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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1
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1answer
54 views

Origin of $\sigma$-algebra

In what paper, article or book was the notion of an $\sigma$-algebra first defined or mentioned? Or at least how far could this concept traced back?
1
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3answers
87 views

Good algebra book to cover these topics?

I will be studying two algebra modules next year and I am looking for a comprehensive book that will cover both of them, however due to having very minmal exprience with algebra I am looking for your ...
-4
votes
1answer
53 views

I need this book by Michael Weinstein, Between nilpotent and solvable [on hold]

I need this book by Michael Weinstein, Between nilpotent and solvable. I live in iran and i can't find this book. Please help me.
0
votes
1answer
109 views

Is there a term in graph theory called 'GRAIL'?

I've been a talk with a PhD student about some graph issue and told me about GRAIL graph and have drawn it for me as you see in the picture, however, I try to generalize so-called "Grail graph" to ...
1
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0answers
16 views

Introductory Reference for Mathematical Physics

I'm a senior undergraduate student studying differential geometry. I have experience with smooth manifolds, some elementary theory of Lie groups, and a little multi-linear algebra. I understand this ...
1
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1answer
44 views

About a matrix identity.

In a document named as "The Matrix Cook-Book" I saw two expressions of which I do not get any clue how they are derived. For $n = 3:$ $\det(I + A) = 1 + \det(A) + Tr(A) + 1/2\ Tr(A)^2 − 1/2\ ...
0
votes
1answer
11 views

Proof for the fact that the method of characteristic equations is a valid method to solve recurrence relations

Could someone kindly point me to a proof of the fact that the method is characteristic equations is a valid way of solving recurrence relations? It seems fairly arbitrary to me. I would be grateful ...
6
votes
0answers
42 views
+50

Interval arithmetic with different definitions of intervals

Interval arithmetic normally deals with intervals defined as $[a,b]$ with rules like $$[a,b]\cdot[c,d]=[a+c,b+d]$$ I am interested in interval arithmetic with different interval definitions such as ...
77
votes
23answers
22k views

Complete course of self-study

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
3
votes
3answers
412 views

For Maths Major, advice for perfect book to learn Algorithms and Date Structures

Purpose: Self-Learning, NOT for course or exam Prerequisite: Done a course in basic data structures and algorithms, but too basic, not many things. Major: Bachelor, Mathematics My Opinion: Prefer ...
15
votes
5answers
9k views

Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
3
votes
5answers
588 views

Technique for proving four given points to be concyclic?

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how ...
0
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0answers
6 views

Property of locally cyclic groups

I am having difficulty proving that: A group $G$ is locally cyclic if and only if $G$ is isomorphic to a subgroup of $\mathbb{Q}$ or $\mathbb{Q/Z}$. Is there any easy way to prove it? Thanks.
2
votes
1answer
28 views

Multiplicative version of convex hull

The convex hull of a finite set of points, $(x_i,y_i) \in \mathbb{R_+}^2$ ($i=1,...,n$), is defined as: $$\left\{(\sum_{i=1}^{n} \alpha_i x_i,\sum_{i=1}^{n} \alpha_i y_i) \mathrel{\Bigg|} (\forall i: ...
0
votes
1answer
617 views

Expected state of a Markov chain

Let's start with a slightly trivial Markov chain defined as follows: the beginning state is called $1$ and the set of states is $\mathbb{N}$. At each step, when the current state is $n$, the ...
0
votes
0answers
11 views

Automorphism group of a locally cyclic group

I am having difficulty proving that: The automorphism group of a locally cyclic group is commutative. Is there any easy way to prove it? Thanks.
3
votes
1answer
93 views
+50

Mathematical structures textbook recommendation

I am busy doing an undergraduate course called "Fundamentals of Mathematics". It is not well-defined as there is no syllabus nor recommended textbook (there are lectures and notes), but the course ...
0
votes
2answers
70 views

Soft Question: Weblinks to pages with explanation on quadratics.

