This tag is for questions where the poster seeks 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
20 views

Finite measure on positive integers

Disclaimer: I am sure that this idea is not at all new, but I have had trouble locating content directly related. I humbly accept that this question may be the result of a brain fart. Suppose that ...
2
votes
2answers
66 views

Good reference book for quadratic integer rings?

Could anyone direct me to a good reference book(s) for quadratic integer rings? Ideally, the reference would begin with their elementary properties and then proceed through their ring-theoretic ...
1
vote
1answer
41 views

Does this notion of the “directed area” of a closed curve in $\mathbb R^3$ have a standard name?

Given an oriented surface $\Omega$ in $\mathbb R^3$, consider the quantity $\mathbf A(\Omega)=\int_\Omega\hat n\,\mathrm dA$. We may call this the "directed area" of the surface because, when $\Omega$ ...
2
votes
1answer
58 views

Develop good understanding of Linear Algebra

I am self studying Linear Algebra from book by Kenneth Hoffman and Ray Kunze, and currently I'm on 2nd Chapter of vector spaces, though the text is easy to follow, specially the exercises that follow ...
5
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0answers
46 views

Type-definable Forcing or forcing in a non-first order setting

Roughly speaking, in set forcing the forcing notion is a set from ground model's perspective and in class forcing its a definable subset of the ground model given by solutions of some formula with ...
4
votes
2answers
219 views

Is there any category theoretic proof for independence of Continuum Hypothesis?

Both of set theory and category theory could be a foundation for mathematics. Many set theoretic arguments could be translated to a category theoretic argument and vice versa. Question: Is there ...
11
votes
2answers
134 views

Partitioning the plane into three sets each intersecting the vertices of every square with side 1?

Q1. Is it possible to partition the plane into three sets such that each of them contains at least one vertex of every square with side 1 ? (I mean all squares of side-length 1, not just those with ...
1
vote
2answers
57 views

$\prod\limits_{i=1}^n \frac{3a_i+2}{2a_i+1}, a_i\geq 1$

$$\prod\limits_{i=1}^n \frac{3a_i+2}{2a_i+1}, a_i\geq 1$$ Claim: This product is never an integer ($a_i$ integer).
2
votes
1answer
80 views

Tannaka reconstruction: reference request

What is a classical and perhaps even original reference for the following result, often called Tannaka reconstruction? Let $G$ be a group and $R$ be a commutative ring in which $0,1$ are the only ...
1
vote
1answer
33 views

What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult?

What is Neyman-Pearson lemma? Why is this proof of Neyman-Pearson's lemma look so diffcult? I am consider taking a undergraduate course in my college called mathematics of statistics and in the ...
2
votes
2answers
35 views

The existence of conjunctive/disjunctive normal forms?

I am studying propositional logic/calculus and I am currently learning about normal forms. The algorithm to construct a conjunctive/disjunctive normal form from any given formula is straightforward. I ...
2
votes
0answers
22 views

Books on pseudocomplemented lattices and Heyting algebras

I was wondering if anyone knows a good reference for pseudocomplemented lattices and/or Heyting algebras. Ideally, it should be something like Givant & Halmos's Introduction to Boolean Algebras, ...
0
votes
1answer
81 views

who, by doing what, can make major contributions (breakthrough/discoveries) in math research?

I am a Math Ph.D student, had already published two small articles. I want to ask more experienced mathematician a question. What kind of person, by doing what, can make major contributions ...
1
vote
1answer
34 views

looking for specific recreational math puzzle book

Long time ago, I read a (recreational) math puzzle book and I remember was that in the pocket book there was a puzzle where the parents of a worm were deciding how big the blanket for their baby ...
3
votes
1answer
49 views

Demystifying the asymptotic expression for the partition function

A partition of an integer $n$ is a way of writing $n$ as a sum of integers. The partition function $p(n)$ counts the number of distinct partitions of $n$. In 1918, Hardy and Ramanujan proved the ...
4
votes
0answers
90 views

Why exactly is Bourbaki difficult?

