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.

learn more… | top users | synonyms (3)

0
votes
0answers
10 views

Reference Request: Subgroup of free abelian group is free abelian

I have the following reference Question, meaning that I search for a reference for the following statement: Let $F$ be a free abelian group of finite rank and $U$ be a subgroup. Then there is a basis ...
0
votes
0answers
6 views

Reference on Malcev completion

I need a reference for learning Malcev completion, its associated group scheme and Lie algebra. Thanks!
0
votes
2answers
29 views

Prove (or derive) the de Polignac formula for the prime decomposition of $n!$

I can't seem to find any papers published dedicated to show that the de Polignac formula has a rigorous derivation. From Wikipedia's entry for the formula: Let $n \geq 1$ be an integer. The prime ...
0
votes
0answers
11 views

Inverse Laplace operator $\Delta^{-1}$ in $H^1_0, \ H^{−1}$.

Let open domain $\Omega \subset \mathbb R^n$, $u : \Omega \rightarrow \mathbb R$, $u \in H^1_0 (\Omega)$ and $f \in H^{−1}(\Omega)$. I'm looking for some known expressions of the inverse Laplace ...
2
votes
1answer
27 views

Jacobi Elliptic Functions built from Jacobi theta functions

I believe I understand the general theory of elliptic functions to an extent. What I can't seem to find is the distinct method which was used to show that a particular combination of Jacobi Theta ...
-1
votes
0answers
29 views

Partial Differential Equations Solver

Anyone knows a good website/program in which you enter your partial differential equation with the initial conditions and it simply solve it?
-2
votes
0answers
32 views

Asking for an article [on hold]

I tried to download this article: M. N. Huxley, Area, lattice points, and exponential sums, London Mathematical Society Monographs. New Series, vol. 13, The Clarendon Press Oxford University Press, ...
2
votes
5answers
122 views

Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”

If $C$ and $A$ are the circumference and area of a circle, then $$ \frac{C^2}{A}=4 \pi\; . $$ I'm looking for a reference to an elementary but rigorous proof of it. I'm particularly interested in ...
0
votes
0answers
28 views

Books for Real analysis similar to or having same essence like Charles Pinter Abstract algebra

I am looking for book which is similar to spirit of pinter's book mentioned in question that is which is suitable for self study and beginners. Can anyone recommend? Thanks
5
votes
1answer
93 views

Two questions on the Grothendieck ring of varieties

1) In the definition of the Grothendieck ring of varieties over a field $k$, which definition of the various notions of "variety" is chosen? Finite type and separated, or maybe more? 2) If ...
1
vote
0answers
11 views

An example of frame operator.

A sequence of distinct vectors $\{f_1,f_2,...\}$ belonging to a separable Hilbert space $H$ is said to be a Frame if there exist positive contants $A$, $B$ such that, for $A<B$ and for all $f\in ...
0
votes
0answers
24 views

Finding references about modular forms and symmetric power $L$-functions

I want to write an introduction to my thesis which is about modular forms and symmetric power $L$-functions. Could you give me good references to these two topics as simple as possible to get an ...
1
vote
0answers
26 views

Class field theory of imaginary quadratic fields

Can someone give me a good source that deals in detail with the Class Field Theory of imaginary quadratic fields? The sources on CFT that I have at hand only deal with CFT in general and then proceed ...
2
votes
2answers
32 views

Positiveness of partial sums of type $ \psi * D_N $

In his paper about Extremal Functions for the Fourier Transform (see, for example, here? https://projecteuclid.org/download/pdf_1/euclid.bams/1183552525), Jeffrey Vaaler, while trying to build ...
1
vote
2answers
82 views

Hardcore Abstract Algebra Book Request

I am going to start learning Abstract Algebra soon. I was originally going to start with Dummit and Foote, but I am starting to abandon that idea. I want to use a "hardcore" algebra book. I don't mind ...
0
votes
4answers
83 views

In need of a group theory textbook.

