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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0
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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 ...
-2
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0answers
125 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 ...
0
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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 $E$, ...
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
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 $$ \langle a,b\mid a^{4m}=b^2=1,ab=ba^{2m-1}\rangle $$ ...
1
vote
1answer
43 views

A reference for multi-dimensional characteristic functions

I'm looking for a well-written, rigorous and self-contained treatment of multidimensional characteristic functions, specifically Lévy's continuity theorem and the uniqueness theorem (which states that ...
4
votes
1answer
52 views

Derived functors - homotopical vs homological approach

In a first course in homological algebra, the lecturer introduced derived functors as universal $\delta$-functors, whose universal property is splicing short exact sequences into long ones. It so ...
0
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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
43 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 ...
3
votes
1answer
49 views
+150

References on cancellation of critical points

I'm not sure if I am using the terms correctly. Suppose you have, for example, a Morse function $f : S^2 \rightarrow \mathbb{R}$ with 2 critical points of index 0, 1 critical point of index 1, and 1 ...
2
votes
1answer
32 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
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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 ...
8
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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
0answers
41 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
1answer
35 views

Lebesgue measures defined on subspaces of $\Bbb R^n$

For any subspace $V$ of $\Bbb R^n$, we have a special measure $\lambda_V$ which can be described in various ways: Haar measure on $V$, or the measure induced by the metric $V$ inherits from $\Bbb ...
1
vote
1answer
42 views

What is the name of this kind of games?

In game theory, suppose we have a set of players $\mathcal{N}=\{1, 2, \ldots, n\}$, a set of actions $\mathcal{A}_i$ of player $i\in\mathcal{N}$, and a payoff function $u_i$ of player ...
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, ...
2
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0answers
97 views

How to learn QFT from mathematical perspective?

I want to learn QFT, because I have heard of its applications in mathematics, I am not interested in scattering cross sections and such. Where can I start to learn? Only books I found are either way ...
0
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0answers
34 views

In a closed monoidal category, is $[-,-]$ always a bifunctor?

We say a monoidal category $\mathcal V=(\mathcal V_0,\otimes,I,a,l,r)$ is closed if the endofunctor $-⊗Y$ has a right adjoint $[Y,-]$, called the exponential, for every $Y$. The object $[Y,Z]$ for ...
3
votes
0answers
16 views

System of linear congruence, not relatively prime

Consider we have the following set of congruences $$x\equiv b_i \pmod {m_i}$$ for all $1\leq i\leq d$. $m_i$'s doesn't have to be relatively prime, so the Chinese remainder theorem doesn't work here. ...
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 ...
-1
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0answers
29 views

Manual solution of Calculus, vol 2 [closed]

Does anyone know (or have) a link or a pdf of manual solution from Tom. M. Apostol, Calculus, volume 2? This would be life easier. Thanks in advance!
3
votes
1answer
56 views

Is there a name of the dual of quotient?

If $\mathcal{C}$ is an abelian category, we can consider the quotient $B/A$ when $A$ is a subobject of $B$ (i.e. there is a mono from $A$ to $B$.) It satisfies following universal property: For ...
1
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2answers
34 views

Videos for finding the area under curve using integrals?

Can anybody point me in the direction of some good videos for finding areas under curves using integrals? Currently studying for a calc 1 final, have found good videos on khan academy and ...
7
votes
4answers
147 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
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0answers
18 views

Interpretations of a weighted adjacency matrix's eigenvectors and eigenvalues?

Suppose that I have weighted undirected graph $G$, and the corresponding adjacency matrix which is a symmetric matrix $A$. Suppose that the edge between node $i$ and $j$ has weight $w_{ij}$, then $$ ...
8
votes
2answers
73 views

Good video lectures in Differential Geometry

I was not fortunate enough to learn Differential Geometry during my Masters. As now I am having my thesis in PDEs, and I miss a lot of mathematics from the people who do PDEs on Manifold setting. I ...
2
votes
0answers
43 views

Semiring of formal power series with non-negative coefficients

Has the semiring $\mathbb{Q}_{\geq 0}[[X]]$ of formal power series with non-negative rational coefficients been studied somewhere? For example, I would like to be confirmed that the group of units is ...
4
votes
1answer
46 views

Unique factorization in fields

Suppose $A$ is a commutative $R$-algebra and that is also a field. Define: For $x,y \in A$, say that $x$ divides $y$ iff $xr = y$ for some $r \in R$. Call $x,y \in A$ associates iff each divides the ...
0
votes
0answers
20 views

Linear Algebra and Its Applications Gilbert Strang-Solutions-Unable to find

I am trying to find Linear Algebra and Its Applications Solution Handbook by Gilbert Strang but I am unable to find it any where. I am more focused on this particular book and not anyone else since it ...
0
votes
1answer
18 views

