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0answers
17 views

Does the determination of integer values have a limiting efficiency?

I was reading this. The solution of the problem involves bounding with inequalities, however, to solve the inequality, one has to "test" values until the set of solutions includes an integer. In ...
0
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0answers
29 views

How do mathematician make sense of “outcome” and “events” in probability?

One of the biggest challenge for me to understand probability is to make sense of this concept of outcomes and events. To put it plainly, it just doesn't feel like mathematics anymore when we talk ...
4
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1answer
32 views

Stating the induction hypothesis

I would like to ask about the best way to state the induction hypothesis in a proof by induction. Just to use a concrete example, suppose I wanted to prove that $n!\ge 2^{n-1}$ for every positive ...
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1answer
13 views

Zeitz's ACoPS vs Larson's PSTP

Which of the following books is better to prepare for a mathematical competition at the undergraduate level? The art and craft of problem solving (ACoPS) or Problem solving through problems (PSTP). ...
1
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2answers
38 views

How to document solutions for future use? [on hold]

I'm taking courses of math at university level, it's kind of the equivalent of master degree in mathematics, I'm from Argentina. The way to learn mth in my university is this: We attend lectures, we ...
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0answers
49 views

Magic of the number $2000+15$ [on hold]

What is the most clever way of getting the number $2015$ using only addition, subtraction, and multiplication?
4
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3answers
53 views

Motivations for Hyperbolic Geometry

Why would one study hyperbolic geometry? I am only aware of the motivation where you give axioms for elementary euclidean geometry and then start to wonder wether the parallel axiom is necessary. You ...
2
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0answers
62 views

Struggling to stay at current course.

Disclaimer: I'd like to say I've been a member of this site for over a year, so I know this may be a nonstandard question, however, for personal reasons, I'd like to keep this anonymous. I'm a second ...
1
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3answers
65 views

Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted. Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to ...
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0answers
24 views

About Carl Meyer's matrix analysis

I have taught some part of it to myself when i was an engineering student. but now i changed my major to the pure math so now i am studying math as an undergraduate student. i thought the book is ...
2
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1answer
31 views

$f(x)$ be the characteristic polynomial of a matrix $A \in M_n(\mathbb R)$ ; then is it true that $f(1)=1+\operatorname{trace}(A)+O(\|A\|^2)$?

Let $f(x)$ be the characteristic polynomial of a matrix $A \in M_n(\mathbb R)$; then is it true that $f(1)=1+\operatorname{trace}(A)+O(\|A\|^2)$ ? I need a proof if it is true ; or any modification ...
2
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0answers
60 views

Measuring the set-theoretical complexity of sets/spaces encountered in general analysis

In analysis, it is common to encounter subsets of $\mathbb R$ (or even $\mathbb R^n$) which appear to be "well-behaved", especially with regard to properties like being measurable, compactness, etc. ...
2
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1answer
48 views

Can anyone please help to clarify the sentences “ into a fat tail part in L2 plus a fat body part in L1.”

In the link https://en.wikipedia.org/wiki/Fourier_transform#On_Lp_spaces what does this sentences mean: into a fat tail part in L2 plus a fat body part in L1? Would anyone please help?
5
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3answers
443 views

What is the pre-requisite knowledge for generating my own integer sequence?

I've recently come across the On-Line Encyclopedia of Integer Sequences and I'm completely fascinated by it; something about how easy integers are to grasp and yet how complex the sequences are. I ...
1
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2answers
72 views

Conceptual differences between the notations $\int_{a}^{b}f$ and $\int_{[a,b]}f$

Let $[a,b] \subset \mathbb{R}$ and let $f: [a,b] \to \mathbb{R}$ be continuous. Then $f$ is Riemann-integrable. What are the conceptual differences between the two notations $\int_{a}^{b}f$ and ...
2
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4answers
109 views

Is $i^i$ mathematically valid? [duplicate]

WARNING: SLIGHT NSFW http://www.smbc-comics.com/index.php?db=comics&id=2934#comic Uhh...guys, mathematically speaking, how accurate is this comic. From what I remember in High School $$a^b= ...
3
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0answers
75 views