I am in need of a group theory textbook for a good summer review. I have already studied from various books (mostly "group theory" part from basic algebra books) and the lecture notes of my teacher, ...
5
votes
0answers
34 views

Mathematically rigorous books on programming and computer science

I would like a mathematical approach to programming languages and computer science, not just the theoretical aspects of computer science. Is there any such text out there? After all, the world has a ...
4
votes
2answers
44 views

About Mordell's Theorem (Elliptic Curves)

I've just finished the proof of Mordell's Theorem given in the book "Rational Points on Elliptic Curves " by Silverman. One of the key lemmas used in the proof of the theorem is: Let ...
-6
votes
0answers
41 views

Which harvard course should I take? [on hold]

apologies if I'm on the wrong website or anything. I'll be starting math at Harvard next year but am at a loss as to which course I should start with. I have a good background in competition math (so ...
0
votes
2answers
31 views

Reference request for this topics

I need a good reference to learn these topics Markov Chains in discrete time.    1.1. Classification of states, recurrence notions of transience.    1.2. Stationary measure.    1.3. ...
3
votes
1answer
84 views

Difference between proof-based calculus and analysis?

When I asked a teacher at school what the difference between calculus and analysis he said that calculus is essentially analysis without proofs. So where does proof-based calculus lie? Is it somewhere ...
6
votes
1answer
130 views

What proof uses both the Riemann Hypothesis and its negation?

Some time ago I happened to see a proof that was remarkable in that it used both the Riemann Hypothesis and its negation. That is, it considered the two cases: RH is true, and RH is false, obtaining, ...
1
vote
0answers
42 views

Proof of the formula for dimension of moduli of stable vector bundles on smooth curves

Let $C$ be a smooth curve of genus $g \ge 2$ over an algebraically closed field of positive characteristic. If I understand correctly, the dimension of the moduli space of vector bundles on $C$ of ...
2
votes
2answers
34 views

What are good references for the action of $\Gamma := \pi_1(S)$ on $S^1 = \partial \mathbb{H}^2$, where $S$ is a closed hyperbolic surface

To give some examples: what can we say about the action of $\Gamma$ on the set $V$ of points of $S^1$ that are not fixed for any element of $\Gamma$? Does there exist a Borel fundamental domain for ...
0
votes
0answers
24 views

Looking for reference to solve a problem (representation theory, I think?)

this question appeared on an algebra qualifying exam: Let $R$ be the group algebra $\mathbf{C}[S_3]$. How many nonisomorphic, irreducible, left modules does $R$ have and why? Would I be able to ...
0
votes
0answers
45 views

Does the restriction of the Thom class of a submanifold to the cohomology of the submanifold give the Chern class of the normal bundle?

Let $X$ be a compact complex manifold of (complex) dimension $d$, let $i\colon Y\hookrightarrow X$ be a regular complex submanifold of (complex) codimension $k$, let $\mathcal{N}_{Y/X}$ be the normal ...
0
votes
0answers
39 views

Why do we call a linear mapping “linear mapping”? [migrated]

What are the historical reasons that created the term "linear mapping"?
0
votes
0answers
49 views

How to prove it and how to solve it

Tomorrow I will begin my studies, real analysis, however I have some difficulties in making statements so I thought before starting the study in real analysis, learn how to do demonstrations properly. ...
2
votes
1answer
30 views

Lie algebra and Lie group cohomology, reference request

Who can give me a good reference (better if introductory/motivated) about Lie group cohomology, Lie algebra cohomology, and the link between the two? Thanks.
5
votes
0answers
67 views

How can I calculate the formula of this fractal-like structure?

I did the following fractal-like structure manually, and I was trying to convert it to a formula (or an algorithm including formulas) to compute some parts of the drawing, but I get lost due to the ...
0
votes
1answer
42 views
+50

Modeling, Measuring, and Maximizing “Mixedness”

Background: My class has $10$ students and $3$ tables; naturally, the students are distributed with $3, 3,$ and $4$ seated at the individual tables. On the second day of class, students sat in the ...
2
votes
0answers
64 views

Categories that differ in morphisms

Let $C_1$ and $C_2$ be two (small) categories defined over the same set of objects: that is, $C_1$ and $C_2$ differ only in their hom-sets. Specifically, $Hom(C_1) \neq Hom(C_2)$, and $Hom(C_1) \cap ...
2
votes
0answers
34 views

Set of functions from a finite field to the integers

Has the set of functions $\mathbb{F}_q \to \mathbb{Z}$ endowed with pointwise addition and additive/multiplicative convolution been studied? Does anyone know a reference or keywords to search for? ...
-2
votes
0answers
34 views

“Elementary Set Theory - Leung, Chen” - Solution manual? [closed]

I'm trying to study some ST on me own :-) ! I have found a very nice book with lots of problems but without any solution to the problems. Do you guys know whether someone have made a solution manual ...
0
votes
1answer
23 views

Reference help about fuzzy logic and fuzzy set

Good afternoon, I'm trying to learn about Fuzzy alone, I was using some texts on the Internet about it, but it was very difficult to learn. I want to learn about Fuzzy set as shaper of uncertainty. ...
1
vote
1answer
18 views

Reference for the statement “bilinear form $a$ is symmetric if and only if the operator $S$ is self-adjoint”

Thanks to Riesz representation theorem, a continues bilinear (sesquilinear) form on Hilbert space $$a: \mathcal H\times \mathcal H\rightarrow\mathbb R \ \ (\text{or} \ \ \mathbb C)$$ can be ...
1
vote
1answer
14 views

Is optimal bound for Alcuin's triangular city problem known?

