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1
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1answer
53 views

Is this a correct perspective?

Consider I have a sensor which is measuring some disturbance and I am converting the disturbance into complex numbers at a regular rate. I have done it for some time and therefore I get a series of ...
0
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1answer
45 views

Unknowledgable of single variabled integral

Browsing Stack-Exchange and other sites, I have noticed this come up quite a few times, an integral with only one letter or number! This would be a great example: $$\int_{a}$$ What in the world does ...
1
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1answer
33 views

Introduction to Lebesgue Integration for Statistical Use

I am studying statistics at the graduate level and have a moderate background in real analysis however I unfortunately have no experience with Lebesgue integration. Does anyone have some recommended ...
2
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1answer
85 views

Where does the “CW” in CW-complex come from?

I've heard people say that the "CW" in CW-complex comes from the "CW" in JHC Whitehead, though nobody has ever given me a reference for this. Does anyone know where the "CW" in CW-complex comes from?
0
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1answer
40 views

Prerequisites for Cox's Galois Theory

I am planning to read Cox's book 'Galois theory' but I don't know any abstract algebra. In the preface which you can read here there is no indication of the assumed knowledge. Could someone please ...
5
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1answer
78 views

Elegant applications of advanced techniques to “olympiad” problems

I am interested in applications of somewhat "advanced machinery" (with respect to the usual machinery involved in these cases, which is usually elementary) to olympiad or (high school-level) contest ...
1
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0answers
21 views

Example of a theory that requires infinitely many axiom schemas

Before asking this question, I want to know if anyone has formalized what an axiom schema is. Assuming that there is a formalization, many theories we normally encounter have a finite number of axiom ...
6
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0answers
86 views

When a function is a dimension?

The concept of dimension is used in many different contexts. Generally a dimension is a function that has as domain some family of sets ad has value on a set that, in the most common situations, is ...
4
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1answer
75 views

Order in writing composed morphisms

When we have a function $f: A \rightarrow B$ between two sets, and we want to explicit that we are applying it to some element $x \in A$, we write $f(x)$. After this, is natural to write $f(g(x))$ ...
3
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7answers
401 views

Grasping the concept of equivalence classes more concretely

I have read about equivalence classes a lot but unable to understand exactly what they are. I know about equivalence relations, but I am having a hard time understanding what equivalence classes are ...
0
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1answer
46 views

Examples of how abstract algebra is used to find concrete solutions to a mathematical model?

All references I've seen to abstract algebra show how it helps in the representation of mathematical models...are there any examples of using abstract algebra to calculate actual solutions to a ...
4
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0answers
55 views

Alternative Proof of Heine-Borel Theorem

This is regarding the proof of Heine Borel Theorem for closed intervals on real line as given in Hardy's Pure Mathematics. Heine-Borel Theorem: Let $[a, b]$ be a closed interval with $a < b$ and ...
5
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3answers
136 views

Explain branches of geometry for non-mathematician

Some background - I'm an advanced physics undergrad and lately was motivated to self study basic contemporary geometry to get a better grip on general relativity (maybe there is a more appropriate ...
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8answers
816 views

How to explain your area of study to non-math people [duplicate]

I'm sorry in advance if here is not the suitable place to ask this question, and people can feel free to vote to close this if that's the case. However, since I'm not sure about this issue, I'll ask ...
5
votes
2answers
156 views

Chess rating calculating algorithm

In competitive chess tournaments, there is a complex rating system that evaluates your rating based on how you do well you do playing games. I am referring to the FIDE system not USCF. Are there FIDE ...
2
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3answers
123 views

If $AB\not=BA,$ then do $A$ and $B$ have to be matrices

Is this solvable? Or are there other things that fit the bill for $A$ and $B$?
0
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1answer
63 views

Why is functional analysis so obsessed with sequences?

