This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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4
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0answers
57 views

Does a space with peoperty A have a topological name?

As we know, If $X$ is a Tychonoff pseudocompact space, then for every decreasing sequence $\cdots\subset W_2\subset W_1$ of nonempty open subsets of $X$ the intersection $\bigcap_{i=1}^{\infty} ...
1
vote
0answers
48 views

Suggest a reading list to start TQFT

What would be books that would give the necessary prerequisities to study TQFT? I want to read something like Kock's Frobenius algebras and 2d TQFTs, I only know enough math that got me through a ...
6
votes
1answer
56 views

Books that start with questions? [closed]

Does anyone know of any books that start with a relevant question, study it from different perspectives and then show some mathematics? I would appreciate it if you posted any that you know of, ...
2
votes
1answer
27 views

Is there a standard term for this generalization of the Euler totient function?

Let $\phi_k(n)$ be the number of integers $m$ in $1\le m\le n$ for which $\gcd(m,n) = k$. Then $\phi_1(n) =\varphi(n)$, the standard totient function. This function arises in the analysis of the ...
7
votes
4answers
148 views

Can we still learn from the old masters?

So, let me first describe how my doubt originated: out of curiosity I started to study Newton's Opticks, a book written more than 300 years ago. I was doing some of the experiments described on it, ...
1
vote
1answer
17 views

Slight generalisation of the distribution of Brownian integral

I think I have seen once that if the processes $\sigma$ and $W$, a Brownian motion, are independent then one has that $$ E \left[\exp \left(iu\int_t^T \sigma_s \, dW_s\right) \mid \mathcal{F} \right] ...
3
votes
1answer
130 views

Sets that are convex in two different metrics

Let $(M,g)$ be a complete Riemannian manifold, and let $C$ be a subset of $M$. We will say $C$ is convex if for any points $p,q \in C$, there exists a unique normal minimal geodesic $\gamma$ joining ...
6
votes
8answers
491 views

Books or site/guides about calculations by hand and mental tricks?

Any ideas about books I can get, from amazon? I need to get really good at mental math and math by hand because I'm taking an exam soon and that without a calculator. Thanks.
-2
votes
0answers
129 views

how mental math is helpful to learn math? is it any scope for research or to improve new vedic math tricks? [closed]

Many peoples said vedic math is not math. its only collection of tricks but i have question that can we improve this tricks? is it any one try to improve that kind of tricks? if yes! what result they ...
2
votes
0answers
170 views

Property similar to subadditivity

A function is called subadditive such that $f(x+y)\le f(x)+f(y)$ holds for any $x$, $y$ in the domain of $f$. (Let us say that, for example, the domain is some subset of $\mathbb R$ closed under ...
1
vote
1answer
39 views

Inverse Laplace Transform of $1/(s+1)$ without table

The pole is on the left half plane, so $\gamma =0$ $$\frac{1}{2i\pi}\int ^{i\infty}_{-i\infty}\frac {e^{st}}{s+1}ds$$ substituting $iu=s$ $$\frac{1}{2i\pi}\int ^{\infty}_{-\infty}\frac ...
1
vote
0answers
22 views

Classification of $\mathbb{G}_m$-torsors?

Is there a nice proof or reference to one of the theorem that any $\mathbb{G}_m$-torsor is isomorphic to $\mathcal{L}\setminus z(S)\to S$? Here I am denoting by $\mathcal{L}\to S$ to be a line bundle ...
2
votes
0answers
42 views

Hilbert's reduction of second order logic to first order logic

I have read on the internet a theorem of Hilbert that says that we can reduce every second order theory to a first order theory. So there exists only one logic: first order logic. I cannot find it ...
2
votes
0answers
31 views

How should I learn the Mathematical Proofs?

S.E advisers, What is the most efficient way to learn the basic proof methodologies, which are essential for studying the mathematical analysis and number theory? I am very interested in studying ...
7
votes
1answer
81 views

Is there any relationship between the Riemann z function and strange attractors?

I have this question in mind since the first time I saw a graphical representation of the zeta function (like in the sample below). Just by looking to them I wondered if there is any relationship ...
1
vote
1answer
22 views

Tutorials on LDPC error correction codes

Please consider this as soft question. Recently, I have been studying channel coding and in particular error correction codes. I am looking for best tutorial (easy to understand) on LDPC error ...
0
votes
0answers
16 views

Is there an explicit formula for the Fourier transform of $(z-|\xi|^{\alpha})^{-1}$ on $\mathbb{R}$?

