]

Is there any immediate advantage to the usage of Cayley-Dickson constructions over Clifford algebras besides a preference of notation?
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0answers
30 views

Is there a name for family of these “well behaved” functions.

I am looking for right nomenclature for functions that exhibit following two properties $\max f(x_1,\cdots,x_n)<\infty$ $f(x_1,\cdots,x_n)\rightarrow 0 \quad \text{as}\quad x_i>N_i, \quad \...
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votes
1answer
64 views

Examples that show that AC is not that natural

I recently took a course in set theory and I was wondering the following: Let's "accept" that the axioms of $ZF$ are all natural and close to our intuition. As we know, $ZF$ can neither prove $AC$ ...
1
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1answer
32 views

Artificial vs naturalness

I don't know if it is appropiate to ask this, but I'm a little bit confused when mathematicians say a problem is artificial or has artificial methods. That one would prefer what is natural. I quite ...
0
votes
1answer
17 views

What notation would you use to indicate element-wise exponentiation?

The context is I have a matrix of feature vectors $x = [x^{(1)}\ \ x^{(2)} \ \cdots \ \ x^{(n)}]^T$ but each $x$ is raised to the powers $0 \leq j \leq M$. So it looks like this: $$ \left[ \begin{...
2
votes
1answer
47 views

Is this “A unified theory of logic”?

(Apologies for the (near) click-baity pun title.) I want to point out that I do have doubts about posting this since it's a very soft question that could just as well fit in at philosophy....
1
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1answer
37 views

Motivation for the definition of a differentiable structure on a manifold

I'm writing a report on differentiable manifolds and while I know that using an atlas of smooth charts gives a incredibly useful definition of what it means for a function on a manifold M to be ...
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1answer
50 views

What does the drift and diffusion coefficent of a solution to an SDE tell us in general?

Solutions of SDE's are most often written of the form $$X(t)=X(0)+\int_{0}^{t} \beta (X,s)ds + \int_{0}^{t} \alpha(X,s) dW(s).$$ I think about this as essentially the same thing as $$dX(t)=\beta (s)...
2
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0answers
29 views

Auctions - Placing Points to get into Classes

At my university there are not enough places in every class to accommodate every student. The scheme the university set up to solve this problem is as follows: Each student gets $1000$ points per ...
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0answers
24 views

What is the relationship between information in the sense of Shannon entropy and information for the human brain?

In an informatic theoretic sense, complete randomness maximizes information. For instance, an image of randomly distributed black and white pixels has a very high entropy/information. For a human ...
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0answers
83 views

Motivation of the Continuum Hypothesis

Why do mathematicians care about the Continuum Hypothesis? Does it have philosophical implications? If it was true or false, would it have had some sort of implications in mathematics? Does the ...
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0answers
15 views

A question about reduction forumulae

In my old college calculus textbook, Calculus of a Single Variable by Ron Larson and Bruce Edwards they list the reduction formula for the integral, $\int\csc^nu du=-\frac{\csc^{n-2}u\cdot\cot u}{n-1}+...
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0answers
10 views

How to select set of functions for convolutional orientation estimation?

If we have a function with neighbourhood, say $f({\bf x}), |{\bf x}| < R$ and we want to estimate candidate points $\{\bf x_0,\cdots, x_N\}$ for which some rotation that has happened to another ...
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0answers
63 views

Do there exist functions which are differentiable everywhere but analytic nowhere?

Once upon a time, when the earth was still young and innocent I studied one complex variable. In this course I learned that a function can be complex analytic, but that there are far fewer functions ...
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1answer
16 views

Intuitive understanding of complex tori

First part: I want to understand intuitively when two complex structures on a torus agree. Is it true that it all just comes down to the fundamental lattices being similar, i.e., having the same ...
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0answers
33 views

Null homologous loop and orientable surface

I am reading Algebraic Topology: A First Course written by Greenberg and Harper. On page 67 of this book it is stated that Let $\gamma$ be a loop in $X$ regarded as a map $f:S^1\to X$. For $\chi[\...
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0answers
49 views

What's a good way to get an intuition for making forcing posets?

A while ago, I took a long break from set theory and came back recently. Now, I've been more able to understand concepts which used to be completely foreign to me, for example ultrapowers and mice in ...
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0answers
15 views

Tensor fields or operators of order $\geq 2$ being diffused by tensor fields of order 2?

Background: I am aware that in for example physics tensor fields can be used to describe things like properties of materia. Like heat conduction in macroscopic media (imagine a thermos, heat can flow ...
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0answers
65 views

Soft question about mathematical finance-Is it really applicable?

I met with one of my professors today. For some background, he is a professor in the mathematics department who studies statistics (specifically kernel density estimation and nonparametric curve ...
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2answers
50 views

Equations of two circles coincide (Soft question)

As the title suggests, I would like to ask if I have two equations of circle that coincide, are they considered tangent to one another? I am currently working on a proof of Feuerbach's Theorem (...
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0answers
9 views

A case of discrete filter factorization.

Based on this question, where in the language of signal processing the difference of a self convolution and a lazy filter becomes the convolution of two other filters. One slightly longer and one ...
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1answer
23 views

The restrictiveness of assumptions

Sometimes we can make assumptions without loss of generality. Sometime we restrict the problem a lot, sometimes just a little - it is with hardly any loss of generality. What is the jargon for the ...
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0answers
25 views

detecting the position of an error

I am looking for code that detect an error and it's position (or an aproximation of it), this is more than an error detector code but a little less than a correcting code. Do you know something like ...