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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1answer
626 views

Introduction to Linear Algebra 4th Edition by Gilbert Strang fully written solutions / or another book with fully written solutions!

I have gotten my hands on the following book Introduction to Linear Algebra 4th Edition by Gilbert Strang and it's not sufficient for my learning needs, at least not on it's own. I have access to the ...
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2answers
24 views

Suggested measure theory books for certain exercises

I was wondering if anyone knows books with difficult exercises of the theorems of monotone and dominated convergence and if the motto of Fatou possible. I use Bartle but it does not have many ...
1
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1answer
49 views

Resource for coordinate geometry

I am looking for a good resource (preferably in the form of textbooks) for coordinate geometry. Rather than a comprehensive coverage of topics, I am looking more for depth in a particular topic. It is ...
4
votes
1answer
145 views

euclidean geometry books…

I consider myself poor in plane euclidean geometry. so I need a good geometry book which contains very good theory, and a collection a large number of solved problems, and the end of each part.This ...
0
votes
1answer
25 views

Reference Request for Calculus

I'm a first-year math student and have studied single-variable calculus for quite some time. However, with so many proofs and theorems, it's easy to get lost and forget how everything links together ...
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0answers
19 views

Coupled Complex Dynamics

Consider two dynamical systems $$Z_{n+1}=f(W_{n},Z_{n-1}) $$ $$ W_{n+1}=g(Z_{n},W_{n-1})$$ where $w_0, w_{-1}, z_{0}$ and $z_{-1}$ are given complex numbers. If $f$ and $g$ are two functions on ...
3
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2answers
216 views

Proof of Proposition 5.11 of David Cox's Primes of form $x^2+ny^2$?

I'm just beginning to read the paper Finding Eisenstein Elements in Cyclic Number Fields of Odd Prime Degree.* On the third page, in Lemma 2, the author references Proposition 5.11 of David Cox's ...
3
votes
1answer
32 views

Existence of a probability space

Let us assume that we are given a family of Markov chains $(X^\alpha_t)_{t\geq0}$ in continuous time. Kolmogorov's result ensures that for each $\alpha \in I$ there exists a probability space ...
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3answers
120 views

Understanding infinity

I want to understand in a greater depth the concept of infinity. Can someone give me any reference/ text from where I can study and understand about the concept of infinity in mathematics? I would be ...
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0answers
56 views

FLT (Fermat): Combinatorial approaches?

Such a simple equation like $x^n+y^n=z^n$ is bound to have a nice/natural combinatorial interpretation. One very crude one is: Let the number of ways of choosing $n$ objects from $x$ objective, ...
2
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1answer
37 views

$E_6$ lie algebra and its representation

I've just started learning about Lie theory (only just finished up to basic classification of semisimple lie algebras) and I've got the following questions: How do I show that the complex lie algebra ...
3
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1answer
55 views

Sheaves in Philosophy

I once found a book on google.books. It was about the applications of sheave theory to philosophy or more general to social studies. I don't remember for sure. i just know it was not the book Sheaves ...
0
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1answer
39 views

Book Recommendation: Multiple variables calculus [duplicate]

What would be a good book learning Multiple variables calculus? Basically, I'm only interested with the theorems of continuity and differentiation
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1answer
53 views

Possible values of $\gcd(a+b, a\times b)$

Main Question: Let $N \in \mathbb{N}$. What are the possible values of $\gcd(a+b, a\times b)$ given that $\gcd(a,b) = N$? Fact 0. If $\gcd(a,b) = N$, then $N \leq \gcd(a+b, a\times b) \leq ...
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3answers
327 views

Every invertible linear transformation can be perturbed a bit without destroying invertbility, Neumann series

Let $T: V \to V$ be any linear transformation on a real or complex vector space $V$. Show that there exists $\epsilon_0 > 0$ $($depending on $T$$)$ so that $I + \epsilon T$ is invertible for any ...
3
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1answer
73 views

Applications of computer science to mathematics

I have been introduced to algorithms, computability and computational complexity (as part of my minor in CS). What are some mathematical topics that I can tackle with the new perspectives I ...
1
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0answers
31 views

Method for defining a number of connected components of real algebraic surface

The question is simple: given the concrete polynomial $f(x,y,z)$ ($x$,$\,$ $y$ and $z$ are real numbers), is there any method for answering this question for a surface $f(x,y,z) = 0$? I'm interested ...
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0answers
17 views

