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Questions tagged [reference-works]

Reference works include encyclopedias, dictionaries, books of tables (which may include numerical tables, tables of integrals, series, and products, tables of Fourier transforms, tables of finite groups, tables of combinatorial designs, etc.).

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How to get intuition in topology concerning the definitions?

Most topology texts go on directly to give definition of topology, then they give some examples and that's it, like they directly tell you right Let $X$ be a set and let $τ$ be a family of subsets ...
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11answers
5k views

Reference for general-topology

Though there are several posts discussing the reference books for topology, for example best book for topology. But as far as I looked up to, all of them are for the purpose of learning topology or ...
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10answers
3k views

Entering math through the side door [duplicate]

I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact. A lot of times if I want to implement some code I ...
16
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4answers
2k views

Encyclopedia of mathematics (?)

I'm currently studying an engineering degree and I got fascinated about math. The issue here is that I want a single source to learn mathematics; I mean, I want to learn every single math topic pretty ...
14
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3answers
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What is the meaning of the expression Q.E.D.? Is it similar to ■ appearing at the end of a theorem?

I am curious about the meaning of the word Q.E.D. that is often written after a proof of a theorem (some math books use this convention). Edit: Is it similar to the box being placed after a proof of ...
12
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7answers
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Wanted : for more formulas to find the area of a triangle?

I know some formulas to find a triangle's area, like the ones below. Is there any reference containing most triangle area formulas? If you know more, please add them as an answer $$s=\sqrt{p(p-a)(...
12
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6answers
2k views

Advice on self study of category theory

I'm very intrested in start to study category theory with aim to use this in algebraic geometry. I already took courses (besides the basics) on commutative algebra and general topology with a soft ...
11
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1answer
315 views

How does one do research in any field? [closed]

I have started my PhD in this academic year.The topic which I have been given to work on is Spectral Graph Theory. As I have just completed my Master's Course which was very straight forward for me ...
10
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4answers
314 views

Encyclopedia of Groups

I was wondering whether or not there was an online encyclopedia of groups--finite or infinite. If there isn't, would you suppose that such a thing would be useful?
9
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1answer
4k views

Are the Cram101 books any good for studying mathematics?

I found the book "a Gateway to Modern Geometry: The Poincare Half-Plane" by Saul Stahl, a bit over my budget. but browsing amazon I came across: "Studyguide for a Gateway to Modern Geometry: The ...
8
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3answers
432 views

Encyclopedic dictionary of Mathematics

I'm looking for a complete dictionary about Mathematics, after searching a lot I found only this one http://www.amazon.com/Encyclopedic-Dictionary-Mathematics-Second-VOLUMES/dp/0262090260/ref=sr_1_1?...
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2answers
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Is there a canonical database of theorems?

Does a (public) database of theorems exist, as integer sequences are cataloged in the Online Encyclopedia of Integer Sequences (OEIS)?
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7answers
2k views

Dictionaries and resources for translation of mathematical terminology

Nowadays English seems to be the most frequently used language in mathematics. (Although plenty of papers and books are published in other languages, e.g., Russian, French, German and Chinese.) ...
6
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3answers
2k views

Quotient of a graph?

I want to understand quotient of a graph (also called quotient graph), my teacher says that the terms quotient of a graph and a modulo of a graph should be synonyms (even though modulo of a graph ...
6
votes
2answers
346 views

Future learning for a math graduate in applied mathematics references

As a mathematics graduate with focus on programming we did a whole lot of coding of some mathematical statements (as well as proving them), but yet rarely giving real life examples and applications ...
6
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1answer
114 views

$q$-series and modular forms

Is there a way/database such that given a modular form $$f(q) = \sum_{n}a_nq^n$$ with $q=\exp(2\pi i \tau)$, $\tau = \{ z \in \mathbb{C} | \Im(z)>0 \}$ the upper half plane, to find if it can be ...
6
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0answers
503 views

Has Number Fields by D. Marcus ever been typeset using TeX by anyone yet? [closed]

As the title suggests, has anyone yet "latexed" Number Fields by Marcus yet? It's a classic book on number theory and I was thinking of slowly typesetting it in LaTeX during my free time, if no one ...
5
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2answers
415 views

