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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1
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1answer
92 views

Foundations book using category theory?

I'm about to embark on a PhD in mathematical biology. My major is in computer science. I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research ...
0
votes
3answers
66 views

Is there any book about inequality? [closed]

I heard there is a book name 'inequality'. But I couldn't find the book. Is there any site or book about inequalities? What i want is collection of inequalities.
2
votes
0answers
22 views

Reference Request: Algebraic Serre's Duality Theorem for Curves

Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne and ...
1
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3answers
104 views

What is the “Principle of permanence”?

While reading the book "The Number-System of Algebra (2nd edition)." term "Principle of permanence" occurred to me. I remember I had read this in the book "Beginning algebra for college students.". I ...
11
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3answers
201 views

Homology Whitehead theorem for non simply connected spaces

(One version of) the Whitehead theorem states that a homology equivalence between simply connected CW complexes is a homotopy equivalence. Does the following generalisation hold true? Suppose ...
0
votes
0answers
297 views

How to present calculus? Asking for some excellent intuitive referance.

$\text{Dear}$ mathematicians, amateurs, learners, students et al; I learned calculus when I was 13 years old, I was at the time able to evaluate some easy derivatives, integrals, some tricky limits ...
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0answers
60 views

Recommended Textbook/Resources

I'm looking for a textbook or resources my younger brother could use. (He is in year 9, equivalent to US high school freshman) He is wanting to advance upon his math, he currently does exercises out ...
-5
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1answer
98 views

Lee, Introduction to Smooth Manifolds Solutions

Does anybody know where I could find the solutions to the exercises from the book Lee, Introduction to Smooth Manifolds? I use the freely available online version ...
11
votes
2answers
204 views

Putting down axioms for some symbols. Playing with their consequences qualitatively and symbolically. Building theories. The book?

I am interested in the design and building of theories. By building theories, I mean putting down axioms of various kinds, over various fields, exploring their perhaps interesting, or probably boring, ...
3
votes
1answer
53 views

Intuitionistic Linear Logic

I am currently going through some papers that use the "intuitionistic version" of Girard's Linear Logic. Problem is, i seem to find very little literature on it. There is a lot done on Linear Logic ...
2
votes
0answers
32 views

uniform equivalence to unit vector basis of $\ell_p$

Let $(e_n)$ be the unit vector basis of $\ell_p$, $1\leq p<\infty$. It is well-known that if $(x_n)\subset\ell_p$ is seminormalized and weakly null then it contains a subsequence equivalent to ...
3
votes
2answers
64 views

What is the best book to learn statistics?

Right now I'm taking a 3 part course on probability and statistics using Schverish & Degroot Probability and Statistics and it is just not helpful. For the first part, which was on Probability, I ...
0
votes
0answers
13 views

Space of almost complex structures on a compact manifold

According to the book by Huybrechts, Complex Geometry: An Introduction, this is a nice space and may be regarded, after some form of completion, as an infinite-dimensional manifold. How is this done, ...
4
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0answers
37 views

Looking for a a measure-theoretic treatment of “differential entropy”

If $X$ is a discrete random variable, its entropy $H(X)$ is usually defined as something along the lines of $-\sum \def\P{\mathbb{P}}\P(x) \log_2( \P(x))$, where the sum ranges over all the possible ...
0
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0answers
7 views

Homological Algebra for Characteristic Classes

how much homological algebra should I know to make a rigorous study of characteristic classes? Furthermore, what would be other requisites? References on both homological algebra and characteristic ...
0
votes
0answers
32 views

Module and bimodule categories equivalent to a 2-functor

Let $A$ be a tensor category (i.e. monoidal category). A (right) module category of $A$ is a category $M$ with a coherent action $\mu\colon M\otimes A\to M$. Denote $BA$ be the one-object bicategory ...
2
votes
1answer
24 views

Fourier series with a weighted mean square norm

I am interested in Fourier series with a non-uniformly weighted error norm. What I mean by this is that the usual Fourier series of a periodic function is a minimizer of the mean squared error: $$ J_N ...
2
votes
2answers
50 views

Odd and even functions.

