This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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4
votes
3answers
162 views
+200

Method of solving no-homogeneous recurrence equation

I need to obtain a closed form of $M(t)$, satisfying the following recurrence equation: $$M(t+1)=a+bM(t)+\frac{c}{t+1}\sum_{t'=0}^tM(t')+df(t)$$ Where $f(t)$ is a known function and $a$, $b$, $c$ ...
6
votes
7answers
445 views

Books or site/guides about calculations by hand and mental tricks?

Any ideas about books I can get, from amazon? I need to get really good at mental math and math by hand because I'm taking an exam soon and that without a calculator. Thanks.
1
vote
1answer
6 views

Reference request: Topological space of polygonal chains and its properties

I'm interested in approximations of $C^1([a,b])$-functions by polygonal chains: image File:NURBstatic.svg by User:WulfTheSaxon licensed under GNU Free Documentation License A polygonal chain can be ...
34
votes
8answers
46k views

What is the best book to learn probability?

Question is quite straight... I'm not very good in this subject but need to understand at a good level.
0
votes
0answers
9 views

Reference request for conditional and unconditional covariance of n-times integrated Brownian motion

I'm working through an old Diaconis paper on Bayesian numerical analysis, and am currently calculating the details behind his brief comments on using $n$-times integrated Brownian motion as a function ...
5
votes
1answer
420 views

Min Max Principle and Rayleigh-Ritz-Method for eigenvalues of unbounded operators?

Finding eigenvalues of matrices using the Rayleigh-Ritz quotient is well-known, c.f. http://en.wikipedia.org/wiki/Min-max_theorem Does the following generalization of that fact also hold? Theorem: ...
2
votes
0answers
41 views
+50

Why are logrithms of trigonometric functions useful

I have noticed that in many trigonometric tables the logarithm of the trigonometric values are given. Why this is given and not the actual values of the trigonometric functions? For example, instead ...
2
votes
1answer
38 views

Is $f(z)=\sum_{k=1}^{\infty}\frac{1}{(k+\frac{1}{k})^{z}}$ somehow related to Riemann's zeta function?

I was looking at this series $$ f(z)=\sum_{k=1}^{\infty}\frac{1}{(k+\frac{1}{k})^{z}} $$ and wondering if it is somehow realted to the Riemann's zeta function $$ ...
1
vote
0answers
33 views

A good book to read with Chapter III of Neukirch's “ANT”

The book Algebraic Number Theory from Neukirch is a beautiful book in ANT, but it still have a serious lack in examples and motivation to the concepts. I've already read the first two chapters of the ...
0
votes
2answers
13 views

PDE Solving: Difference between Similarity Solution and Characteristics?

As far as I understand, both the method of characteristics and similarity solutions allow us to reduce certain partial differential equations to ordinary differential equations which can then be ...
1
vote
0answers
9 views

Laguerre's theorem on power of a point w.r.t. an algebraic curve

So on Wikipedia article for a power of a point there is a short section about Laguerre's theorem. The problem is, the article has no references, and whenever I'm trying to Google it the only things I ...
2
votes
1answer
31 views

Natural action of $\operatorname{Aut}(G)$ on sets of subgroups of $G$ of same order is transitive.

I am looking for the classification of those finite groups whose automorphism group acts transitively on sets of subgroups of same order. Let $G$ be a finite group and $d$ be a divisor of the order ...
1
vote
1answer
25 views

Non-uniqueness of worst-case (max-min or min-max) optimization

I have a worst-case optimization problem, where i want to maximize the minimum from the uncertainty set (uncertainty is given as an ensemble of 100 realizations, so an ensemble based approach). It is ...
0
votes
1answer
302 views

Book on discrete mathematics for self study

I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read ...
0
votes
1answer
10 views

What are existing methods to count colored subgraph frequencies in a large colored directed graph?

I have a directed colored large network or graph. By 'color' I mean that nodes are of different categories. There are some small 3 or 4 node colored directed subgraphs. I need to know how to count ...
0
votes
0answers
16 views

How to figure out whether PCA can be performed on a data set or not?