May Algebraic Geometry be appropriate for me? [on hold]

I am a student of Mathematics who have to choose its area of specialization. I am trying to obtain as more information as possible, by asking a lot of questions to more experienced people, trying to ...
7
votes
1answer
112 views

What is $\varphi(0)$? [duplicate]

$\varphi$ is Euler's totient function. My question is: When/if $\varphi$ is defined at $0$, what is it usually defined as? Is there a "most natural" or more commonly accepted definition of ...
4
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0answers
96 views

Why I can't use Latex editor? [closed]

I cant use latex editor because I need 10 reputation, so what should I do?
1
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0answers
39 views

Can we have different methods to estimate elements from Lp spaces?

Sorry if my question is vague. Consider I have some time samples and it is known to be summation of sinusoidal. Problem is to estimates the frequencies. Generally, Fast Fourier transform (FFT) is the ...
6
votes
2answers
242 views

What is the interest of duality in algebra, and in general in mathematics?

Before to ask my question I precise I'm a chemist, I ask this question because it makes me crazy to don't understand something I learnt in school. So I had two years ago a small chapter about ...
0
votes
3answers
25 views

Quick and simple funtamental question about sets

Please feel free not to read this its just a prelude: Ok I am sorry for making this question since as far as I can tell the level of the other questions here is higher by far compared to mine, but I ...
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0answers
22 views

Does a ratio of PDFs have any usable meaning?

I'm calculating the probability that a standard Brownian motion path will cross a boundary. I have $A$ and $B$ representing the PDFs for the Brownian motion going above a boundary function $a$ and ...
0
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0answers
23 views

Why can't the pseudosphere be completed in $R^3$?

Without appealing to Hilbert's theorem on the non-embeddability of complete hyperbolic surfaces in $R^3$, is there a way to "see" that one can't extend the pseudosphere / surface of revolution of a ...
0
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0answers
22 views

What does a functional integral evaluation look like?

I've read the Wikipedia page on functional integration, but it really isn't very easy to understand. There don't seem to be any online videos on the subject either. In addition, when I search online, ...
1
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1answer
37 views

Generalizations of Inverse Function Theorem

A beautiful exercise in Guilleman and Pollack asks us to show the following generalization of the Inverse Function Theorem: Suppose $f: M \to N$ is a map of smooth manifolds, and $Z$ is a ...
4
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1answer
51 views

Is there an English version of Johann Bernoulli's integral calculus lectures?

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral"; I must mention that, ...
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votes
3answers
68 views

In the real domain, are there any theorems or definitions that state all functions are differentiable? [closed]

I want to ask about basic theory of calculus, say differentiation. We know that not every function can be integrable, but as far as I know all functions are differentiable in the real domain. My ...
0
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1answer
61 views

Background for Graduate Real Analysis I Class

This semester, I have signed up for a graduate Real Analysis I course (really a course in measure theory/Hilbert Spaces/Lebesgue integration) and have thus far attended two lectures. However, from ...
1
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2answers
50 views

Thought Provoking Reads [closed]

I apologize if the gist of this question has been covered before: I tried to find posts relating to it, but nothing I could find was asking for quite what I was looking for. I am an undergrad in ...
0
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0answers
37 views

Does any one have a link to Jorm Steuding's Probablistic Number Theory? [closed]

I was reading it through the browser and the link on CiteSeer died. :( I will download it this time. Thanks. Regards, -EM
1
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0answers
29 views

What is the terminology of the collection of all possible combinations of the element of a set?

Let me explain my question better: Suppose I have a set $(1,2,3)$. Clearly, I have 6 ways to choose some elements from it: $$ (1),(2),(3),(1,2),(1,3),(2,3) $$ and I can make a collection to ...
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0answers
46 views
+50

Soft Question: Weblinks to pages with explanation on quadratics.

I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of ...
0
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1answer
33 views

Program languages recommended for complexity theory

I am an undergraduate studying mathematics and one of my interests include complexity and computability theory. I have no experience in programming. The computability theory books I looked into didn't ...
1
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1answer
32 views

Where can I find “On the significance of the principle of excluded middle in mathematics, especially in function theory”?

