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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3
votes
1answer
42 views

Is it possible that every set can be specified?

Is it possible for there to be a model of ZFC with the property that, for every set $S$ in the model, there is a unary predicate in the language of ZFC such that $S$ is the is the only set satisfying ...
2
votes
1answer
65 views

two questions about primes

I'm very ignorant about results in number theory concerning the primes. Please let me know if these are open conjectures or easy problems: There are infinitely many primes of the form $n!+1$ There ...
2
votes
0answers
17 views

Materials for teaching the axioms of the real numers to high school students

I suddenly felt the urge to teach the axioms of the real numbers (i.e. the complete ordered field axioms) to a bright Year 10 student that I tutor, with an emphasis on the consequences of the field ...
0
votes
0answers
63 views

The hemisphere is contractible [on hold]

Please, where can i find the proof of the fact that The hemisphere is contractible ? I read that we must prove that the hemisphere is homotopoic to a disc, but how to find this homotopy? We ...
0
votes
1answer
53 views

Which topology textbook has the greatest amount of ancillary support available on the Internet?

I'm considering to begin upon the study of topology and am wondering which book would the best option. I've even started reading Munkres and G. F. Simmons, but the problem is neither book has any ...
0
votes
1answer
25 views

Books to intuitively grasp mathematics that provide a solid foundation, as well as books on mathematics for physics and engineering. [on hold]

I am a junior in high school and I've become increasingly interested in physics and engineering. I took a physics course that covered classical mechanics and the math was rather simple and straight ...
5
votes
6answers
80 views

coordinate free proof that $\text{div}(\nabla f \times \nabla g) = 0$

Let $V$ be a Euclidean $3$-dimensional space. Does there exist a coordinate-free proof that for any two $C^1$-functions $f, g: \mathbb{R}^3 \to \mathbb{R}$ we have $$\text{div}(\nabla f \times \nabla ...
3
votes
0answers
58 views

A question regarding a paper of M. Magidor [on hold]

I am interested in the following paper of M. Magidor: "On the role of supercompact and extendible cardinals in logic", Israel Journal of Mathematics, 05/1971; 10(2): 147-157. The abstract (which I ...
1
vote
1answer
32 views

Reference request: comprehensive handbook of combinatorial formulae

I am searching for an handbook that collects a comprehensive list of formulae in combinatorics. Could you point out one such reference?
1
vote
1answer
51 views

philosophy : first axiom of geometry and variable curvature

The very first axiom of geometry can be described as: Two different points lay on one and only one line. And I was wondering are there surfaces where this axiom irrecoverably fails? and I found ...
15
votes
0answers
157 views

Learning roadmap request: compiling a “Mathematics Stack Exchange Undergraduate Bibliography” [migrated]

[Book recommendation] questions are quite popular on this website, which is, at least for me, one of the best places to get useful and insightful suggestions ...
2
votes
0answers
54 views

Big list of references [divided by categories] that collect commented open problems and conjectures

The aim of this question is to collect a big list of books or survey papers or websites which collect an up-to-date, comprehensive, well-organized, and possibly commented list of open problems. I ...
0
votes
0answers
32 views

TQFTs and categories - references?

This question is in similar spirit to this question, but I'm asking for references that contain: a general formulation of the theory of TQFTs from the mathematics perspective that also explains the ...
2
votes
0answers
20 views

Difficulties with the “correspondence” between essential singularities and formal Laurent series

To fix terminology that I'm not 100% sure is universal, let the ring of Laurant series about $0$ be $\mathbb{C}[[z]][z^{-1}]$, and the ring of formal Laurant series about $0$ be ...
7
votes
0answers
44 views

The least subset of $\mathbb{R}_{>0}$ that includes $1$, and is closed under addition, multiplication, reciprocation, and exponentiation.

Let $S$ denote the least subset of $\mathbb{R}_{>0}$ that includes $1$, and is closed under addition, multiplication, reciprocation, and the function $x,y \in \mathbb{R}_{>0} \mapsto x^y.$ ...
0
votes
0answers
19 views

What are some good books to study finite dimensional lie algebras?