Alcuin's triangular city problem is Problem 28 from Propositiones ad Acuendos Juvenes. There is a triangular city which has one side of 100 feet, another side of 100 feet, and a third of 90 ...
0
votes
1answer
19 views

Intervals of integers modulo n

Do the following related concepts appear anywhere in literature? Denoting an "interval" in the integers modulo $n$ by $[i,j] = \{i, i+1, \dotsc, j\}$. For example, in modulo 6, $[5,3] = ...
1
vote
1answer
25 views

What is this 2-D array of numbers called?

Define $c(n,r)$ ($n\in\Bbb N;r\in\Bbb Z$) by setting $c(0,-1)=-1$, $c(0,0)=1$, and $c(0,r)=0$ otherwise, with all further $c(n, r)$ given recursively by $$c(n+1,r)=rc(n,r-1)-(r+1)c(n,r)$$(rather in ...
6
votes
1answer
93 views

Good resources for studying independence proofs

I've finished most of Enderton's set theory. And I intend to spend some time studying independence proofs. I'm more interested in independence of axiom of choice not CH. From I know so far, there ...
0
votes
0answers
17 views

Quartic spline explanation

I need to use a quartic spline (natural spline) for a robotics application. However, most of the documents explaining splines focus on quadratic and cubic splines. Could you please give me some ...
7
votes
0answers
146 views

What is known about the sum $\sum\frac1{p^p}$ of reciprocals of primes raised to themselves?

Consider the following series: $$\sum_{p\in\mathcal{P}}\frac{1}{p^p}$$ where $\mathcal{P}$ is the set of all prime numbers: $\mathcal{P}=\{2,3,5,7,11,13,\ldots\}$. My question is: Is this a ...
0
votes
0answers
45 views

Math study plan for first year uni [closed]

firstly apologies if threads like this aren't allowed on this site. I will be starting undergraduate math next year. At the moment I have no background at all in higher math. Here are the books I am ...
0
votes
2answers
48 views

On proving $(f^{-1})'(b) = \frac{1}{f'(a)}. $ where $b = f(a)$.

Could somebody kindly provide a proof or a reference to a proof of this fact: Let $ I $ be an open interval, and suppose that $ f: I \to \mathbb{R} $ is one-to-one and continuous on $ I $. If $ f ...
2
votes
0answers
24 views

Need ''The diameter of the prime graph of a finite group'' by Lucido

I need a paper by Lucido, I am studying prime graphs to make a presentation in Group theory class, which is here on degruyter. Now, my college doesn't have access to degruyter (although is has to many ...
-1
votes
0answers
58 views

Blogs by mathematicians of our days [closed]

Please, provide a link to blogs of mathematicians( not those of Terence Tao, Timothy Gowers[and which are present on their pages] say, as I'm already familiar with them).
1
vote
0answers
17 views

Discrete version of Sylvester's Law of Inertia

Given a matrix $A\in\mathbb{C}^{n\times n}$, we denote by symbol $\mathrm{In}_d (n_<,n_>,n_1)$, the discrete inertia (or inertia w.r.t. the unit circle) of $A$, where $n_<,n_>$ and $n_1$ ...
2
votes
1answer
27 views

The 1-Norm on a Quantum Group as a Supremum

To this MO question, Yemon Choi comments that If $\tau$ is a faithful normal trace on a von Neumann algebra $M$, then IIRC $\tau(|x|)$ is equal to the supremum of $|\tau(xy)|$ as $y$ runs over all ...
0
votes
0answers
29 views

The equivalent of least squares, but for vectors

Given a set of poins, one can use a fitting method such as least squares to find the straight (or the parabola, or the 3rd grade equivalent) that's closest to all points at the same time (via ...
3
votes
1answer
59 views

Reference Book for Calculus

I've made this post as detailed as I can so as to give you a fair idea of my level. Calculus (particularly Integration) is my passion and frankly I spend all my free time learning as much of it as I ...