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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literature on advanced calculus

I need your opinions on this particular textbook: Advanced Calculus by Robert C. Buck. In my first year in college I finished two semesters of single-variable calculus and now I'm looking for a proper ...
0
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1answer
16 views

A road-map through “Combinatorial Set theory: With gentle intro to independence proofs”

I'm going to study independence proofs form Halbeisen's book. It seems that some material is not needed to study independence proofs, so it seems that the book contains more material than my needs. ...
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0answers
15 views

Any online videos on a course taught from Munkres?

Are there any vidoes available on the Internet --- for watching online or for download --- of any (general) topology course taught using the book Topology by James R. Munkres, 2nd ed? If so, please ...
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1answer
47 views

Mathematics in Chemistry [on hold]

What are the applications of mathematics in chemistry, biology ? Please give some references including text books if any.
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2answers
77 views

Ayn Rand and athematics

I am an honors undergraduate in mathematics. I have taken an interest in objectivism. I came across a discovery of Ms. Ayn Rand's in mathematics: In a triangle the inscribed circle touches the ...
0
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0answers
9 views

Eigenvalues of normalized adjacency matrix

Can anyone introduce some references on the eigenvalue estimation of normalized adjacency matrix, i.e., $W=D^{-1}A$ ($D$ is the degree matrix and $A$ is the adjacency matrix of the corresponding ...
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0answers
45 views

Books for Ordinals and Cardinals

I am looking for a nice introductory book to read to learn and master ordinals and cardinals. Please help me!
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1answer
32 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 ...
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0answers
9 views

Reference on Malcev completion

I need a reference for learning Malcev completion, its associated group scheme and Lie algebra. Thanks!
0
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2answers
30 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 ...
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0answers
12 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
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1answer
31 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
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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?
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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, ...
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5answers
124 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 ...
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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
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2answers
104 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 ...
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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 ...
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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 ...
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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
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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 ...
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2answers
84 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 ...
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4answers
85 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
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0answers
36 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 ...
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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 ...
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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 ...
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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. ...
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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
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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
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0answers
43 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
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2answers
42 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 ...
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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 ...
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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 ...
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0answers
39 views

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

What are the historical reasons that created the term "linear mapping"?
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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
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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
1answer
85 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
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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 ...
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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
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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? ...
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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. ...
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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 ...
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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 ...
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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
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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 ...
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1answer
95 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 ...
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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 ...
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0answers
147 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
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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 ...