Matrices over noncommutative rings

I am wondering whether matrices over noncommutative rings have gone undergone a systematic study, particularly noncommutative group rings? I would appreciate sources, if any are available. Thanks!
5
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2answers
346 views

Need good reference or a proof on regularity of solution to Neumann problem

Let $\Omega\subset \mathbb{R}^d $ be a bounded open subset ($d\in \mathbb{N}$) and denote $\partial\Omega$ its boundary which we assume to be Lipschitz. The classical inhomogeneous Neumann problem ...
5
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2answers
141 views

soft question - differential geometry and topology book recommendations

I just need a few book recommendations for studying on my own. I know the basics (trig, calc, etc.) and on my free time, I studied multivariable and vector calculus, in addition to differential ...
5
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2answers
179 views

Good blogs for undergraduate mathematics? [closed]

I search some useful blogs talking about undergraduate and graduate mathematics, like terry tao So any suggestions? Thanks in advanced.
5
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1answer
196 views

A curious exercise in Spivak's book on calculus

On chapter 9 of the said book there is an exercise in which Spivak asks the reader to prove that Galileo "got his facts wrong". More specifically, Spivak asks one to to show if a body falls a distance ...
4
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2answers
160 views

Encyclopedia of integers

Many years ago I read something that mentioned a book I would like to find. Apparently this book is sort of an encyclopedia for integers; each entry lists interesting mathematical facts about that ...
4
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1answer
98 views

Editions of Niven-Zuckerman book on number theory

There are several editions of this popular introduction to the theory of numbers. Are they substantially different from one another? Do you think the edition in which Hugh Montgomery appears as co-...
4
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2answers
237 views

Can I skip part III in Dummit and Foote?

I am reading Abstract Algebra by Dummit anfd Foote. I have already taken an introductory course in linear algebra, mostly at the level of Strang's MIT OCW Linear Algebra. My question is: Can I skip '...
4
votes
1answer
115 views

Why was Frobenius concerned the groups which today called “Frobenius Group”?

From their work, it seems that the Ancient mathematicians were investigating a mathematical object not as a fun, but to solve some problem occurred in earlier work of someone. Lagrange, Galois, Abel ...
4
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2answers
252 views

What is the most complete book of integrals and series?

I'm looking for something like "If it's not in this book, it's not known". I've got a copy of Gradshteyn and Ryzhik, which seems pretty good. But I'm hoping there are some better ones out there.
4
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1answer
130 views

Where to get 'The American Mathematical Monthly' reprints

Is it possible to obtain printed books containing important articles from The American Mathematical Monthly since it started?
4
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0answers
63 views

The leatest research regarding ergodic operators

I always ask myself the following question which states: Where might the leatest research regarding ergodic operators be found ? It is undoubtedly I am not asking for the books that illustrate the ...
3
votes
3answers
160 views

How many way ,we can show $(e^x)'=e^x$

It is famous enough that $f(x)=\exp(x) \to f'(x)=f(x)$ . For example we can show it by taylor series like below : $$\quad{e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+...\\ (e^x)'=0+1+\frac{2x}...
3
votes
3answers
137 views

Encyclopedia of Mathematics? (non-alphabetical)

Do you know any encyclopedia of mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level? And what's the difference between say, ...
3
votes
1answer
161 views

Concrete examples of elliptic pseudo-differential equations

Remember that $p \in S^{m}_{1,0}(\mathbb{R}^n \times \mathbb{R}^n)$ or that $p: \mathbb{R}^n \times \mathbb{R}^n \longrightarrow \mathbb{C}$ is a simbol if it is a smooth function such that \begin{...
3
votes
1answer
83 views

Sequence of polygons converging

Let $P$ be a polygon ($P$ doesn't have to be regular, convex... it's just $n$ distinct points of $\mathbb{R}^2$). We construct the sequence $(P^{(n)})_n$ with $P^{(0)}=P$ and $P^{(n+1)}$ is the ...
3
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1answer
59 views

Text for study of subgroup lattices of finite abelian groups.

I want to study the subgroup lattice of a finite abelian group. I have found a text on the subject: Subgroup Lattices of Groups by Roland Schmidt, de Gruyter 1994. This book is about subgroups of any ...
3
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0answers
326 views

Equivalence between Brouwer fixed-point theorem and Borsuk-Ulam theorem. Is there a simple proof of equivalence between them?