Beginning functional analysis I thought I would learn about generalized properties of functions and operators but yet I am flipping through pages after pages of texts on cauchy sequence, convergence, ...
1
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0answers
20 views

L1 and L2 regularization and L1 and L2 space

I am looking to characterize the difference of the function obtained in the solution process of $L^1$ and $L^2$ regularization. It is known that $L^1$ regularization gives sparse solutions. In $L^2$ ...
1
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0answers
59 views

Recommendations for a thorough logic textbook

I'm looking for a (possibly introductory) textbook on logic that covers the motivation behind conventions in logic, like the definition of the implication. Prof. J. Lau has an excellent webpage, ...
1
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2answers
130 views

Which should I study first: Logic or set theory?

I'm an undergraduate student in a college of sciences and technics studying maths, physics, computing and some chimestry so we studied elementary materials in logic and set theory. As I am interested ...
-2
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2answers
56 views

Function undefined at non-integer values [closed]

Is there a function $f(x)$ which is not defined at integer values? Please do NOT answer $f(x) = \begin{cases} a, & \text{if } x \in \mathbb{Z}, \\ \text{undefined}, & \text{otherwise} ...
10
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2answers
186 views

Natural isomorphisms: what is the status now of “the Eilenberg/Mac Lane Thesis”?

The Church/Turing Thesis that we all know and love asserts that every algorithmically computable function (in an informally characterized sense) is in fact recursive/Turing computable/lambda ...
12
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0answers
122 views

A “generalized field” with $q$ elements, when $q$ is any number?

It is well-known that if a finite field has $q \in \mathbb{N}$ elements, then $q$ is prime power and $q > 1$. However, various modification of the concept of a "field" have been made in order to ...
6
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0answers
196 views

Becoming an Interuniversal Geometer [closed]

Apart from the extensive amount of studying, are there reasons why I should or should not go into Interuniversal Teichmuller theory when I get older? Is there already a second generation of ...
2
votes
0answers
22 views

composition of relations and multiset relations

As is well known, composition of relations is defined as $$R\circ S = \{(a,b):\exists x: (a,x)\in S \land (x,b)\in R\} \tag 1$$ This is formally the very same definition as for function composition. ...
5
votes
2answers
148 views

Characterizations of the cross-ratio

$$ (z_1,z_2;z_3,z_4) = \frac{(z_1-z_3)(z_2-z_4)}{(z_2-z_3)(z_1-z_4)} $$ What are the most prominent or most interesting theorems of the following form? Theorem: The cross-ratio is the only function ...
3
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0answers
93 views

Convergence to $\frac{1}{\pi}$

Mathematicians of all times found approximations for the value of $\pi$ using infinite sums. But I was asking to myself: is there any infinite sum that approximates $\frac{1}{\pi}$?
42
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14answers
7k views

Can math be subjective?

Often times in math, ever since Kindergarten and before, math has been defined by the fact that there are only one answer for problems. For example: $1+1=2$ and $\frac{d}{dx}x^2=2x$. What I am showing ...
1
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1answer
48 views

Database of unsolved problems in mathematics

Is there a good database of unsolved problems in mathematics?
2
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1answer
92 views

What shall I write for a reason for applying graduate school for algebraic geometry?

I'm a undergraduate applying a graduate school this year and now I'm writing a letter of self-introduction. To be honest, I don't know what exactly is algebraic geometry and I think 99% of ...
1
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1answer
41 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 ...
7
votes
2answers
258 views

Recommendation for books on topology (light reads)

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
48 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 ...
14
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0answers
116 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
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0answers
26 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 ...
2
votes
0answers
55 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 ...
2
votes
0answers
58 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. ...
0
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0answers
16 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 ...
2
votes
1answer
31 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 ...
6
votes
1answer
137 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 ...
8
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0answers
72 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
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0answers
47 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 ...
0
votes
0answers
34 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 ...
0
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1answer
36 views

Difference between stochastic process and chaotic system [closed]

Can anyone please point out some difference and similarity between stochastic system and chaotic system?
1
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3answers
65 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
40 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
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1answer
73 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
103 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
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1answer
175 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
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1answer
58 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 ...