This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
2
votes
2answers
72 views
Universal Cover of a space
I do not know what tools one uses to find the universal cover of a space. In particular I want to find the universal cover of two copies of $RP^3$ glued together at a single point at the endpoints by ...
0
votes
1answer
33 views
Can anyone recommend me a good pdf link to learn B-spline with a lot of examples?
I really hope someone can recommend me a good link to study B-spline with a lot of examples that I could grasp the concept very easily! Thanks! :)
1
vote
0answers
30 views
Usage and determination of “rank” and “dimension” of groups & representations
Physicist here. I seem to see conflicting statements about the rank of some groups I've come across lately.
A paper I'm reading states that $SO(6)$ is rank 3 and therefore its Cartan subalgebra ...
0
votes
1answer
57 views
looking for reference for 2 trig facts
Math people:
I am looking for a reference for two trigonometry facts, one of which I proved myself, and another which a random person had posted on the Web. I have evidence to believe the second ...
1
vote
0answers
69 views
An example of a differentiable manifold class $C^k$ but not class $C^{k +1} $
I'm looking for an example of a differentiable manifold of class $C^k$ but not class $C^{k +1}.$
I found an exercise in Hirsh's book, which suggests that the graph of $f (x) = |x|^{\lambda}$, where ...
4
votes
2answers
69 views
A reference that forcing with a poset of cardinality less than $\kappa$ preserves supercompact cardinals
I'm looking for a reference for the fact that if $\kappa$ is supercompact and $Q$ is a poset of cardinality less than $\kappa$, then $V^Q\models \check{\kappa} \ \text{is supercompact}$.
Apparently ...
1
vote
0answers
22 views
Gelfand-Leray integral for forms with noncompact support
Let $\omega$ be a smooth $n$-form with compact support on domain $\Omega \subseteq{\mathbb{R}^n}$ and let $f \colon \Omega \to \mathbb{R}$ be a smooth function with nonvanishing differential. Then for ...
0
votes
1answer
33 views
Reference request: Projective space $\mathbb{RP}^3$
I have to write seminar paper in Projective geometry and the name of the seminar is (I would try to translate):
Representation of the lines in the projective space $\mathbb{RP}^3-$Kernel, Lineal, ...
3
votes
1answer
26 views
Reference request: Morita contexts
During an independent study I've come across Morita contexts, but I'd like to understand them better. A quick Google search doesn't yield much fruit, so I was hoping to find a good reference on the ...
3
votes
1answer
116 views
Boundary gradient blowup of a parabolic PDE with an unbounded coefficient
I am exploring the boundary gradient blowup of following parabolic PDE on the semi-infinite strip $(-\infty,0]\times[0,1]$:
Let $0< \alpha < 1/2$.
$\partial_t u(x,t) = -\alpha(1-t)^{\alpha - ...
1
vote
2answers
56 views
Good books on conic section.
Can anybody suggest me good books for conics section.I want it for IIT-JEE mains and advanced and also for ISC. It should be available in India .
3
votes
1answer
25 views
Hypergraph Colorability
I'm interested in hypergraphs for which there are known (nontrivial) lower bounds on the chromatic number. If someone could point me to existing literature (survey papers etc) on this topic that would ...
0
votes
1answer
56 views
Is Conway's “Course in Functional Analysis” suitable for self-studying?
Is John B. Conway's book "A Course in Functional Analysis" a good book for self-studying functional analysis?
(I have a solid knowledge of undergraduate analysis and linear algebra, group theory, ...
2
votes
2answers
52 views
Learning Combinatorial Species.
I have been reading the book conceptual mathematics(first edition) and I'm also about halfway through Diestel's Graph theory(4th edition) I was wondering if I was able to start learning combinatorial ...
1
vote
0answers
52 views
Textbook in algebra leading to research
I am searching for a book in commutative algebra with will develop theory from an undergraduate level and lead to areas of current research. Any help is welcome.
5
votes
0answers
97 views
Algorithm to calculate multiple integral.
One of the major difficulties of student in advanced calculus (including myself when student) is to obtain the extremes of repeated integrals to calculate the volume integral in $R^n$ i.e. transform ...
6
votes
0answers
154 views
Priority of the content of a note by Lebesgue from 1905
I refer to a note by Lebesgue Remarques sur la définition de l'intégrale, Bull.Sci.Math. 29 (1905) 272-275 not very known (see pdf for an exposition in English).
