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
19 views

Suggest any Comic based books for Learning calculus and Statistics?

I seen some manga comics for learning statistics and calculus. Suggest other books.
1
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1answer
23 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
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1answer
21 views

which algebraic number theory book with answers to selected questions for self-study?

All: Can anyone recommend some easy to follow algebraic number theory books with answers (hints) to selected questions for self-study ? If a have no answers to questions, but if you know if some ...
1
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0answers
20 views

looking for origin of number theory problem on 4x-floor-sqrt (maybe IMO)?

this problem was recently posed by BS in the number theory chat room. he thinks it may originate from the International Math Olympiad & he says he has a solution. has anyone seen it there? looking ...
1
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0answers
47 views

Learning roadmap in Algebra

I am a senior undergraduate student in mathematics, I have a sound knowledge in the following areas: a) Commutative Algebra b) Field Theory and Galois Theory c) Homological Algebra My question is ...
1
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0answers
24 views

Finding the source for minimizer of a functional for all $C^2$-curve $x(t_0)=x_0$ and $x(t_1)=x_1$

I am trying to find where this problem comes from and it's corresponding proof for my students, but I cannot find the source anywhere. If anyone can find the source of this, or has any ideas where I ...
1
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0answers
15 views

Books for difficult quantitative aptitute and logical reasoning questions.

I am preparing for some exams that contains difficult quantitative and logical reasoning(not mathematical logic) questions. This is the syllabus: Please suggest some books that contain: ...
1
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0answers
39 views

About the adjoint concept.

I read somewhere the adjoint concept has some sort of philosophical implications. Some way to describe it in terms of logic without math. Is there a book on Category Theory that explains it without ...
12
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6answers
934 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 ...
1
vote
1answer
37 views

Pulsating waves of zeta function

Below is an animation of the partial sums of $\operatorname{li}x-2\Re\sum_{k=1}^{N}\operatorname{Ei}(\rho_k \log x)-\log2+\int_{x}^{\infty}\dfrac{\text{d}t}{t(t^2-1)\log t},$ for $1\leq N\leq100$ ...
0
votes
0answers
21 views

Frobenius splitting from viewpoint of commutative algebra

First I define two terms: Let $R$ be a commutative ring with identity,let char$R$ = $p$, let $F:R\rightarrow R$ be the Frobenius ring homomorphism. This makes $R$ into an $R$-module with respect to ...
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3answers
45 views

Proofs about Matrix Rank

I'm trying to prove the following two statements. I can prove them easily by considering the matrix as a representation of a linear map with a given basis, but I don't know a proof which uses just the ...
1
vote
1answer
23 views

Monte Carlo p-test and early stopping

Say you have a coin with some probability $p$ of falling on heads. You would like to determine if this probability is less than or equal to $0.05$ with some reasonable degree of confidence and stop ...
3
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0answers
28 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
0
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0answers
24 views

'Popular mathematics' resource about infinite ordinals

The 'popular mathematics' literature (think Martin Gardner, William Dunham, Hofstadter, and the like) abounds with material on the mathematics of infinite cardinals, starting - and quite often ending ...
1
vote
1answer
47 views

Types realized in ultrapowers consisting of definable functions

Let $\mathcal{M}$ be a nonstandard model of arithmetic and let $M$ be its universe. Let $U$ be a nonprincipal ultrafilter over $M$ and let $\mathcal{N}$ be the ultrapower $\mathcal{M}^M / U$. Let $F$ ...
0
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0answers
14 views

A class of function to study Fourier analysis, which is a subset of BV functions.

In Fourier analysis, while talking about pointwise convergence, we generally start with the class of functions called, BV functions (functions of bounded variation), which have a finite total ...
0
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0answers
25 views

what is wrong with my (too strong to be true) generalization of a Gromov result?

In his paper "Volume and bounded cohomology", page 59 (267), Gromov proves the following result: "Let $V$ be a smooth $n$-dimensional manifold, and let $P$ be a piecewise smooth polyhedron of ...
0
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2answers
37 views

Mathematical background for one wishing to study Chaos/Complexity Theory

I don't have a very strong mathematics background. In fact I quite abhorred mathematics during my Middle/High School years. I'm currently applying for PhD programs in the field of literature as that ...
1
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2answers
39 views

Reference Request for calculus self study

I'm wishing to learn calculus in a detailed manner. could any one help me by giving suggestions? I'm looking for books with good illustrative examples and figures.
0
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0answers
11 views

The number of lattice points in d-dimensional ball

The following paper states that the number of lattice points in a $d$-dimensional ball of radius $R$ is $V_d R^d + O(R^\alpha)$ where $\alpha = d - 2$ and $V_d$ is the volume of the unit ...
1
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0answers
27 views

Reference for the following equation

Can someone suggest me references about the following equation $$u_t+A\cdot\nabla u=i\Delta u$$ with $A$ a smooth vector field.
1
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0answers
34 views

Every Banach space is quotient of $\ell_1(I)$

I'm looking for a book containing the proof that for every Banach space E there is an index I so that E is a quotient space of $\ell_1(I)$. If I can't find the book on google books, it would be great ...
2
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2answers
55 views

Good analysis texts

I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, ...
0
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0answers
25 views

Solutions to Groups and Symmetry by M.A. Armstrong

I am learning group theory (on my own) using the 'Groups and Symmetry' textbook by MA Armstrong. Does anyone know of a book/website/blog where I can find solutions to the Exercises (so I can check my ...
0
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0answers
21 views

Good book for self-studying Binary Relations

I am studying economics and I frequently encounter Binary Relations. But without any good knowledge of it, I get confused. Here is some background, if it's helpful: I know calculus(single and ...
7
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1answer
77 views

Is there anything “nice” about the set of normal matrices (over $\Bbb R$ and $\Bbb C$?)

