Tagged Questions

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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2
votes
1answer
36 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 ...
2
votes
0answers
23 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 ...
3
votes
1answer
175 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 ...
2
votes
0answers
12 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 ? Q2. Let $n$ be the largest integer such that the plane ...
1
vote
2answers
45 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
0answers
15 views

Solutions manuals to Dynamical systems textbooks

Is there a solutions manual to "Introduction to Dynamical Systems" by Brin and Stuck, "Introduction to Modern Theory of Dynamical Systems" and "A First Course in Dynamics" by Katok and Hasselblatt? ...
1
vote
0answers
43 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
24 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
22 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
16 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, ...
1
vote
1answer
63 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
26 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
39 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 ...
5
votes
0answers
71 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
93 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
16 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
33 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
0answers
61 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
15 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
45 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
41 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
votes
0answers
20 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
votes
0answers
17 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
vote
0answers
18 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 ...
-2
votes
0answers
24 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
56 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
3answers
63 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 ...
2
votes
0answers
27 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
14 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
122 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
35 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
39 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
19 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
votes
0answers
62 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
vote
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
vote
0answers
34 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 ...
0
votes
0answers
13 views

Books for difficult questions on limits, continuity, differentiability of functions of two variables [on hold]

i have done basic limits conti diff questions on functions of two variables but need some more difficult questions or question bank for these topics for my upcoming exam .
2
votes
0answers
20 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 ...
2
votes
0answers
65 views

Second reading on set theory?Any recommendations?

I have in past six-ish months studied through the Herbert Endertons 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
30 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 ...
12
votes
1answer
90 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.
1
vote
1answer
33 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 $u_t = \Delta u$ ...
1
vote
1answer
41 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
36 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
34 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 ...
2
votes
3answers
61 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
89 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 ...
0
votes
0answers
19 views

What are such pairs of monotone mappings?

Let $P, P'$ be some partial orders and $f$ and $g$ two monotone mappings of type $P \to P'$. Consider the property $g(f(x)) \leq f(x)$, for all $x \in P$. My questions: Have you encountered such ...