Rotationally non-symmetric Sine Gordon application

Has the intrinsic Sine-Gordon equation been ever used to define asymptotic lines on constant negative Gaussian curvature surfaces of Kuen, Breather or other rotationally non-symmetric surfaces ? ...
2
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0answers
32 views

Properties of a modified Zariski topology

For any set $I \subseteq \mathbb{C}[X_1, \dots, X_n, Y_1, \dots, Y_n]$ of polynomials let us define $$V'(I) := \{ x \in \mathbb{C}^n : f(x,\overline{x}) = 0 \text{ for all } f \in I \}.$$ In analogy ...
2
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3answers
80 views

geometry developments during the Islamic Golden Age (7-13 century)

Can anybody refer me to publications on geometry during the Islamic Golden Age? My interest is especially on Arab geometry an non-Euclidean geometry. But searching for sources was a saddening ...
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4answers
3k views

Undergraduate/High-School-Olympiad Level Introductory Number Theory Books For Self-Learning

I don't know whether the books metioned in Best ever book on Number Theory are beyond undergraduate/high-school-olympiad level. Please recommend your favourite.
3
votes
1answer
551 views

Good book resources (not websites) to learn number theory on my own? [duplicate]

Possible Duplicate: Undergraduate/High-School-Olympiad Level Introductory Number Theory Books For Self-Learning I took number theory this semester and loved it but don't feel like I learned ...
0
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1answer
245 views

Permutations and Combinations reference request

I have an exam on Wednesday on Permuations and Combinations and while I understand most of the concepts, I find it difficult to apply it to the questions because I haven't done many practice ...
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0answers
42 views

Solution of a linearly constrained quadratic programming problem

What is the solution of the following optimization problem: \begin{align} &\min{\mathbf{p}^\mathrm{T} \mathbf{B} \mathbf{p}}\\ &\text{subject to}: \mathbf{0}\leq{\mathbf{p}}\leq \mathbf{1}. ...
1
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1answer
51 views

Can $\pi(x)-\operatorname{Li}(x)=O(\sqrt x\log(x))$ be proven without using $\psi(x)$?

Assuming the truth of the Riemann hypothesis, $\pi(x)-\operatorname{Li}(x)=O(\sqrt x\log(x))$. Apparently the proof that $\psi(x)$ approaches $1$ for sufficiently large $x$ proves the error term. ...
1
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1answer
62 views

Relationship between the cocountable and standard topologies on $\mathbb{R}$

Where can I find a proof of the fact that the cocountable topology on $\mathbb{R}$ is coarser than, finer than, or not comparable with the standard topology on $\mathbb{R}$? For a seemingly standard ...
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0answers
114 views

Books which explain vector analysis/algebra in detail.

I'm trying to learn vectors but I can't find a decent book which explains vectors in depth. I need a book which explains vectors from the beginning, using a beginner's approach(assuming the reader ...
4
votes
1answer
87 views

A doubt about Differential Geometry Books.

I intend to read "Physics for Mathematicians" by Spivak, and he says that vols. 01 and 02 of "A Comprehensive Introduction to Differential Geometry" are necessary to understand the book. Are those ...
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0answers
54 views

any online video course for analytic number theory or elementary number theory?

All: I am looking for online video course on analytic number theory for self-study. On Youtube, there are a few seminars, but no complete course for a semester or a year. Can anyone point out if ...
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7answers
636 views

A book for abstract algebra with high school level

Any book that I find on abstract algebra is somehow advanced and not OK for self-learning. I am high-school student with high-school math knowledge. Please someone tell me a book can be fine on ...
1
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1answer
42 views

$\int_\Omega |\nabla u^+|^2 \, dx$ is not differentiable with respect to $u$ in $W_0^{1,2}(\Omega)$

Let $u \in W_0^{1,2}(\Omega)$, where $\Omega$ is some domain in $\mathbb{R}^N$, $N \geq 1$. Denote $u^+ := \max\{u, 0\}$. (It is know that $u^+$ also belongs to $W_0^{1,2}(\Omega)$ (see, e.g., ...
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0answers
7 views

Reference request random time changes representations and weak convergence

I was reading the Kurtz's book 'Markov Processes: Characterization and Convergence' and I need to prove a similar theorem as theorem 1.5 on chapter 6 of that book, that basically states that if $Y$ is ...
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1answer
80 views

Ham Sandwich theorem used in combinatorics problem involving beads on a necklace

Ok, so according to a friend of mine you can use the ham sandwich to prove the following theorem: Suppose there is a necklace with $m$ types of beads and $2n_1,2n_2...2n_m$ beads of each colors. So ...
4
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1answer
119 views

Are strongly close maps homotopic?