I keep hearing people say that Bourbaki is difficult for most undergraduates but I still don't understand why. Surely if it starts from definitions/axioms then practically anyone should be able to ...
6
votes
1answer
101 views

Please help me find a complex number book suitable for me

Its been two weeks since I've joined this site, and I have received wonderful answers to my complex number questions at the shortest time. I am specially very weak in Complex numbers, and I see ...
3
votes
0answers
18 views

examples of k-invariants of spectra

The homotopy groups of commonly used topological spectra (like KO, S, MO, MSO, etc) are easy to find in literature, even appearing on Wikipedia's List of Cohomology Theories; however, I have had some ...
1
vote
1answer
42 views

Reference Request: Discrete Dynamical Systems for Undergraduates

I am looking for a primer text in discrete dynamical systems for an undergraduate level of understanding in mathematics. I have taken introductory courses in numerical analysis and computational math, ...
3
votes
1answer
90 views

Except First year Abstract Algebra and commutative Algebra, what else do i need to start read Algebraic Geometry text?

Except First year Abstract Algebra and commutative Algebra text, what else do i need to read before start read Algebraic Geometry texts? I am refer to the beginning texts: "Algebraic geometry an ...
0
votes
0answers
18 views

A geometric inequality involving the sum of distances of an interior point in the triangle $\bigtriangleup ABC$ to its vertices.

Let $\bigtriangleup ABC$ be a triangle in the plane and suppose that $P$ is an interior point of $\bigtriangleup ABC$. Now, I recall seeing somewhere that $$ s < PA + PB + PC < 2s,$$ where $s$ ...
3
votes
1answer
51 views

What is a list of book that i need to read as a prerequisite before start reading “lectures of logic and set theory vol.1 by George Tourlakas”?

What is a list of formal textbook that i need to impose myself to read as a prerequisite before start reading a book called lectures of logic and set theory vol.1 by George Tourlakas? That book is ...
1
vote
1answer
51 views

What is the definition of “Augmentation Ideal Filtration”?

Let $A$ be an algebra. What is the definition of the Augmentation Ideal Filtration of $A$? Any answer with reference will be greatly appreciated.
0
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0answers
23 views

How to define probability density function in Hilbert space??

Consider the space of random continuous functions $f:(0,1)\rightarrow\mathbb R$. Suppose we assume that this is a Hilbert space. Is there any notion of probability density function in the Hilbert ...
2
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0answers
18 views

Reference Request: Johnson Filtration

I need to learn the Johnson Filtration, which I believe is defined on the automorphism group of free groups. Can anyone recommend some reference to this topic? I know one paper called "On the ...
1
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0answers
21 views

Show that it is a element of $(H^1(\Omega))'$

Let $\Omega$ a open regular subset of $\mathbb{R}^n$, $n\ge 1$. I want to prove that if $u\in L^2(\Omega)$, the distribution $\partial_{x_i} u $ is an element of $(H^1(\Omega))'$ (for $1\le i \le ...
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0answers
33 views

Any complete analytic number theory course online?

All: I am studying analytic number theory by myself. Just wonder if there is any complete analytic number theory course online ? (either for undergraduate or graduate level). I did a search on ...
1
vote
1answer
62 views

reference needed in real analysis

I believe I have a proof of the following result, which I need as a lemma. Indeed I have seen oblique references to this result using Google. But I would prefer a specific citation. Can anyone ...
2
votes
0answers
14 views

SAT self-learning

I want to take SAT, but i don't know which textbook is good to learn on Mathematics II. At least more than 1 textbook, or just textbook for each curriculum. I really need suggestion.
3
votes
4answers
110 views

Which texts do you recommend to study universal algebra and lattice theory?

As I'm planning to study some algebraic logic (a lot of!), I found that some knowledge of universal algebra, lattice theory and boolean algebras is a must. I wonder if you have any recommendation to ...
3
votes
0answers
39 views

Reference request for Fourier analysis on local fields

I am studing Class field theory. I need a good reference books, notes e.t.c which explains the following topics : Ideles and ideals, haar volume measure and integration on local fields, Fourier ...
0
votes
0answers
17 views

3-Dimensional proof of Miquel's Theorem?

