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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3
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1answer
49 views

Modular arithmetic - Suggestions to begin

I've always wanted to start studying modular arithmetic to try to solve problems like: $$\text{find } n \in \mathbb{N} : 4n^2 \equiv 1 ~(\text{mod }{10^4})$$ I have a good basis in mathematical ...
4
votes
2answers
103 views

Toy examples for Kan extensions

Background: If $\mathcal{C}$ is a cocomplete category and $f : I \to J$ is a functor between small categories, then $f^* : \mathrm{Hom}(J,\mathcal{C}) \to \mathrm{Hom}(I,\mathcal{C})$ has a left ...
-2
votes
0answers
37 views

Solutions that are easy to sketch but difficult?

I am wondering if there are any famous problems in math where everyone knew how the solution should proceed, but the sheer mental effort required to execute that solution was itself what made no one ...
2
votes
0answers
34 views
4
votes
1answer
170 views

Recommended books/articles for learning set theory

What is the recommended reading for thoroughly learning set theory? I'm currently studying Kunen's book [1]. But what then, and in what order? One needs to learn large cardinals, inner models and ...
4
votes
2answers
120 views

Reading on Mathematical Logic

I am looking for books to read, so as to dive into mathematical logical and related disciplines like set theory, model theory, and topos theory. I have a decent background in category theory and ...
17
votes
6answers
7k views

What are good books/other readings for elementary set theory?

I am looking to expand my knowledge on set theory (which is pretty poor right now -- basic understanding of sets, power sets, and different (infinite) cardinalities). Are there any books that come to ...
1
vote
5answers
600 views

Books on theorems of Basic set theory after Logic…?

I have good knowledge of Propositional and Predicate Logic.I want to begin set theory. I am looking for books that explain set theory principles using Logic. and also books which have lots of theorems ...
2
votes
2answers
196 views

Logic and number theory books

I've recently decided to start preparing for uni, so I figured I need to learn logic and some number theory. I picked up Burton's Elementary Number Theory and wasn't quite comfortable with it, seemed ...
2
votes
5answers
872 views

Logic and set theory textbook for high school

Do you have any advice for a textbook or a book for high schools students which completely adresses basics of logic (proposition, implication, and, or, quantifiers) and set theory (intersection, ...
2
votes
3answers
98 views

Good references on Riemannian Geometry

I'd like a textbook that covers do Carmo's contents (can be more), but that isn't do Carmo. I did not like his writting style. That being said, I particularly like the styles of: Walter Rudin ...
4
votes
3answers
274 views

Any suggestions about good Analysis Textbooks that cover the following topics?

I am an undergraduate math major student. I took two courses in Advanced Calculus (Real Analysis): one in Single variable Analysis, and the second in Multivariable Analysis. We basically used Rudin's ...
0
votes
0answers
47 views

Revisiting maths through self study

I am a practicing commercial engineer having studied 3 Maths courses during undergraduate college (2004-2008). Now I want to return to my real passion i.e. astrophysics/ quantum mechanics on my own. ...
1
vote
1answer
270 views

How to learn problem solving (IMO and IPhO)

I'm not interested in IMO and IPhO actually, but one of the most prestigious universities in my country admits students using a test which is composed by 5 IMO and IPhO questions (or slighly lower). ...
0
votes
0answers
18 views

A reference for finding a theorem

I want a reference to find the proof of the following Theorem on real analysis: Thanks
3
votes
0answers
72 views

Motivation behind automorphism bases?

Given a model $\mathcal{M}$ with a domain $M$ and $B \subseteq M$, $B$ is an automorphism base for $\mathcal{M}$ iff $\forall f \in Aut(\mathcal{M}). (\forall b \in B. f(b)=b) \implies f = ...
0
votes
3answers
594 views

Which Linear Algebra textbook would be best for beginners? (Strang, Lay, Poole)

I am looking at buying 1 of the 3 following Linear Algebra texts for my reference. Introduction to Linear Algebra by Gilbert Strang 4th edition Linear Algebra and its Applications by David Lay 4th ...
7
votes
1answer
2k views

Restricted Three-Body Problem

The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...
1
vote
4answers
50 views

Proofs for statistics and normal distributions

I am studying statistics, and it it, we are given many different results about what kind of estimations we can make and what kind of distributions these estimations have. For example, assume ...
1
vote
3answers
362 views

Video lectures and reference book Multivariable calculus

I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning ...
2
votes
1answer
271 views

Looking for first course textbooks on probability and statistics for math majors

I am taking a probability and statistics course soon and would like to find a text book that is targeted more towards math majors rather than engineers (which is what this class is). The book my ...
0
votes
0answers
18 views

How is Lagrange's $2\sqrt{D}$ bound on partial denominators proven for periodic regular continued fractions of quadratic irrationals

For the quadratic surd: $$ \zeta = \dfrac{P + \sqrt D}Q $$ the wikipedia article on periodic continued fractions mentions that Lagrange proves that the largest partial denominator of a regular ...
0
votes
1answer
29 views

equivalence of any two polynomials of same degree

Let $P$ and $Q$ be two polynomials of same degree with real coefficients. Assume that $P$ and $Q$ have no real roots. It seems to me that $P$ and $Q$ are equivalent in the sense that there are some ...
1
vote
1answer
100 views

Best self study book with answers to selected questions for analytic number theory?

