Articles of reference request

Learning Model Theory

What books/notes should one read to learn model theory? As I do not have much background in logic it would be ideal if such a reference does not assume much background in logic. Also, as I am interested in arithmetic geometry, is there a reference with a view towards such a topic?

Reference for the subgroup structure of $PSL(2,q)$

This material is covered in detail in Dickson’s “Linear Groups with an exposition of the Galois Field Theory”, chapter XXII and Huppert’s “Endliche Gruppen”, chapter II, paragraph 8. Since I don’t speak german and Dickson’s treatment often requires deciphering, I was wondering if there is a “modern” account of this somewhere.

Looking for references about a tessellation of a regular polygon by rhombuses.

A regular polygon with an even number of vertices can be tessellated by rhombuses (or rhombii, or lozenges), all with the same sidelength. The three following figures display a common structure. I had already seen this kind of tessellation, and I met it again in a recent question on this site (Tiling of regular polygon […]

Good math bed-time stories for children?

What are some good references/books/articles from which to derive some good bed-time math stories to pique a child’s interest in math? I am fascinated by math (used to hate it as a kid) and want my kids to be curious about it and fond of playing with the subject. I was thinking a good way […]

Pollard-Strassen Algorithm

I’m aware that the Pollard-Strassen algorithm can be used to find all prime factors of $n$ not exceeding $B$ in $O\big(n^{\epsilon} B^{1/2}\big)$ time. This is really useful because I need to find all factors less than $n^{1/3}$ to determine if n is squarefree, which could therefore theoretically be done in $O\big(n^{1/6+\epsilon}\big)$. However I can’t find […]

Requesting abstract algebra book recommendations

I’ve taken up self-study of math. (How smart can that be?) I’ve just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus. I was thinking of trying abstract algebra. I would appreciate any book recommendations. Thanks in advance. Andrew

How many $N$ digits binary numbers can be formed where $0$ is not repeated

How many $N$ digits binary numbers can be formed where $0$ is not repeated. Note – first digit can be $0$. I am more interested on the thought process to solve such problems, and not just the answer. If anyone can cite some resources for learning how to solve such problems would be great.

Good problem book on Abstract Algebra

I am currently self-studying abstract algebra from Artin. In that background, I am looking for a problem book in a spirit somewhat similar to Problems in Mathematical Analysis by AMS so that I have a lot of problems to solve.

A Book for abstract Algebra

I am self learning abstract algebra. I am using the book Algebra by Serge Lang. The book has different definitions for some algebraic structures. (For example, according to that book rings are defined to have multiplicative identities. Also modules are defined slightly differently….etc) Given that I like the book, is it OK to keep reading […]

What is the best way to define the diameter of the empty subset of a metric space?

This question is related to Why are metric spaces non-empty? . I think that a metric space should allowed to be empty, and many authorities, including Rudin, agree with me. That way, any subset of a metric space is a metric space, you don’t have to make an exception for $\varnothing$, and you can ascribe […]