While reading about various results related to density of smooth functions in the space of continuous functions with strong topology, I've got the impression that it is a general fact that for any ...
0
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1answer
39 views

Set family closed under symmetric difference

I have been looking for information on (finite) set families $\mathcal F$ such that if $X,Y \in \mathcal F$ then $X \,\triangle \,Y \in \mathcal F$. Are these kind of families (possibly with extra ...
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1answer
917 views

Difference between Gilbert Strang's “Introduction to Linear Algebra” and his “Linear Algebra and Its Applications”?

Could someone please explain the difference between Gilbert Strang's "Introduction to Linear Algebra" and his "Linear Algebra and Its Applications"? Thank you.
3
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2answers
791 views

Study of Set theory: Book recommendations?

Can you suggest a good book for set theory? I have just started reading about Group theory and want to learn set theory on my own. Thanks in advance
1
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1answer
46 views

Is there any good text introducing a part of Borel-hierarchy which is in need in measure theory

Is there any good text introducing a subpart of Borel-hierarchy which is in need in measure theory, which can be done in short time? Say, 1~3 days if possible. (Assuming I'm studying about 14hours a ...
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2answers
860 views

The way into set theory

Given that I am going through Munkres's book on topology , I had to give a glance at the topics included in the first chapter like that of Axiom of choice, The maximum principle, the equivalence of ...
4
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0answers
75 views

Every irreducible character of $G$ is an irreducible character of $H$?

Let $H$ be a proper subgroup of $G$ such that for all $\chi\in Irr(G)$, $\chi_H\in Irr(H)$. That is, the restriction of every irreducible character of $G$ to $H$ is an irreducible character of $H$. ...
5
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2answers
61 views

Jones Polynomial from Statistical Mechanics

I've been told that, given a knot projection, there is a way of associating a statistical system in such a way that the partition function of the system corresponds to the Jones polynomial of the ...
1
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1answer
94 views

Reference request - Outline of Edward Nelson's Inconsistency Proof

Edward Nelson retracted his inconsistency proof before it was published. Unfortunately, the outline given by Nelson has been removed. Is there a copy of it on the web? I am interested in how the ...
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3answers
592 views

Is the configuration space of a connected space connected?

Let $X$ be a topological space. Given an integer $n\ge 2$, let $F_n(X)$ be the set of all ordered $n$-tuples $(x_1,x_2,\dots,x_n)\in X^n$ such that $x_i\ne x_j$ whenever $i\ne j$. Being a subset of ...
6
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3answers
339 views

Linear algebra and geometric insight: a rigorous approach to vector spaces, matrices, and linear applications

I'm searching for some material (books or lecture notes) that extensively uses a geometric approach to explain the meaning of the concepts realted regarding to vector spaces, matrices, and linear ...
2
votes
1answer
21 views

Resources that describe schemes for nondimensionalization of ODEs and PDEs?

I am able to find plenty of notes that give examples of how a few particular examples may be non-dimensionalized, but I am wondering if there is something more general worth studying? A benefit of a ...
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0answers
31 views

Lagrangian and Hamiltonian Mechanics

I am interested in how Lagrangian and Hamiltonian mechanics and then symplectic geometry was developed starting from Newtonian mechanics. We can start by assuming that Newtonian mechanics tells us ...
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1answer
60 views

Modular property of Weierstrass $\wp$ function

For $\tau\in \mathbb H=\{ x+iy\in \mathbb C \lvert x,y\in \mathbb R, \, y>0\}$ and $z\in \mathbb C$, let us define $$ \wp=\wp(\cdot,\tau): \mathbb C \rightarrow \mathbb P^1\, , \quad z\mapsto ...
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0answers
21 views

Finite Groups of Isometries of Euclidean spaces

Six years before, I had a collection of articles on finite groups of rotations of sphere, from Monthly, Gazette, Intelligencer. But I lost these articles. Since I am teaching this topic, I would like ...
2
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1answer
89 views

Modern treatment of Topology that focuses on intuition and is full of explanations and visual insights.

I'm interested in a modern treatment of Topology (point-set, and general topology at the undergraduate level) that focuses on intuition and is full of explanations and visual insights. This will be ...
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0answers
23 views

Uniform limits of pathological functions

I'm interested in the following (perhaps somewhat artificial) problem: Suppose $f$: $\mathbb{R}\longrightarrow\mathbb{R}$ is a function taking open subsets $U\neq\emptyset$ to dense subsets. It's ...