Reciprocity for Lagrange multipliers

Does anyone know of a textbook with explicit examples of Lagrange multiplier problems of the following type? Compare the results of : (a) optimizing $f(x,y)$ [max or min] subject to the ...
0
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0answers
18 views

Integral kernels of self-adjoint operators

If the integral kernel $k(x, y)$ of an operator $T : C^\infty_c(M) \to \mathcal{D}'(M)$ is symmetric ($M$ is a compact manifold), then the operator $T$ is symmetric. Is the converse true? That is, ...
1
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0answers
25 views

Inclusionwise maximal linear subvarieties of a projective variety

Let $X\subseteq\mathbb P^n$ be a complex, projective variety. A linear subspace $L\subseteq\mathbb P^n$ will be called a maximal linear subspace of $X$ if $L\subseteq X$ and for any linear subspace ...
1
vote
1answer
14 views

Picture of the first homology group

I have to draw a picture of the base of the first homology group over $\mathbb{Z}$ of $C$, where $C$ is a compact Riemann surface of positive genus. How can i draw it? Is there some free programm wich ...
-2
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0answers
62 views

Any mathematical analysis text that covers Rudin but is written like Munkres? [closed]

Is there any book on mathematical analysis that covers (all) the (same) topics (as) in Principles of Mathematical Analysis by Walter Rudin, 3rd edition, but which is written like Topology by James R. ...
0
votes
1answer
51 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: ...
4
votes
1answer
65 views

Suggest a follow up book to Axler's Linear Algebra Done Right?

So I know that a similar question has probably been asked about alternatives or compliments to this book, but I think my situation is different enough to warrant slightly different advice. So I've ...
0
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0answers
29 views

Is this type of Markov chain known?

I am looking at a situation where we have $N$ urns and $K\le N$ balls. Consider some allocation of the balls to the urns. When any urn contains two or more balls, we call it a colliding urn. The ...
1
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0answers
55 views

Is this ordered square mathematically interesting?

Build a $5\times5$ (say) square using $\frac{1-\left(\frac{3}{2}\right)^n}{(2 m-1) 2^n-1}+1$, $$ \left( \begin{array}{ccccc} 0.5\hfill & 0.9\hfill & 0.944444 & 0.961538 & 0.970588 \\ ...
0
votes
0answers
19 views

Are there prerequisites to “Geometry: Euclid and Beyond” By Robin Hartshorne?

I saw that the "Geometry: Euclid and Beyond" By Robin Hartshorne seemed like a good book to learn geometry. Is this text suitable for someone who doesn't have a lot of geometry knowledge ? Thank you
2
votes
1answer
71 views

Learning Combinatorics Further

I have completed most of the basic parts in Combinatorics like Generalised Permutation & Combination, Recurrence relations, Pigeonhole Principle, Formal power series, Stirling no, Catalan no, ...
1
vote
1answer
30 views

Holomorphic maps between smooth algebraic curves

I am looking for a reference for the following statement: Let $X$ be a smooth projective curve over $\mathbb{C}$. Every holomorphic function $f: X \to \mathbb{P}^1_{\mathbb{C}}$ is in fact a morphism ...
0
votes
1answer
22 views

Best trigonometry book for complete beginner

What are some best trigonometry books for complete beginner I can't decide between S.L loney and I.M Gelfand which would be better for understanding concepts from scratch
0
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2answers
49 views

Prerequisite knowledge required to efficiently understand 'The Art & Craft of Problem Solving'

I would like to improve as a Mathematician and I am currently doing A-Level Mathematics in England. I have come to learn that this book is a fantastic resource for anybody serious about a career in ...
1
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1answer
49 views

book on real analysis.

could anyone suggest me a problem book that comprise interesting problems on topics like series , sequence , functional identities. a good problem book on real analysis is what I'm looking for.
1
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0answers
24 views

How many shuffles are really needed for bridge?

According to the Gilbert-Shannon-Reeds model (which apparently models reality well), one should riffle shuffle seven times to achieve a suitably randomized $52$ card deck. However, it occurs to me ...
6
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1answer
56 views

Distance between theorems

In automated proving one can define the best proof of a theorem as the one which minimizes the length of the proof. Given a set of known statements one could define the difficulty of a theorem as the ...
0
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0answers
16 views

Theory around the Cellular Sheaf

I have lately stumbled upon cellular (co)sheaves, which look very interesting. To understand them better, I would like references that systematically develop the theory behind them (preferably in ...
11
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0answers
154 views

Textbooks on higher category theory

What textbooks on higher category theory are there? What books do you recommend? I am looking for self-contained introductions, no research reports. There are lots of informal summaries and arXiv ...