I like conceptual books, which have helpful examples too. Thanks
3
votes
0answers
35 views

Homological algebra and Grothendieck Topologies

I have recently became familiar with the theory of Grothendieck Topologies and Cech cohomology for sheaves over a site. It seems that many of homological concepts in algebra, can be formulated in ...
1
vote
0answers
17 views
+50

Examples of applications of mononotone and pseudomonotone operators

Hi I am aware that the following question is quite broad, but I would appreciate any feedback even if it is in the form a reference. I am interested in some standard examples in engineering (or any ...
3
votes
4answers
160 views

Analysis Textbook

Does anyone have an recommendations for an Analysis textbook for beginners? I'm looking for a textbook that's like Calculus Third Edition by Smith and Minton in that it's hardcover, has good ...
1
vote
4answers
86 views

Reference request: self-contained rigorous introductions to “cool” topics

I am looking for some self-contained (i.e., providing all necessary background information) rigorous introductions to topics perceived as "cool" to propose to (really) advanced high school students ...
5
votes
1answer
75 views

Prerequisites for Linear Algebra Done Right by Sheldon Axler.

I've read some notes online and I learned so far: $\{\overset{\displaystyle\ldots}\ldots$ Systems of Two Linear Equations ...
2
votes
3answers
139 views

“Methods of Theoretical Physics for Mathematicians”

I read in the Princeton Companion to Mathematics that even pure mathematicians should know some theoretical physics. However, I see that there are many reference books of mathematical methods for ...
1
vote
1answer
29 views

Neural networks and mathematical modelling

Could you point out some reference books [accessible to an undergrad math student] that deal with the mathematical modelling aspect of neural networks?
6
votes
1answer
48 views

Künneth formula in topology, show isomorphism

Where could I find a proof of the isomorphism aspect of Theorem 2.4 in this pdf: http://math.stanford.edu/~conrad/diffgeomPage/handouts/tensor.pdf For vector spaces $V$ and $W$, consider $V$ and ...
4
votes
1answer
92 views

Is Hoffman-Kunze a good book to read next?

I'm planning on self-studying linear algebra, and trying to decide on a book. I'm thinking of using Hoffman and Kunze. What sort of experience is required to handle Hoffman and Kunze? So far, I've ...
3
votes
1answer
51 views

Help needed in understanding the basics of Cartan decomposition of a Lie algebra

I am trying to learn the basics of Cartan decomposition of Lie algebra, and have come across the following example. Consider $\mathfrak{gl_n}$ as the Lie algebra of endomorphisms of $\mathbb{C}^n$. ...
2
votes
0answers
65 views

Looking for an existing proof for a property of triangles

In my paper, I need the following lemma. I can prove it, but it is a little lengthy to be put inside the paper. I am wondering is there any existing proof that I can quote. Lemma 1: Let the nodes ...
5
votes
0answers
121 views
+50

Collections of undergraduate research projects

I would like to compile a "big list" of undergraduate research projects in the following areas: calculus; analysis; abstract algebra; linear algebra; number theory; geometry; mathematical physics; ...
1
vote
0answers
32 views

Request a paper by Gelfand and Ponomarev

I am looking for the following paper by Gelfand & Ponomarev: I. M. Gelfand and V. A. Ponomarev, Problems of linear algebra and classification of quadruples of subspaces in a ...
0
votes
2answers
48 views

Connections of theory of computability and Turing machines to other areas of mathematics

The question is quite straightforward: Could you point out some reference papers that highlight (in a way that is fairly accessible) the connections between (1) theory of computability, algorithms, ...
0
votes
1answer
18 views

List (of) all cubic planar graph with 30 vertices

Where can I find the list of all possible cubic planar graphs (without triangles) having 30 vertices? Are there online databases for that?
4
votes
2answers
190 views
+50

On progress in mathematics: some long-open problems and long-standing conjectures

I would like to ask a question here on Math Stack Exchange taking inspiration (and therefore combining) from two well-known threads on MathOverflow: (1) Not especially famous, long-open problems which ...
1
vote
1answer
29 views

Probability and Measure Theory by Ash

Has anyone used the textbook above? If so how does it compare with billingsley, Chung and similar such books in terms of rigor, coverage, and ease if use for self study?
4
votes
2answers
94 views

Solving min-max optimization problems in original ways (that is, avoiding the frenzy of differentiation)