I'm looking for L.E.J. Brouwer's article "On the significance of the principle of excluded middle in mathematics, especially in function theory". I've searched my university catalogues and every open ...
0
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0answers
19 views

Adding a website in bibliography. [closed]

I have taken information from this link for my project report. I want to add the website link in the "bibliography" section. But I don't know how is to cite this. Any help is appreciated. Thanks.
0
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2answers
74 views

What does exactly “giacche” mean here?

While translating some Italian paper with Google translator of the following sentence Gli elementi di $G_\nu $, che godono la detta proprieta, formano evidentemente gruppo e questo gruppo, giacche ...
0
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1answer
36 views

Are these inequalities useless for getting better estimates? If not what is needed?

Are these inequalities useless for getting better estimates? If not what is needed? My motivation for asking this question is to get a glimpse to the mind of masters that can tell if a line of ...
2
votes
1answer
71 views

Topology(meaning) [closed]

When we define Topology we say that a topology on a set(let's say X) is a collection of subsets of X having certain 3 properties. Now, here what do we actually mean by saying "topology on a set". What ...
1
vote
2answers
66 views

Notation seen in “awfully sophisticated proof…” I don't understand

I want to understand what the definition of $f_n$ given here means? I tried to seek on the net but I not succeeded. I precise I do chemistry, maths are "just" a curiosity for me. I should be glad, ...
3
votes
1answer
56 views

High School Geometry Text?

This year I will be teaching 8 hard-working home-educated teens a Geometry course. Back in 1994-1999 I worked full time as a High School educator, taking a turn teaching everything from Pre Algebra ...
0
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0answers
14 views

Looking for some good introductory level resources for Gibbs Sampling

In context of a course in bayesian modelling Im following, im looking for some good resources (videos, lecture slides, texts) about Gibbs sampling.
6
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0answers
44 views

What should I do with a paper I've translated? [migrated]

Aside from reaping the personal benefits, what should one do after translating a paper? It would be nice to offer it to others, but I assume it is a copyright violation to post it online. Sending it ...
-1
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0answers
63 views

students do not care about math techniques … [closed]

I could not find whether this question has been asked before. Students do not care about math techniques and this gets worse and worse: Everybody has a pocket PC, name it apple or ...
1
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0answers
10 views

Is there relation between vector valued RKHS and interpolation space?

Vector valued RKHS which is covered extensively in the book "Pick Interpolation and Hilbert function spaces" . On the other hand interpolation space which is defined in the wikipedia link: ...
2
votes
0answers
46 views

How does commutative and/or differential algebra think about total derivatives?

If we apply the "operator" $\frac{d}{dx}$ to the polynomial $xy$, we get the expression $y+x\frac{dy}{dx}.$ (Source: high school.) Thinking of $xy$ as an element of the polynomial ring ...
1
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1answer
33 views

Transforming a sequence to distinguish a limit

This might be the wrong place to ask this question, but I figured I might get some creative answers: I have a decreasing sequence $\{a_n\}_{n \geq 1}$ with $a_k \in (0,1)$ for all $k$ and $a_n \to ...
1
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3answers
78 views

If $a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0=0$, must we have always $-\frac{a_0}{a_n} \in \mathbb{Z}$?

Let consider the polynomial with integer coefficients: $$f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$$ If $f(x)=0$ and $x \in \mathbb{Z}$ with $a_n\neq 0$ If all the roots are integers, must we ...
0
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0answers
76 views

Does there exist a continued-fraction for geometric series

I would like to know if there exists a continued fraction representation of a geometric series.Motivated by the fact that,many elementary functions in math can be represented as such,I wondered if ...
2
votes
1answer
55 views

Can we make a subgroup of a group by selecting exactly one element from each distinct left cosets of a subgroup of the given group?

Let $G$ be a group and $H$ be a subgroup of $G$ ; can we select exactly one element from each distinct left coset of $H$ such that the set of all those elements form a subgroup of $G$ ? How do we ...