Normal matrices are of course useful to any linear algebra buff, not least because of the spectral theorem. However, taken as a whole, they tend to have some not-so-nice properties. For example: ...
0
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0answers
16 views

when does bijective map exist for any pair of rational function?

Let me ask kind of different questions than former ones. Given $$\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}\text{, and }\frac{P_3(y_1,y_2,\dots,y_n)}{P_4(y_1,y_2,\dots,y_n)}$$ where $P_i$ ...
1
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0answers
33 views

Proof of Minkowski determinant inequality

I wonder where can I find the proof for the Minkowski determinant inequality? ( i.e., given two positive definite n x n symmetric matricies A and B, $det(A+B)^{1/n}\ge det(A)^{1/n}+det(B)^{1/n}$ ) ...
5
votes
0answers
51 views

Indiscernible subsequences

Work in a saturated model $\cal U$ of sufficiently large cardinality. Are there assumptions on $\kappa<|\cal U|$ that guarantee that any sequence $\langle a_i:i<\kappa\rangle$ has an ...
1
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0answers
21 views

Any good resources for Lagrangian and Hamiltonian Dynamics? [migrated]

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
1
vote
0answers
50 views

Does such a polynomial map always exist?

First question: given $$\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}=\frac{P_3(f(x_1,x_2,\dots,x_n))}{P_4(f(x_1,x_2,\dots,x_n))}|\det (J(f(x_1,x_2,\dots,x_n)))|$$ where $P_i$ is ...
2
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2answers
78 views

Are addition and multiplication on naturals algebraically distinguishable?

Suppose (N, +) and (N, *) are the structures of addition and multiplication on N, the natural numbers with 0. Let S be the set of equational identities that hold in (N, +), and let T be the set of ...
4
votes
2answers
80 views

Bartle vs Rudin, which one is better for real analysis?

I'm in high school and I want to study real analysis, and I can choose between The elements of real analysis by Robert G. Bartle and Principles of mathematical analysis by Walter Rudin, so, from the ...
0
votes
0answers
33 views

Request topics for presentation [on hold]

I'm in need of some interesting topics (in applications of mathematics, like treasure hunt) to present paper. especially I'm looking for topics in applications of Group theory or basic calculus. ...
2
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1answer
47 views

What is the importance of Jacobian Conjecture and any progress on it?

What is the importance of Jacobian Conjecture?Are there any important central problem with the conjecture as precondition? and any progress on it?
1
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1answer
37 views

Book to self-learn probability

I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one ...
0
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2answers
67 views

Best E-books and online-resources for Probability and its applications(especially games of chance)

I am very much interested in studying games of chance and the probabilities related to our daily life instances but I need an online resource or some e-book to study them. I am a self-learner. Can ...
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0answers
20 views

Ehrhart Polynomials Modulo Prime Integers

Are there any results known about computing Ehrhart Polynomials modulo prime integers?
2
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0answers
14 views

Probablistic bound for $\|RR^TM\|$ for uniformly random orthonormal matrix $R$

I am stuck on a finding a probablistic bound on a nonstandard random matrix. I looked around on the internet and couldn't find any results. This could be because I don't know the key words or because ...
1
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0answers
35 views

Question regarding advanced calculus textbooks

I'd like to start off by mentioning that I'm gonna begin studying Computer Science at the local polytechnic university. As I found out, the study of mathematics stops after two years. Recently I've ...
2
votes
1answer
89 views

Should I change my Linear Algebra Textbook?

I know there are many questions related to linear algebra, but the textbook I'm using is not that widely used as other books, I guess. My university uses 'Finite-Dimensional Linear Algebra' by Mark ...
0
votes
1answer
24 views

Applications of random walks

I am searching for a clear and interesting exposition of an application of random walks to some physics topics accessible to advanced high school students.
5
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3answers
54 views

Where to study $2$-category theory?

Is there any place where I can read about $2$-categories? I am looking for a proper treatment - there is a section in Borceux's Handbook of Categorical Algebra, but it only sketches some parts of the ...
1
vote
1answer
82 views

Relation between the covers by sets of small diameter and the size of uniformly separated sets

Sorry I didn't find a better title. Here is the problem and my solution so far, I'd appreciate if someone could told me if is correct and for the last point, which at first sight seems to be ...
2
votes
2answers
50 views

“Reverse” quotients.

Given a set $A$ and a equivalence relation $\sim$ on $A$, one can construct the quotient $A/{\sim}$. But what about the opposite? More precisely, given a set $X$, is there a way to know whether exists ...
0
votes
0answers
38 views

Are there any general results about the irrationality of $a^{\frac{p}{q}}$?

Are there any general results about the irrationality of $a^{\frac{p}{q}}$ for $a\in\mathbb{Z}^+$, $p,q\in\mathbb{Z}$, $q\neq 0$ and $a\neq 1$?
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0answers
35 views

What is an easy to read book on category theory including the introduction of some killer apps for the theory? [duplicate]

What is an easy to read book on category theory including the introduction of some killer apps for the theory ?
1
vote
1answer
53 views

Periodicity with irrational numbers

Recently, I invented the following theorem and found a proof, it seems strange since it is very counter-intuitive to me. The proof is long and non-conceptual. Is there a place or a branch of math ...
0
votes
0answers
18 views

Papers related to Tomography and compressive sensing.

Recently I studied about Radon transformation and its applications. I got to know that they are lots of application in tomography and am very much interest after reading that. Now I wanted to read ...