I was watching a topology lecture and the lecturer claims that it is possible to prove Miquel's Theorem as follows. Miquel's Theorem (statement): Consider any 3 mutually intersecting circles (where ...
4
votes
4answers
144 views

Good books written by great mathematicians

I read many of Richard Fenynman's books and I found them both very entertaining and moving, showing the human side of a brilliant scientific mind. I recently read also a collection of P.A.M. Dirac's ...
2
votes
1answer
44 views

Request a reference in group theory

Although the book "A Course in the Theory of Groups" by Derek J.S. Robinson is an excellent up-to-date introduction to the theory of groups and covers various branches of group theory, it is hard for ...
3
votes
1answer
47 views

Self-learning Book recommendation for topics in ring-theory

I failed badly in my Internal examination in ring theory , and at any cost want to improve upon my grades in the final eamination,with a month and a half to go .... I haven't yet covered the below ...
0
votes
0answers
22 views

Any book on timeline of progress of Math concepts and applications

I was wondering if there is any book that chronicles the progress of Math over the centuries and also mentions about how/when applications of various theories were discovered/invented. I have been ...
6
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0answers
84 views

Books to read to understand Terence Tao's Analytic Number Theory Papers

I tried to understand Terence Tao's Analytic Number Theory Papers. For example, this paper, Every Odd Number Greater Than 1 is The Sum of at Most Five Primes. Which books shall I read to prepare ...
1
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0answers
39 views

Looking for a book about Math

This may be almost entirely off topic so i apologize to the moderators in advance. Please redirect or suggest. I read a book a number of years that was absolutely phenomenal and i have yet to find ...
1
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0answers
35 views

Elimination theory in Hartshorne

Does anyone know a good reference for elimination theory (Theorem 5.7A) mentioned in Hartshorne? The reference he gives is Van der Waerden modern algebra volume two, but it didn't feel locally ...
2
votes
0answers
22 views

Prerequisites: Dirichlet Lectures Number Theory

I am interested in getting Dirichlet's Lectures in Number Theory but I'm afraid I don't know that much advanced math. Do I need to know things like Determinants for this book? Any list of ...
5
votes
1answer
154 views

Second reading on set theory? Any recommendations?

I have in past six-ish months studied through the Herbert Enderton's Elements of set theory book. Up to the point the book is great,I loved most parts of it and learned almost everything up to the ...
0
votes
0answers
37 views

Differential inequality involving derivatives

I'm having trouble with a differential inequality. Consider a smooth function $f(x)$ defined for $x>0$ with $f'>0$. Given $0< a < b$, show that there exists smooth functions $g(x)$ and ...
13
votes
1answer
107 views

Consequences of the negation of the Riemann hypothesis

There are many sources documenting the consequences of the Riemann hypothesis, but I can't find one discussing the consequences of its negation, particularly concerning the prime distribution. Can ...
2
votes
1answer
44 views

Connections between SDE and PDE

I have encountered a number of situations where the solution of a PDE and a certain expectation associated to a Markov process are equal. Two examples include: The heat equation $u_t = \frac{1}{2} ...
1
vote
1answer
43 views

How did Fourier series lead to the development of rigorous analysis?

Once I've heard that the studies of Fourier series have lead to rigorous definitions of such concepts as function, convergence, integral, limit. And also that Cantor's study of Fourier series led him ...
4
votes
0answers
45 views

What's a good text to read before Coxeter's Geometry Revisited?

I am interested in reading Coxeter's famous text Geometry Revisited. It's not clear to me what the prerequisites for this text are, however. I'm sure I have enough mathematical maturity: I know ...
0
votes
0answers
35 views

Who invented complex geometry?

Same as title: What is the first ever major book on complex geometry in its modern form? (People who string together previous results into one comprehensive work)
0
votes
1answer
24 views

Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems: Let $f(x)$ be a convex funtional ...
3
votes
3answers
75 views

Books that follow axiomatic approach?

What are some maths textbooks that follow the "axiomatic approach"? (I would call it "theorem-proof" approach, but I'm more after books that start from the complete basics in a branch of math) What I ...
3
votes
3answers
94 views

Formal notion of computational content

In constructive mathematics we often hear expressions such as "extracting computational content from proofs", "the constructivity of mathematics lies in its computational content", "realizability ...