I have a book which says: If a function $f$ satisfies $f(-x)=f(x)$ for all $x$ in its domain, then $f$ is called an even function. However, if $f(-x)=-f(x)$ for every $x$ in the domain of $f$, ...
5
votes
2answers
85 views

Looking for a specific female maths writer

This is going to be an annoying question, but I have to ask it as it is annoying me. I once read a book on infinity that was written by an American female maths writer. She was very easy to read and a ...
1
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0answers
33 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
1
vote
1answer
35 views

Abstract Algebra book where student must make most of the work?

I am looking for a nice compact book in abstract algebra (especially group theory) which develops the material by asking questions the reader must answer. An example of what I'm looking for is ...
1
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2answers
47 views

Choosing a calculus book for self-study

Which one to choose for self-education? What are your recommendations? Calculus - James Stewart or Calculus - Anton, Bivens, Davis Thanks in advance.
0
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0answers
11 views

Carrier maps between simplicial complexes

Simplicial complexes are useful in proving things about distributed systems. We define and use simplicial maps between two such complexes, and these maps also seem to be standard objects of study in ...
0
votes
2answers
46 views

Comprehensive, rigorous calculus book with a small number of exercises?

I'm looking for a calculus book that (1) is comprehensive and rigorous enough for Calculus I-III (but pre-Spivak/Apostol in terms of rigor -- they can come later perhaps) (2) has only a small number ...
1
vote
2answers
49 views

What does $e^b$ means?

What does it mean $a^b$ where $a$ and $b$ are real numbers not integers, not rationnals (I do not know the name of this set). Real numbers means $\mathbb{R}$ but $1\in \mathbb{R}$ So, what does it ...
2
votes
0answers
23 views

Muirhead's Inequality (software?)

I just started learning about inequalities: Schur's, Karamata's, Muirhead's, etc... They are beautiful but it seems that in the case of more than two variables, some of the computations become a ...
2
votes
0answers
33 views

Inner automorphisms of Lie groups

I have a few questions about $Aut(G)$, when $G$ is a Lie group. It was proven by Hochschild that if $G/G_0$ is finitely generated, then $Aut(G)$ is a Lie group with at most countably many components. ...
1
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0answers
14 views

Generalized permutahedron and random polytopes

The Birkhoff polytope $B_n$ is defined as the convex hull of the set of permutation matrices, which gives us the set of doubly stochastic matrices. A concept which is intimately related is that of the ...
0
votes
1answer
15 views

Morse theory on construction from Morse function on a manifold

Morse Theory. It's a beautiful construction of a cell complex from a Morse function on a manifold. As a result, there are inequalities estimating the number of critical points by ranks of homology ...
2
votes
2answers
79 views

I would like some textbook recommendations for model theory

I am a 3rd year undergraduate math student and would like to study model theory. . I have some background with set theory, ordinals etc and also with mathematical logic. This is purely for self study ...
0
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0answers
22 views

Question about a created problem by me [migrated]

If I created a problem(inequality), can I post the question here to see how other solutions can I receive? Or if the problem is too easy? Thanks!
1
vote
0answers
33 views

Free lecture notes to Carl Bender's Mathematical Physics video lecture course?

I am just watching Carl Bender's Mathematical Physics video lecture course (about asymptotics and its application in physics) http://www.perimeterscholars.org/328.html which is great! Are there any ...
1
vote
1answer
33 views

A literature reference for Sobolev mappings $W^{m,p}(M,N)$ for M, N smooth Riemannian manifolds

Anyone know a respectable reliable reference for the definition of Sobolev mappings $W^{m,p}(M,N)$ for M, N smooth compact Riemannian manifolds. It suffices for m natural and $p\geq 1$
4
votes
1answer
41 views

A (possibly) easier version of Bertrand's Postulate

While attending a math puzzle contest, my friend (a math student) asked me to prove that $$\sum_{k=1}^n \frac{1}{k} \notin \mathbb{Z} \quad \forall n \geq 2$$ Being the first time seeing this ...
0
votes
0answers
18 views

Divergence of a Tensor Examples?