All: Can anyone recommend Best self study book with answers to selected questions for analytic number theory ? If a book have no answers to questions, but if you know if some professors choose the ...
0
votes
0answers
21 views

Please recommend the most easy to read analytic number theory book for self study [duplicate]

All: Can anyone recommend the most easy to read analytic number theory book for self study ? Prefer with hint to exercise. I have Apostol's, Introduction to Analytic Number Theory, just want to see ...
11
votes
1answer
114 views

Rings in which binomial theorem holds for at least one integer $n>2$

Let $R$ be a ring ; if $(a+b)^2=a^2+2ab+b^2 , \forall a,b \in R$ , then we know that $R$ is commutative ; also if $R$ is commutative then we know that $(a+b)^n=\sum _{r=0}^n {n \choose r} a^{n-r}b^r , ...
1
vote
0answers
18 views

Compactness of Pseudo-differential Operators on $H^s(\mathbb R^n)$?

The Sobolev space of order $s\in\mathbb R$ in $\mathbb R^n$, denoted by $H^s(\mathbb R^n)$, is defined as follows: $$H^{s}(\mathbb R^n):=\{u\in\mathscr{S}^{'}(\mathbb R^n): \exists f\in ...
1
vote
0answers
14 views

Introduction to Euler structures

I am looking for a basic text on Euler structures, in particular smooth Euler structures, and the relation to combinatorial Euler structures; It is known that given a combinatorial Euler structure on ...
2
votes
1answer
29 views

Derivative with respect to another function

I stumbled on this calculus problem here: Let $f(x) = \ln|\sec x + \tan x|$ and $g(x) = \sec x + \tan x.$ Find the fourth derivative of $g(x)$ taken with respect to $f(x)$ A)$\\$ $f'(x)$ ...
1
vote
1answer
28 views

Geometrical shapes overwiev [closed]

I am looking for huge summary with hierarchical structure of solid geometrical shapes with exact definition, solid properties (e.g. number of edges, faces, corners, regularity, symmetry and many ...
4
votes
2answers
73 views

How does Ulam's argument about large cardinals work?

I am looking for either a reference, a proof, or a suitable proof sketch that can explain Ulam's original argument about measure theory and measurable cardinals. Here is the result I am looking for: ...
1
vote
2answers
26 views

Clifford Algebras for Projective and Conformal Geometry

According to Clifford Algebra: A Visual Introduction, A Clifford Algebra over $\mathbb{R}^3$ may describe the rigid motions in space (namely, conjugation acts as a reflection by a plane). A ...
0
votes
0answers
48 views

What are the sequels to Rudin's Functional Analysis?

Briefly speaking my purpose, I'm looking for the sequels to Rudin's Functional Analysis. How about the following books by Stein? Are there any other nice ones? Harmonic Analysis: Real-Variable ...
0
votes
0answers
14 views

an oscillatory integral with two parameters

Consider $$I(a,b)=\int_{\mathbb{R}}e^{i(ax^2+bx)}\psi(x)\,dx$$ where $\psi$ is smooth and supported in $\{x:|x|\in[1/2,2]\}$. How to control $I(a,b)$ in terms of $a$ and $b$? Moreover, is there an ...
4
votes
1answer
78 views

General bibliography for the work of Grothendieck

I'm reading the first volume of Scharlau's Grothendieck biography (eagerly anticipating the other two/three volumes) and the Grothendieck-Serre correspondence as part of a historical-philosophical ...
17
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8answers
866 views

Definition of definition

I was wondering if there is a good way to "define" what definition means exactly in mathematics. Since the answers may be subjective or philosophical, I want to ask only for references on this topic. ...
0
votes
0answers
3 views

Reference request: Generalized Hurst Exponent

I'm looking for some references on the Generalized Hurst Exponent of a time series, more than what is on wikipedia. The Generalized Hurst Exponent, $\mathbb{H}_q$ is defined by ...
2
votes
0answers
30 views

Spin group Spin(4,1)

i'm interested in the spin group $Spin(4,1)$ wich correspond to the symplectic group $Sp(1,1)$. The only source that I could find about it was wikipedia (http://en.wikipedia.org/wiki/Spin_group). It ...
4
votes
1answer
424 views

Conformal parametrization of an ellipse

I am looking to a formula for the conformal map from the unit disc in the interior of an ellipse centered in $0$ and with semiaxes $a,b>0$. I know that depends on elliptic function, but I didn't ...
13
votes
6answers
1k views

Is there any book/resource which explain the general idea of the proof of Fermat's last theorem?

I look for a book/resource which display the general idea of the proof of Fermat last theorem in a simple manner for the public. I mean, books which is not for mathematicians but for the general ...
4
votes
2answers
315 views

Models of hyperbolic geometry

Wikipedia states the following: [The Poincaré half-plane model of hyperbolic geometry] is named after Henri Poincaré, but originated with Eugenio Beltrami, who used it, along with the Klein model ...
4
votes
2answers
181 views

Dynamical systems and differential equations reviews/surveys?

I would be very glad if someone could point me to modern reviews/surveys on these topics. To be concrete, I'll provide some examples: S. Smale, Differentiable dynamical systems D. V. Anosov, On the ...
1
vote
1answer
522 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 ...
1
vote
2answers
23 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
vote
1answer
45 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
143 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 ...
0
votes
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
votes
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
31 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 ...