It is a pedagogical note containing a ...
1
vote
0answers
29 views
Problem 4.2 Gilbarg/Trudinger
Problem 4.2 Prove lemma (4.2) if $f$ is Dini continuous in $\Omega.$
Lemma: Let $f$ bounded and locally Hölder continuous (with exponent $\alpha \le 1)$ in $\Omega,$ and let $w$ be the Newtonian ...
6
votes
0answers
67 views
Accessible introduction to category theory from the point of view of preorders. [duplicate]
Are there books renowned for introducing category theory in a very accessible way? An emphasis on the point of view that categories generalize preorders would be especially appreciated.
My goal is to ...
1
vote
1answer
109 views
Does a bound on a solution to an ODE allow for it to be defined over all $t \in \Bbb R$?
Consider the ODE $$ x^{(n)}(t) = f(t, x, x^{(1)}, \dots, x^{(n-1)})$$
Much of the books I have read through talk about results for very loose conditions on $f$. My first question is are there any ...
4
votes
1answer
90 views
Find area bounded by two unequal chords and an arc in a disc
Math people:
This question is a generalization of the one I posed at Find area bounded by two chords and an arc in a disc . Below is an image of a unit circle with center $O$. $\theta_1, \theta_2 ...
2
votes
0answers
53 views
Books similar to “Primes of the form $x^2+ny^2$”
Are there any other books which are similarly to the book "Primes of the form $x^2+ny^2$"? Basically, I want a book which starts with a very important classical problem ( in this case which primes can ...
4
votes
2answers
113 views
What is known about the quotient group $\mathbb{R} / \mathbb{Q}$?
Let $G = \mathbb{R} / \mathbb{Q}$. Is this an interesting group to study?
Is it isomorphic to any more natural mathematical objects?
1
vote
2answers
28 views
Finite index subgroups of infinte groups
I want to use the following Theorem:
If $H\leq U\leq G$ are (maybe) infinte groups. And $|U:H|<\infty$, $|G:U|<\infty$. Then
$|G:H|=|G:U|\cdot |U:H|$.
I think, i could proof it, but i don't ...
2
votes
1answer
69 views
An introduction to Khovanov homology, Heegaard-Floer homology
I am interested in knot theory and low dimensional topology. I would like to start studying Khovanov homology and Heegaard-Floer homology.
I (partially) read the original paper of Khovanov and then ...
0
votes
0answers
79 views
Example of well-written theses
Among the books of pure mathematics, Rotman's book on Group Theory and any book of J. P. Serre are best examples, as I feel, of writing a mathematics book (many experts in different areas of ...
11
votes
1answer
141 views
Is there such a thing as a mathematical thesaurus?
I want this for two reasons:
When writing proofs, I am constantly in need of synonyms of basic words like thus, there exists, for all, such as, contains, etc.
A lot of mathematical concepts have ...
0
votes
0answers
40 views
What do I need to know to understand Lagrange multipliers?
I've seen Lagrange multipliers used as a powerful method for tackling inequalities and some IMO problems, and I'm aware that it's a part of calculus. I'm currently taking BC Calculus in high school, ...
12
votes
2answers
305 views
Is Serge Lang's Algebra still worth reading?
Is Serge Lang's famous book Algebra nowadays still worth reading, or are there other, more modern books which are better suited for an overview over all areas of algebra?
EDIT: My main concern is ...
3
votes
1answer
39 views
asking for referrence in topological properties of matrices
can anyone tell me about some books or references where I can find different topological properties(such as compactness , connectedness , completeness , open , bounded , dense , nowhere dense etc....) ...
13
votes
3answers
259 views
Exceptional books on real world applications of graph theory.
What are some exceptional graph theory books geared explicitly towards real-world applications?
I would be interested in both general books on the subject (essentially surveys of applied graph ...
0
votes
1answer
38 views
Metric Spaces needed for Differential Geometry
I've asked here about some texts about differential geometry which doesn't assumes that the reader knows general topology. I've got good references as Do Carmo's Differential Geometry of Curves and ...
1
vote
2answers
24 views
Reference for proof of harmonic number asymptotic expansion
Can anyone show me where I can find a proof of the following?
$$H_n \sim \ln{n}+\gamma+\frac{1}{2n}-\sum_{k=1}^\infty \frac{B_{2k}}{2k ...
0
votes
0answers
32 views
Complete Highschool Textbook?