Let $0<\alpha< 2$, and $z=\lambda+i\mu$, where $\mu\ne 0$. Consider the following Fourier transform on $\mathbb{R}$ $$g(z,x)=\int_{\mathbb{R}}\frac{e^{ix\cdot\xi}}{(z-|\xi|^{\alpha})}d\xi$$ ...
1
vote
0answers
17 views

Arc length in curvilinear coordinates - reference request [closed]

Can someone recommend a website or a book with solved problems regarding (advanced mathematics): Transformation from cartesian to curvilinear coordinates Parametrization of the spatial curve Arc ...
1
vote
2answers
45 views

Looking for examples of finite loops and monoids

I am looking for examples of (small) finite loops and monoids that are not groups for demonstrating what happens if you omit some of the group axioms. Does anyone know some ressources for this? I ...
10
votes
2answers
6k views

recommending books for GRE math subject test

I wonder if anyone could recommend some books (other than Princeton Review) to prepare for the GRE math subject exam. I've heard that the REA books have lots of typos, though it has 6 practice exams. ...
2
votes
2answers
26 views

explain the solution and/or suggest a different one

I have come across the following problem, in my calculus II course, about improper integrals: problem: Find the following limit, if it exists. $\displaystyle\lim_{x\to 1} \int\limits_{x}^{x^2} \! ...
0
votes
2answers
41 views

Open conjectures in number theory that is easy to do some programming for

I have a to do a project in number theory that we are assigned that we should do some programming for that is not the collatz conjecture, so any suggestion would be really great.
0
votes
1answer
31 views

information about semi-dihedral groups.

my question is about the elements and the generalized format of caylay table of groups called semi-dihedral groups which have the presentation $$ \langle a,b\mid a^{4m}=b^2=1,ab=ba^{2m-1}\rangle $$ ...
0
votes
0answers
19 views

Looking for a paper on Weakly uniform bases

I want to find an old paper: R.W. Heath, R.W. Lindgren, Weakly uniform bases, HOUSTON JOURNAL OF MATHEMATICS. 2(1) (1976) 85–90 Could someone help me? A link is also welcome. Thanks!
3
votes
1answer
58 views

Is it known whether any positive integer can be written as the sum of $n$ different squares?

Is it known whether any sufficiently large positive integer can be written as the sum of four different squares? I know that every positive integer can be written as the sum of four not necessarily ...
6
votes
3answers
564 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 ...
8
votes
2answers
211 views

Do two closed subsets of $[0, 1]$ with measure $\frac{1}{2}$ intersect?

Let $A$ and $B$ be two closed subsets of $[0,1]$, each with a length of $1/2$. Is it always true that $A\cap B\neq \emptyset$? My intuition is yes, because: Either they intersect in their interior; ...
1
vote
0answers
26 views

Reference request: Measure theory books using $\omega(\alpha) = |\{f>\alpha\}|$

I am working from Wheeden and Zygmund's Measure and Integral, and they prove theorems such as $\int_E f = -\int_{-\infty}^{+\infty} \alpha d\omega(\alpha)$ where $\omega(a) = |\{x: f(x)>\alpha\}|$ ...
9
votes
2answers
2k views

Is there a solution manual for Royden fourth edition?

I bought the fourth edition of Royden Real Analysis, this book is awesome and is quite different of third edition that has less excersices. I have the solution manual for the third edition. Is there ...
0
votes
0answers
26 views

Where can I find Kan's paper “On c.s.s. categories” from 1957.

Does anyone know how I can find the following article by Daniel Kan: Kan, D. M. On c.s.s. categories Bull. Soc. Math. Mexicana (1957), 82-94. Quillen lists it as a reference in his paper Rational ...
2
votes
0answers
20 views

Reference request: Cohomology of Elliptic Curves

Is it true that the group $$H^1(Gal(K^{ab}/K)/\mu_{\nu}(Gal(K_{\nu}^{ab}/K_{\nu})),E_{p^n})$$ is always p-divisible? Or are there any conditions which, when satisfied, guarantee its p-divisibility? ...
0
votes
1answer
24 views

Conditional expectation, pinching

Let $\mathfrak{C}$ be a unital $*$-subalgebra of the full matrix algebra $M_n(\mathbb{C}).$ Let $\mathbb{E}_\mathfrak{C}$ be the orthogonal projection from $M_n(\mathbb{C}),$ endowed with the ...
0
votes
0answers
24 views

Pontryagin classes of a tensor product of bundles

This question is related to " How to calculate characteristic classes of tensor products? " but interested in the Pontryagin classes instead of $c_1$. Specifically, given two real vector bundles $E$, ...
4
votes
3answers
3k views

What are the real-world applications of real analysis?