I wonder if Brouwer's fixed-point theorem and Borsuk-Ulam's theorem are equivalent. Brouwer's fixed-point theorem (simple form). Let $B_{\mathbb{R}^{n}}[0,1]=\{x\in \mathbb{R}^n: \|x-0\|\leq 1\}$ ...
2
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4answers
566 views

More comprehensive General Topology's book than Engelking

Other than Engelking General Topology, I also come across other graduate general topology text such as Dugundji and Kelley, which I also find them interesting. However, I find Engelking's book more ...
2
votes
1answer
123 views

Looking for a specific reference, which is used in the book “Lectures on Advanced Computational Methods in Mechanics”

I need this book "Lectures on Advanced Computational Methods in Mechanics", unfortunately I did not find it in the library of the university .If someone has it, I just want to know the reference [61] ...
2
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1answer
50 views

Is there a version of mean value property for $p$-harmonic funcions?

We know by mean value property that harmonic functions satisfies the equalities \begin{equation} u(x) = \dfrac{1}{|B_r|}\int_{B_r}f dx = \dfrac{1}{|\partial B_r|}\int_{ \partial B_r}udS. \end{equation}...
2
votes
1answer
72 views

Book on structure of the unit group of group rings

I am looking for a book named "The structure of the unit group of group rings" by Dennis, R.K. , Lecture Notes in Pure and Applied Math. vol 26, Marcel Dekker, New York, 1977. This book is referred ...
2
votes
1answer
49 views

bialgebras and hopf algebras over a category

I am currently looking for a reference on how to define a bialgebra over a category or a Hopf algebra over a category, I have consulted in several texts of Hopf algebras but only define these ...
2
votes
1answer
1k views

Can somebody explain with one example the concepts: Lemma-Hypothesis-Theorem-Assumption-Proof-Axiom-Thesis-Determination-Definition-Proof [closed]

It would be great if someone can give me for each concept a simple explanatory example ! What is the difference between: Lemma Hypothesis (Hypothese) Theorem (Satz) Assumption (Annahme) Proof (...
2
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2answers
142 views

Probability spaces over graphs: which area has focus on them?

Suppose a simple graph $G$. Now consider probability space $G(v;p)$ where $0\leq p\leq 1$ and $v$ vertices. I want to calculate globally-determined properties of $G(v;p)$ such as connectivity and ...
2
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1answer
442 views

On the Princeton Lectures

I've heard nothing but good things about the Princeton Lectures in Analysis and was looking to start reading them. I just have a question for anyone who's read them before. Do they have to be read ...
2
votes
1answer
143 views

Encyclopedia of Mathematical Proofs with no English

I was wondering if anyone is aware of a modern book that builds a subset of elementary number theory from Peano axioms preferably in a Principia Mathematica fashion? Or similarly an encyclopedia of ...
2
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0answers
53 views

Recommendation topic - Numerical Analysis and computational

I'm having a course about 'Numerical Analysis and computational' in my master's. The course is about : Systems of Linear Equations: direct methods (LU factorization and Cholesky decomposition), ...
2
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1answer
90 views

Where are the Optimal Tours of TSPLIB 95 Instances?

I am looking for the optimal tours of the TSPLIB 95 instances as downloadable files. I have checked several places, but all lists I could find contain gaps, despite the fact, that all instances have ...
2
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0answers
175 views

Camille Jordan : Treatise on substitutions and algebraic equations ??

Is there english translation available of the monograph by Camille Jordan, titled: Traité des substitutions et des équations algébriques, which is available easily online in french. The reason for ...
2
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0answers
25 views

List of 2D definite integrals not reducible to products of 1D integrals

I'm writing numerical integration routines for 2D surface integrals. To test it, I'm looking for a list of definite integrals which have analytic forms. I need Integrals in polar coordinates over the ...
2
votes
0answers
228 views

Up-to-date Matrix Cookbook

My copy of the Matrix cookbook is dated November 15, 2012, and is the newest copy I've been able to find. Identities may not change overtime, but the approach to an error-free presentation can be ...
2
votes
0answers
122 views

Which probability measure book is more comprehensive?

I have read Rudin's Principles of Mathematical Analysis. I am now choosing one of the 2 books: Probability and Measure by Patrick Billingsley OR Probability and Measure Theory by Robert Ash I ...