Is there any complete textbook out there that covers all highschool math courses/content (gr.9-12)?
Or maybe a math textbook that prepares you for university or college/software engineering ...
2
votes
1answer
49 views
reference request: Postnikov towers for non-simply-connected spaces
I've read that for a space $X$ which is connected but not necessarily simply-connected, we can no longer obtain the $n^{\rm th}$ layer $P_nX$ of the Postnikov tower for $X$ as the pullback of a ...
0
votes
2answers
63 views
Whats the connection between functions with curl 0 and holomorphic functions
When I first saw the Cauchy-Riemann differential equations they remind me on the conditions for the curl of a function to be zero.
Here some notation I will use:
$$\frac{\partial f}{\partial x} = ...
1
vote
2answers
76 views
How will studying “stochastic process” help me as mathematician??
I wish to decide if I should take a course called "INTRODUCTION TO STOCHASTIC PROCESSES" which will be held next semester in my University.
I can make an un-educated guess that stochastic processes ...
1
vote
1answer
26 views
Reference for classification of space forms
The classification theorem aout space forms tells us, that every simply-connected, complete manifold of constant sectional curvature is isometric to a sphere, flat space or hyperbolic space.
Can ...
1
vote
1answer
59 views
Dirichlets theorem on primes
I want to use Dirichlets theorem on primes for my diploma thesis. I want to use following form
Let $a,b\in\mathbb{N}$, such that $\gcd(a,b)=1$. Then the set $\{a\cdot n+b| n\in\mathbb{N}\}$ contains ...
0
votes
0answers
53 views
Question about queueing theory and queueing systems [closed]
i have presentation about queuing theory and i need some latest journal and article about it please introduce or give latest journal and article (my subject its around markov chain in Queuing theory ...
0
votes
1answer
21 views
Outer measure defined by a continuous and bijective function
This problem is from K.T. Smith's Primer of Modern Analysis:
Let $\psi: \mathbb{R}^d \to \mathbb{R}^d$ be continuous and one-to-one on an open set $\Omega \subset \mathbb{R}^d$ and define $$\nu(A) ...
3
votes
2answers
108 views
A sequel for Elementary Analysis by Ross?
I've been learning real analysis from this book:
Elementary Analysis, K.A. Ross
I really liked the style of this book. It is quite old, and sometimes very difficult, but I guess I liked the way it ...
4
votes
1answer
124 views
Differential Geometry without General Topology
I want to ask if there is some book that treats Differential Geometry without assuming that the reader knows General Topology. Well, many would say: "oh, but what's the problem ? First learn General ...
2
votes
1answer
57 views
Elliptic curve as an intersection of quadrics
Let $E$ be an elliptic curve. If one starts with embedding associated with invertible sheaf $\mathcal{O}(3x)$ where $x$ is some point on $E$ then one gets cubic in $\mathbb{P}^2$ and this embedding is ...
1
vote
1answer
88 views
Name of $a*b=c$ and $b*a=-c$
$A_+=(A,+,0,-)$ is a noncommutative group where inverse elements are $-a$
$A_*=(A,*)$ is not associative and is not commutative
$\mathbf A=(A,+,*)$ is a structure where
1) if $a*b=c$ then $b*a=-c$ ...
3
votes
0answers
119 views
Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils
i was wondering if mathematics learning process require the use of textbooks.
When i was a high school student, i read as a preparation for university, Legendre book on Elements of geometry and ...
2
votes
1answer
119 views
What is a good book to learn number theory?
What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks.
3
votes
0answers
31 views
What is a spherical Gaussian kernel?
In this paper (page 8, Example 3), a spherical Gaussian kernel is defined by the formula $$K(\mathrm x,\mathrm y)=e^{-2\epsilon(1- \mathrm x\cdot\mathrm y)}$$ where $\mathrm{x,y}\in ...
0
votes
1answer
51 views
Topic for presentation on Group Representations, Young Tableaux, Symmetric Group
I need to do a presentation relating to group representations/Young tableaux/symmetric group; however, for all my searching, I cannot find a cool topic that I find personally interesting (and that is ...
0
votes
1answer
34 views
Sigma algebra of a regular borel measure
From the definition I am using and restrict to $\mathbb{R}^d$ only, what can we say about $\sigma$-algebra of $\nu$-measurable sets, $\mathfrak{B}_{\nu}$?
Some more specefic questions:
It contains ...