I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of ...
0
votes
0answers
26 views

Differentiability of parameter-dependent integrals when derivative exists only almost everywhere

This unanswered question asked in 2013 Differentiation under the Integral Sign (let's call this Q-zero) seems to be taken from this (or pdf ver.). The result on differentiation under the integral ...
0
votes
0answers
8 views

Is there a solid reference work that covers optimization for discrete and for continuous domains?

I am looking for a good, comprehensive reference on optimization. Currently, I have Lundberg's "Linear and Nonlinear Programming, 3rd Ed", but this completely omits integer programming, except in the ...
0
votes
0answers
14 views

Study materials for Differential equations and Fourier analysis

In two days, on Monday, a new course called Introduction to differential equations starts, and when that ends in one month another called Fourier analysis and its application starts (Both are actually ...
3
votes
1answer
26 views

Double integral definition of periodic Sobolev spaces

Preliminaries: For $s \geq 0$ define the periodic Sobolev spaces $H^s(\mathbb T)$ with norm $$ \| f \|_{H^s(\mathbb T)}^2 = \sum_{k \in \mathbb Z} \big(1 + |k|^2 \big)^s \, \big|\widehat{f}_k \big|^2, ...
5
votes
1answer
459 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: ...
0
votes
1answer
33 views

What's a somewhat fast introduction to (differential) geometry and algebraic topology for someone who knows a lot of analysis but little else?

I never got to learn much about geometry beyond curves and surfaces in Calculus III, and point set topology. So what is a fast introduction to differential geometry (specifically, differential ...
0
votes
1answer
42 views

What are some easier papers/books I can read? [on hold]

I'm trying to improve my ability in reading mathematics papers. My field is more related to biological sciences, but there are a lot of interesting papers I'd like to read that use more mathematical ...
5
votes
5answers
698 views

Recursion theory text, alternative to Soare

I want/need to learn some recursion theory, roughly equivalent to parts A and B of Soare's text. This covers "basic graduate material", up to Post's problem, oracle constructions, and the finite ...
0
votes
0answers
16 views

Combinatorial Convex Optimization: Russian paper

I'm looking for an electronic version of the paper: David Yudin and Arkadi Nemirovski. Informational complexity and effective methods of solution of convex extremal problems. Economics and ...
0
votes
1answer
42 views

Estimate for partial sums of a series equivalent to the Riemann hypothesis

The sums $$S_N=\sum_{n=1}^N\frac{\mu(n)}{n},$$ where $\mu$ is the Moebius function, are known to tend to 0 as $N\to+\infty$. As far as I remember, there was an estimate on $S_N$ equivalent to the ...
0
votes
0answers
13 views

Application of Multivariate Analysis on Straight Lines [on hold]

Can anyone suggest to me a reference on the Application of Multivariate Analysis on Straight Lines? The reference should contain the part where we use the concept of orthogonality to formulate ...
2
votes
1answer
26 views

What is a good book for learning Stochastic Calculus?

I am in search of a good book for learning Stochastic Calculus from a purely mathematical/statistical point of view. Almost all the books I see are based on Finance. Also, please specify the ...
2
votes
0answers
25 views

Abelian hypersurfaces

Is there any way to tell from its defining equation when an affine hypersurface has a group law? I am aware that all such groups are matrix groups; in that case I might want to ask when a variety over ...
12
votes
6answers
7k views

Resources/Books for Discrete Mathematics

I am going to a Computer Science Course in University next year. I heard that Discrete Mathematics is whats required for Comp Sci so, I am looking for resources/books that I can read to get started ...
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11answers
664 views

Text suggestion for linear algebra and geometry

I want to study more linear algebra over the summer, specifically relating it to geometry. I was originally going to read Shafarevich's Linear Algebra & Geometry, after a recommendation, but it ...
2
votes
0answers
88 views
+100

How much does convolution with a C^m kernel increase the order of continuity.

EDIT: I rewrote the question, see the edit history for my previous attempt. My questions are: Is the following proof/reasoning essentially correct? How do I make it more precise, concise, correct? ...
0
votes
1answer
474 views

Question about the mathematics in actuarial studies

I tried Google but there isn't much information on this and I would really like some insights into actuarial studies, the mathematics involved and how it compars to the mathematics in a bachelor of ...
0
votes
1answer
33 views

Book recomendation for function sequences.