As I see from the students I'm tutoring, once faced with a min-max problem, the average student is taken by the frenzy of differentiation. I would like to show that sometimes it is better to use ...
1
vote
1answer
65 views

I need help organising these books by topic

Okay, this should be a quick and easy question for those of you who've studied calculus. I have a list of books that I want to order by topic, the books are as follows: Michael Spivak - ...
0
votes
0answers
49 views

Reference request: calculus of variations

I am searching for a good book to self-study calculus of variations. It should be fairly complete; build up gradually from the very basics; offer detailed explanations; have some emphasis on ...
1
vote
1answer
43 views

maximum principle for $p$-Laplace equation

Consider $\Omega \subset R^n$ a bounded domain. Let $\varphi \in W^{1,p}(\Omega) \cap L^{\infty}(\Omega)$. Let $u \in W^{1,p}(\Omega)$ with $\Delta_p u = 0$ in $\Omega$ with $u - \varphi\in ...
2
votes
0answers
44 views

How to draw simple lattice diagrams (MathJax syntax) [migrated]

I recently asked a question on TeX SE about how to draw lattice diagrams with MathJax (as in, the TeX commands for creating one, once I already drew it on paper and know what it should look like). ...
1
vote
2answers
99 views

What is some pure math news website by a publisher? [closed]

Why aren't there be any pure math website by a publisher? I google a lot and resulting only applied math news or math journal that is difficult and inaccessible even to advanced reader I am looking ...
0
votes
0answers
28 views

Arrow Space Construction

Is there a paper or book that has rigorously constructed the space of "arrow vectors" and shown that it is a vector space? I'm just wondering how far anyone has followed the heuristic.
2
votes
0answers
49 views
+50

Sobolev space on $M \times (0,\infty)$, $M$ compact closed manifold

I want to know things like definitions of Sobolev spaces on a manifold of the form $M \times (0,\infty)$, where $M$ is a closed compact manifold without boundary. So $M \times (0,\infty)$ is a ...
6
votes
4answers
138 views

Math newbie: what to read? [closed]

Quick question for you all: what should a high school senior who intends to major in CS and math read to become familiar with proofs, calc, algorithms, etc? I know that's incredibly broad, basically ...
2
votes
2answers
101 views
+250

Is there an online calculator in which you can type a number and have it tell you if it could be a Lychrel number or not?

Say you type 7326 into it, it runs a few calculations and tells you it reaches 99099 in three iterations. But if you type in a number like 887, it runs a reasonable number of iterations (say, twenty) ...
2
votes
3answers
101 views

A mathematically mature introduction to Turing Machines and Computability [reference-request]

In the computer science course for mathematicians held at my university Turing Machines have been presented very briefly. So much so that I didn't quite get why they are relevant to mathematics. I did ...
9
votes
4answers
162 views

Lang's Linear Algebra: what's next?

I've completed the study of Lang's Linear Algebra ($3^\text{rd}$ edition). To put it simply, I have enjoyed the subject and I would like to know "what's next". In other words, I would like to know ...
0
votes
1answer
59 views

character theory question [closed]

Can you offer me some useful books in representation and character theory of finite groups? I want to see the applications of group representation theory and character theory in other sciences too.Can ...
0
votes
0answers
29 views

Bounds on the numbe of groups of degree n [duplicate]

What are the best lower/upper bounds on the number of (non-isomorphic) arbitrary groups of degree n? Thanks!
10
votes
0answers
151 views
+150

Probability and Laplace/Fourier transforms to solve limits/integrals from calculus.

I've seen in some answers in Brilliant.org to some very complicated limits and integrals that uses probabilistic arguments (Let $X$ be a random variable from $[0,1]$... some examples are in those ...
1
vote
1answer
53 views

Is there a name for this result in planar geometry?

I found out that the following statement is fairly easy to prove: Let $A$, $B$ and $C$ be thee distinct points in the plane. Let $S_{AB}$ be the circle that has the line segment $AB$ as a ...
1
vote
0answers
33 views

Looking for a partial converse of Rolle's theorem

Let $f: [a,b] \to \mathbb R $ be a continuous function differentiable in $(a,b)$ such that $f(b)=0$ and for some $c \in (a,b) , f'(c)=0$ ; then under what additional conditions can we conclude that ...