I've read the wikipedia article on mathematical analysis and this, but I can't exactly find an answer. Is real analysis just some pure math, or does it really have something to with physical ...
6
votes
3answers
264 views

Symmetries of combinatorial structures.

Studying the automorphism groups of graphs/finite geometries/designs has been quite useful and important for both group theory and combinatorics. I know of the following books which cover the ideas ...
2
votes
0answers
18 views

Lists of negative discriminants by class group?

Is there a handy listing of the discriminants of imaginary quadratic fields having a given ideal class group? It would be nice to use such a resource as a source of examples. For example, we're all ...
0
votes
0answers
34 views

Books covering the basics of Fourier Transform for image processing

I am studying computer science and I would like to improve myself on the subject of image processing. There is just one obstacle, Fourier transformations. Is there any material which covers basics of ...
4
votes
1answer
44 views

A necessary and sufficient criterion for an element of a multiplier $ C^{*} $-algebra to be positive.

I am trying to find a reference for the following assertion: Let $ A $ be a $ C^{*} $-algebra, and let $ M(A) $ denote its multiplier algebra. Then $ m $ is a positive element of $ M(A) $ if and ...
8
votes
3answers
412 views

Books/Notes recommendation request: Multivalued functions/Riemann surfaces

I'm trying to read a document that applies Riemann-Roch left, right and center. I don't know this theorem or the theory it comes from so I need to build up a bit more background before I can tackle ...
0
votes
1answer
53 views

Reverse Order Laws of M-P pseudoinverse

When I was writing a literature survey on Moore-Penrose pseudoinverse (literatures like this one, and this one), I encountered with the following equality which was named as reverse order law: ...
8
votes
0answers
74 views

Classification of all subrings

Let $R$ be an integral domain whose underlying additive group is finitely generated free and whose field of fractions $K$ is a finite Galois extension of $\mathbb{Q}$. Is there a method of ...
2
votes
1answer
33 views

Does this notion of “weak” isomorphism exist in literature?

Let $(M,\circ)$ and $(N,\ast)$ be two magmas. I'd like to relax the notion of isomorphism by defining a notion of "weak" isomorphism in the following way: $M$ and $N$ are "weakly" isomorphic if there ...
1
vote
3answers
44 views

$N^{1/2}$ and randomness

I apologize if this question is overly vague, but part of the reason I am asking is because I don't know a more precise way of discussing these ideas. To state a general question: What, if any, ...
11
votes
0answers
344 views

Analysis of the function $\prod_{n=-\infty}^{ \infty }(1-e^{-a{(x+n)^2} })$

While playing on pruduct series, I noticed interesting function that it has similar behavior to $C\cdot\sin^2(\pi x)$ function . I need help about some results below. ...
-3
votes
1answer
2k views

Lee, Introduction to Smooth Manifolds Solutions

Does anybody know where I could find the solutions to the exercises from the book Lee, Introduction to Smooth Manifolds? I searched on the Internet and found only selected solutions but not all of ...
1
vote
0answers
38 views

How are isomorphisms shown on open sets or using category theory in algebraic geometry? [closed]

I may have seen a few examples of how isomorphisms are shown in algebraic geometry using open sets such as $D\left(f\right)$ and/or category theory methods, but I don't have understanding of the ...
2
votes
0answers
43 views

References for equivariant cohomology

I am studying the paper An introduction to equivariant cohomology and homology, follwing Goresky, Kottwitz, and Macpherson - Julianna S. Tymoczko but there are too many gaps. I can't link most of ...
2
votes
2answers
30 views

Online primitive root modulo n list or tool?

Please does somebody know of an online list or tool (if possible server side, not a Java applet running in my computer) to calculate the primitive roots modulo n, for instance $n \in [1,1000]$ (apart ...
1
vote
0answers
17 views

How to know one book whether has an English version?

I want to find the English translation of Vorlesungen über nicht-euklidische Geometrie written by Klein. Thanks.
1
vote
1answer
81 views

Existence of the Brownian Motion using the Kolmogorov extension theorem

Kolmogorov extension theorem: Let $T$ denote some interval (thought of as "time"), and let $n \in \mathbb{N}.$ For each $k \in \mathbb{N}$ and finite sequence of times $t_{1}, \dots, t_{k} \in T$, ...