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
31 views

When orthogonal polynomials form an Hilbert basis?

Let $\mu$ be a probability measure on $\mathbb R$, and consider the sequence of orthonormal polynomials in $L^2(\mu)$. These polynomials are constructed by applying Gram-Schmidt to the sequence ...
0
votes
0answers
34 views

Notes about the ring of $p$-adic integers $\Bbb Z_p$

I'm studing profinte groups. I'm using Wilson's book "Profinite Groups". Here the ring of $p$-adic integers $\Bbb Z_p$ is introduced as inverse limit of rings $\Bbb Z/p^n\Bbb Z$. I'm searching for ...
5
votes
1answer
72 views

Defining truth predicates in set theory

In this blog post J.D.Hamkins shows that KM set theory can define truth predicate for first-order set theory, which means, I believe, that there is a second-order definition of such predicate and KM ...
0
votes
0answers
27 views

Simplifying square root theorem

My teacher told me about some method to simplify square root which is a part of training for math competitions,I think she told it was Lagrange method but I couldn't find anything such.Anyway other ...
0
votes
0answers
15 views

Typo in Caffarelli-Silvestre?

I am reading two papers by Caffarelli and Silvestre, namely Regularity results for fully nonlinear equations by approximation and The Evans-Krylov theorem for nonlocal fully nonlinear equations. From ...
2
votes
1answer
47 views

William Thurston's 'Knots to Narnia'

http://www.youtube.com/watch?v=IKSrBt2kFD4 Above is the youtube link to the short video called 'Knots to Narnia'. (9 mins) While learning knot theory, I found this interesting video. In the video, ...
0
votes
0answers
15 views

3-Book series on 'Set theory' 'Algebra' and 'Geometry'

I just read book on: 'Set theory and Structure of Arithmetic by Hamilton and Landin' This book mentioned 'This is first book in a series of 3 books' Where 2nd and 3rd book are on algebra and Geometry ...
2
votes
0answers
38 views

pictures or graphs for real analysis.

Most of my previous math courses have had some graphs or pictures to help explain the ideas and concepts. I have tried looking for visual representation of the concepts of Real analysis; however, I ...
2
votes
2answers
36 views

Examples of books giving problems that require more than one branch of mathematics

I want to know if there are books that give problem sets requiring knowledge of two or more branches of mathematics. For example, there could be a problem requiring geometry, set theory, and number ...
0
votes
1answer
43 views

Algebra + Real Analysis video lectures

I'm an undergraduate taking graduate courses beginning a research project. I don't have much time but want to brush up on my Algebra and real analysis at a graduate level. Does anybody know any good ...
2
votes
4answers
95 views

A stimulating book about algebra

I need to fill some gaps in my algebra knowledge. The problem is: While I do realise the importance and utility of the subject, I do not find it appealing. Is there any book around which shows ...
1
vote
1answer
40 views

Engineer searching for calculus and complex analysis books without limits

I am an engineer and I need to study calculus and complex analysis without too much limits or Riemann sums or proofs. I mean on the differentiation and integration levels and higher (not digging ...
-1
votes
1answer
50 views

What are good references for the theory of Cohen-Macaulay rings?

I am studying Cohen-Macaulay Rings from the book Cohen-Macaulay rings by W. Bruns. Please tell me some reference book/notes on Cohen-Macaulay rings theory.
1
vote
0answers
31 views

No simple closed form for Bell numbers

The Bell number $B_n$ is the number of partitions of $[n]$. Unlike other basic combinatorial quantities, $B_n$ has no simple finite closed form. This seems surprising to me. Can anyone explain why ...
2
votes
0answers
44 views

I have one month preparation. Please suggest some books.

I have one month for my GRE subjective Mathematics test. I am from India. I have learnt $75\%$ of the syllabus in my UG and high school mentioned in the ETS. I am starting today, will I be able to ...
4
votes
1answer
46 views

Quantities $g_2$, $g_3$, $\Delta$

This question is somewhat related to this one. Let $\lambda$ be the modular lambda function. Greenhill (Elliptic Functions, p. 57) states that we may put $$g_2 = \frac{1 - \lambda + \lambda^2}{12}, ...
2
votes
0answers
31 views

Partition function proof

I am looking for any online information regarding Hardy and Ramanujan's proof, perhaps the proof itself, that the partition function $p(n)$ is asymptotic to $$\frac{e^{K\sqrt{n}}}{4n\sqrt{3}}$$ where ...
0
votes
0answers
16 views

Relationship between differentiation and integration of vector fields?

Let $V\in\Gamma(T\mathbb{R}^n)$ be a vector field and $\gamma:[a,b]\to \mathbb{R}^n$ a curve. Let $\nabla$ be the Euclidean connection, i.e. $\nabla_XY=XY^k\frac{\partial}{\partial x^k}$. We have a ...
1
vote
0answers
16 views

Injectivity of a map from a homotopy set to a homology group

Let $\Sigma$ be a closed Riemann surface and $X$ a 1-connected topological space. I would like to prove the following fact. (A) The map $[\Sigma,X] \to H_2(X;\mathbb Z)$ defined by $[f] \mapsto ...
1
vote
1answer
51 views

Abstract algebra book suggestion [duplicate]

I have been suggested Artin or Herstein's books. What do you think is more rigorous but at the same time clear and good to read?
2
votes
0answers
34 views

Category of schemes with flat morphisms

Consider the category whose objects are schemes, and for every two schemes $X$ and $Y$, morphisms $\operatorname{Hom}(X,Y)$ consist of flat morphisms $X\rightarrow Y$, only. Does this category have a ...
0
votes
0answers
9 views

Is there an errata for “Introduction to topology and modern analysis” by G.F. Simmons?

Is there an errata for "Introduction to topology and modern analysis" by G.F. Simmons? I've been looking for errata for this book for some time. But I couldn't anything. Does anyone know where I can ...
0
votes
1answer
28 views

Suggest any Comic based books for Learning calculus and Statistics? [on hold]

I seen some manga comics for learning statistics and calculus. Suggest other books.
1
vote
1answer
30 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
1answer
24 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
vote
0answers
23 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
vote
0answers
84 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
vote
0answers
29 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 its 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
vote
0answers
16 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: ...
2
votes
0answers
52 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 ...
13
votes
6answers
976 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
38 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
23 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 ...
0
votes
3answers
49 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 ...
3
votes
1answer
52 views
+50

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
votes
0answers
28 views

Cambridge Maths Tripos Papers

Does anyone know where I can find Cambridge Maths Tripos Papers for the 1980s?
0
votes
0answers
25 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
0answers
55 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
votes
0answers
15 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
votes
0answers
26 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
votes
2answers
39 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
vote
2answers
42 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
votes
0answers
16 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
vote
0answers
30 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
vote
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
votes
2answers
57 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
votes
0answers
34 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 ...
1
vote
2answers
46 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
votes
1answer
79 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
votes
0answers
17 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 $P_i$ ...