I wanted to study about sequences of functions defined in metric spaces. What book/books do you recommend? Thanks!
0
votes
1answer
88 views

Questions on CW-complexes

I am trying to proof the following two statements. If $X_1 \subset \dots \subset X_i \subset \dots$ is a infinite sequence of CW-complexes, then $X = \bigcup X_i$ is a CW-complex and each $X_i$ is a ...
0
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0answers
14 views

Geometrical Interpretation of Risk Ratio (RR) [on hold]

Can anyone suggest any book or article on the topic "Geometrical Interpretation of Risk Ratio (RR)" ?
1
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0answers
23 views

do Carmo or Pressley as introduction to Differential Geometry?

I'm choosing between these authors for self-studying Differential Geometry. The contents seem pretty similar for both books and I was wondering which book I should choose. The level of these books ...
4
votes
2answers
90 views

Gluing diagrams: is it possible to glue a surface with itself in the same point? how is the diagram drawn?

I am learning the basic concepts of Topology, and playing now with the gluing diagrams (describing the fundamental domain of a topological space), this is an excerpt of a basic description I took from ...
0
votes
0answers
9 views

Reference needed: Chi-square goodness of fit test, independence test, …

I want to really understand what is a Chi-square test and how it works: when is it needed, what motivates its use, etc. The same thing is needed for "Independence tests" and analysis of variances. Is ...
1
vote
1answer
24 views

What are those variations of norms called?

Let $V$ be a vector space with a function $\|\cdot\|$ on it that satisfies all the axioms of norms except for scalability condition $\|\alpha \mathbf{x}\| = |\alpha| \|\mathbf{x}\|$ replaced with ...
1
vote
0answers
37 views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general?

(Note: This question has been cross-posted from MO.) Let $\sigma$ be the classical sum-of-divisors function. A number is said to be perfect if $\sigma(N)=2N$. If $q^k n^2$ is an odd perfect number ...
0
votes
1answer
18 views

Reference about conformal map

I am here because I want to know if someone knows of some good e fast books or references about conformal map . More precisely I need of the propeties of the conformal maps on manifolds with boundary. ...
2
votes
1answer
46 views

Error in Billingsley?

Problem 8.25 in the third edition of Probability and Measure by Billingsley (1995, p. 142) is as follows: Suppose that an irreducible [Markov] chain of period $t>1$ has a stationary ...
3
votes
1answer
49 views

graph partition, second smallest eigenvalue.

In spectral graph partition theory, the eigenvector corresponding to the second smallest eigenvalue of the laplacian matrix of a graph, in general, is used to partition the graph. What is the ...
0
votes
0answers
15 views

“Asymptotic” $\mathbb{R}$-algebras

Definition. By an asymptotic $\mathbb{R}$-algebra, I mean an $\mathbb{R}$-algebra $F$ of functions $\mathbb{R} \rightarrow \mathbb{R}$ satisfying: $$\mathop{\forall}_{f:F}\left[\left(\lim_{x ...
3
votes
1answer
465 views

Correspondence theorem for rings.

Could someone provide a reference that includes a full and honest proof of the Correspondence Theorem for rings? Let $A$ be a multiplicative ring with identity and $I$ an ideal of $A$. There is a ...
0
votes
0answers
18 views

What do we call the number that measures how good of an asymptote $g$ is to $f$, and what are the basic results about this number?

Suppose we have a (potentially very complicated) smooth function $f : \mathbb{R} \rightarrow \mathbb{R},$ and we're trying to approximate it (in the limit as the input value goes to $+\infty$) by a ...
2
votes
1answer
2k views

Numerically solving a system of nonlinear ODEs with boundary conditions

I have a system of 6 second-order nonlinear ODEs involving 5 different functions of a variable $t$. Every function has a boundary condition at $0$. I've never taken a differential equations class and ...