I do have idea on the way PCA works but I do not know how to figure out whether a high dimensional data set is suited for PCA compression. I googled for some algorithms but could find any. Are there ...
2
votes
1answer
137 views

Book for Markov Chain Monte Carlo methods

Can anyone recommend a good for MCMC? I have worked with HMMs, Markov Chains in the past but nothing on simulation. So something in the intermediate level would be great. Also, if you know of any ...
1
vote
1answer
72 views

Learning mathematical concepts

Our teacher loves to test us on pure concept based questions and test if we really know what we are doing when learning a particular lesson. For example, when we first started learning about ...
6
votes
6answers
1k views

Casual book on abstract algebra

A friend of mine, who is a high school math teacher and majored in math in college, recently asked me for a good book to read on Abstract Algebra (presumably, group theory). She is looking for ...
2
votes
0answers
23 views

Perimeters Areas and Volumes

I have to write an article for a school magazine. I thought it is better to choose a simple topic like Perimeter, Area and Volume. I am looking for historical fact and surprising facts about ...
2
votes
0answers
15 views

Relationships between affine closures and convex closures

Let $V$ denote a vector space. Then the following concepts make sense: affine subset of $V$ affine closure (affine "hull") of a subset of $V$ Suppose $V$ is in fact a real vector space. Then the ...
3
votes
1answer
36 views

Reference request for stochastic process

I studied the book, "Probability, Random Variables and Random Signal Principles" by Peyton Peebles. And I am a little bit familiar with statistical analysis like signal estimation and detection. In ...
0
votes
0answers
35 views

Help: Studying A-Level Mathematics [on hold]

Although I am a latecomer at the age of 21 years of age, I have enrolled in self taught mathematics A-level with "Edexcel" both mathematics & further mathematics. I am in need of help with ...
2
votes
0answers
28 views

Where can I learn more about the “else” operation / “else monoid”?

(The set of natural numbers $\mathbb{N}$ starts at $0$ for me.) Let $X$ denote a set, and define $X_\bot = X \uplus \{\bot\}.$ Let $\mathbf{else}$ denote the binary operation on $X_\bot$ defined as ...
1
vote
0answers
8 views

Is the co-limit of a chain of normal subspaces necessarily normal?

Suppose $ X_0 \subset X_1 \subset X_2 \subset \dots$ is a chain of normal subspaces of $X$ such that $X= \cup_{i=1}^{\infty} X_i$. Assume that $X$ has the colimit topology w.r.t. these subspaces. Can ...
0
votes
1answer
33 views

Good books about elliptic integralsa, hypergeometric and special functions

Can you please tell me some good books from where I can learn elliptic integrals and special functions like hypergeometric functions?
31
votes
2answers
3k views

Books about the Riemann Hypothesis

I hope this question is appropriate for this forum. I am compiling a list of all books about the Riemann Hypothesis and Riemann's Zeta Function. The following are exluded: Books by mathematical ...
3
votes
0answers
31 views

Multiples of some set has density

Nathanson gives a proof in Elementary Methods in Number Theory (Theorem 7.14) that, if a set $S$ of positive integers has $$ \sum_{s\in S}\frac1s<+\infty $$ then the set of positive multiples of ...
0
votes
0answers
29 views

question about theorem references (who made it, year, etc.) [on hold]

The statement of the theorem that i would like to know some references is this: if we fix two numerical invariant $K^2$ and $\chi$ then there exist a quasi projective moduli space of the canonical ...
1
vote
1answer
28 views

Looking for examples of finite loops and monoids

I am looking for examples of (small) finite loops and monoids that are not groups for demonstrating what happens if you omit some of the group axioms. Does anyone know some ressources for this? I ...
1
vote
0answers
34 views

The Nagell-Ljunngren Equation

I have been trying to find the papers of Nagell and Ljunngren, which deal with the equation $$\frac{x^n - 1}{x - 1} = y^2$$ and solve it completely. Many papers cite these papers, but I haven't found ...
2
votes
2answers
198 views

How to compute the formal group law of K-Theory

Could anyone point me to a reference where the formal group law of (topological or motivic) K-theory is computed in as much detail as possible?
1
vote
0answers
25 views