Would anyone have a reference to a book where explicit examples of things like taking the divergence of a tensor (page 4) are given? Stupid computational examples like the one given here (bottom of ...
1
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0answers
43 views

Integral asymptotics

Is there some kind of a variation of the Laplace's method or some other formula for the asymptotics of integrals of a type $$\int_a^bf(x)e^{mp(x)}\cos(mq(x)+x/2)dx, \ m\to\infty.$$ Here $f,p,q$ are ...
17
votes
2answers
541 views

Riemann's zeta as a continued fraction over prime numbers.

Riemann's zeta function is a function with many faces, I mean representations. I recently derived this one, bellow, as a continued fraction over prime numbers. $$ \zeta(s)=1 ...
1
vote
1answer
30 views

References for a second course in probability theory

I need a probability book that treats all the arguments from the point of view of the measure theory and the Lebesgue integral. I've the basis of "naive" probability theory and of measure theory so I ...
1
vote
1answer
36 views

Suggestion for independent study of mathematical logic

Hello I'm looking for advice on mathematical logic books that are good for self-study. I would really like a text that has some if not all of the answers to exercises so I can check my progress as I ...
5
votes
2answers
124 views

Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
0
votes
0answers
26 views

Your impressions of Mattuck's *Introduction to Analysis*

Has anyone here spent much time with the Mattuck book Introduction to Analysis? What are your impressions of it? A quick browsing showed me that I liked the organization of the material, but the ...
4
votes
0answers
137 views

Conjugation Quandles and… “Quandle-Groups”? From quandles to Groups.

A quandle $(Q,*,/ )$ is a idempotent right-distributive and right invertible structure. 1) $a*a=a$ 2) $(a*b)*c=(a*c)*(b*c)$ 3) $(a*b) /b=(a/b)*b=a$ If we have a group $(G, \cdot, ...
3
votes
2answers
88 views

Any good, undergraduate level introductions to Functional Analysis?

In my lower division math classes, my instructors referenced functional analysis as essentially the extension of linear algebra to infinite dimensional vector spaces along with some real analysis. As ...
0
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0answers
9 views

Proof of theorem about connection between nondeterministic and deterministic Turing machines complexity classes

I need source for proof of this theorem: Every $T(n)$ time nondeterministic Turing machine has an equivalent $2^{O(T(n))}$ deterministic Turing machine. I have book by Michel Sipser, ...
0
votes
1answer
29 views

Reference request: Limits and Derivatives

Could you recommend/suggest a good E-book about Limits and Derivatives with exercise solutions What do you think about that book Limits and Derivatives Made Easy ? looks good but it's not available ...
3
votes
1answer
38 views

Are there books introducing to Complex Analysis for people with algebraic background?

I'm a third year student who is mostly interested in commutative algebra. In Algebraic Geometry a lot of example come from Complex Analysis. So to deepen my understanding/intuition, I'll finally ...
0
votes
1answer
12 views

Interior ball condition in $C^2$ domains

Why a $C^2$ domain satisfies the interior ball condition? I accept a reference too. Thank you.
1
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0answers
15 views

doubt about definition of holomorphic polynomials

In a topic of several complex variable theory (in particular functions on $\mathbb{C}^2$), I came across a term homogeneous holomorphoic polynomial. By the word, I think it is a polynomial in complex ...
2
votes
1answer
49 views

Good book for general topology [duplicate]

I want a book in general topology with many interesting and hard exercises. I mean a book with topics the same as Munkres but with challenging questions to improve my problem solving ability.
0
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0answers
14 views

Is there a good introductory complex-analysis text in general setting, namely Riemann sphere?

I have studied first 1~3 chapters of some complex analysis texts (Ahlfors, Conway, Silverman) Well, i specially like Ahlfors in many ways but this text doesn't seem to develop a theory in a general ...