Defining Lebesgue measure on a subspace of $\mathbb{R}^n$

Let $\bar{w}_1,.., \bar{w}_k$ be linearly independent vectors in $\mathbb{R}^n$. Let $W$ be the subspace spanned by these $\bar{w}_i$'s. I know how the Lebesgue measure is defined on $\mathbb{R}^n$. ...
2
votes
1answer
282 views

Prove that hyperspherical coordinates are a diffeomorphism, derive Jacobian

The explicit form for the transformation into hyperspherical coordinates is $$x_1 = r\sin\theta_1 \sin\theta_2 \dotsb \sin \theta_{n-1} \\ x_2 = r\sin\theta_1 \sin\theta_2 \dotsb \cos \theta_{n-1} \\ ...
5
votes
2answers
336 views

Self-Contained Books / Series / Lectures for Comprehensive Introduction to College-Level Math for Someone with VERY Poor Math Foundation?

I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I ...
0
votes
0answers
17 views

Self contained book on Ricci Flow/Geometric Analysis

Can someone please tell me whether there is any self contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self contained I mean it does not assume that ...
4
votes
1answer
79 views

No Borel well-order of the reals?

I'm told there is no Borel well-order of the reals (in ZFC). I'm told, in fact, that this is because of Borel determinacy. However, this is usually a vague handwave of the form (a) take the usual ...
3
votes
3answers
608 views

Algebra book(s): Beginner through to advanced

I admit, I am not great at Maths; I'm situated in one off the lowest Maths class for my year, partly due to myself losing focus last year. Though, I like maths, I really do. Especially since I do a ...
13
votes
8answers
291 views

Mathematicians' manual of style

I know that there are many styles to write citations and footnotes and that they are all equally good (as long as the reference is complete), but I would like to know if mathematicians follow some ...
19
votes
4answers
789 views

Mathematical and Theoretical Physics Books

Which are the good introductory books on modern mathematical physics? Which are the good advanced books? I read Whittaker's Analytical Dynamics, and I am reading Arnold's Mathematical Methods of ...
4
votes
1answer
83 views

Existence of bijection that reorders elements?

Suppose I have some function $f:\mathbb{R}\to[0,1]$. Does there necessarily exist a bijective mapping $g:\mathbb{R}\to\mathbb{R}$ such that $g(x)\leq g(y)$ implies $f(x)≤f(y)$? If not, does it help if ...
0
votes
1answer
70 views

Linear algebra references for a deeper understanding of quantum mechanics

I'm a graduate student studying quantum mechanics/quantum information and would like to consolidate my understanding of linear algebra. What are some good math books for that purpose?
17
votes
7answers
851 views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
-4
votes
1answer
180 views

Books for difficult quantitative aptitute and logical reasoning questions. [closed]

I am preparing for some exams that contains difficult quantitative aptitude and logical reasoning questions. Please suggest some books that contain: Difficult quantitative aptitude and ...
1
vote
1answer
60 views

Prerequisite books before Hungerford's Algebra?

Prerequisite books before Hungerford's graduate Algebra? I have an pdf version of the book and feel the Hungerford is overcomplicated after i finish some of the books title with something like first ...
0
votes
2answers
38 views

Is there any good software to plot trigonometry graph?

I want to plot trigonometry graph like sine function, cosine function, etc. (degrees, not radians) but I don't find anyway to make it in my computer. I like graph produced by WolframAlpha, but it ...
0
votes
0answers
16 views

Required sub-chapters or more materials needed to learn Statistical Inference other than my textbooks

My school is using new curriculum now and chapter "Statistical Inference" appears in my textbooks. Now I'm at second level of senior high school. I have two books, each of them has own sub-chapters ...
3
votes
0answers
57 views
+50

Textbook on infinite loop spaces

I'm looking for a good update reference covering the material in first three chapters of "Adams, Infinite loop spaces" (specially construction of delooping functors and group completion) with exact ...
4
votes
1answer
40 views

Introduction to proofs. [duplicate]

I am not at all familiar with mathematical proof-writing and would like to learn how to create my own proofs. So, I was wondering whether it would be possible for you to recommend me to any book or ...
1
vote
0answers
22 views

A physical model for pde

Do you know any mathematical model of a physical process such that it satisfies the following equations ? $$\mathrm{u_t=a(t)u_{xx}},\,\,\,0<x<1,\,\,\,t>0$$ ...