-1
votes
1answer
106 views

Crazy Set Theory Analogies

I think the following analogies are too interesting to be ignored: Union = Least Common Multiple If $G_1,...,G_n$ denote a number of sets of points (either linear or in any number of dimensions), ...
0
votes
0answers
112 views

“Deep” maths books in certain subjects [closed]

I would like a suggestion on the 'deepest' books in Calculus and analysis (something along the lines of Rudin's) Linear algebra Abstract algebra Geometry (and topology); (even something along the ...
4
votes
1answer
55 views

References for mathematical theory of summability of divergent series

Once in a while, I can't help it to ask very broad questions. I have read (a portion of) Hardy's Divergent Series. Back then, I think besides in mathematics, divergent series and the need to assign ...
3
votes
4answers
114 views

Examples of Infinite Simple Groups

I would like a list of infinite simple groups. I am only aware of $A_\infty$. Any example is welcome, but I'm particularly interested in examples of infinite fields and values of $n$ such that ...
1
vote
1answer
52 views

What are the problems that you tried to find their solutions and you did not know that it is impossible?

Tell us your story about Mathematics. Have you dream one day to do a big contribution in Mathematics because you are curious and love challenges. What are things that you tried to prove which then ...
0
votes
0answers
19 views

Reference request for papers proving the existence of a special function satisfying the following conditions

Previously in this site it has been proved that there exists at least one prime between $c_n$ and $n$ where $c_n$ denotes the $n$-th composite (see the question Prove that there exists an $m$ such ...
46
votes
46answers
4k views

What was the book that opened your mind to the beauty of mathematics?

Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But ...
9
votes
3answers
257 views

Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ...
14
votes
3answers
329 views

Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
2
votes
1answer
41 views

Good resource for learning braid theory?

I recently heard about braid theory and read the Wikipedia article on it, and it seems really beautiful. What is a good resource for learning more about it? I have a background in mathematics at the ...
16
votes
6answers
1k views

Best Math books or apps for adults to learn math from the beginning

I lost a possible job because I didn't know how to multiply and subtract negative valued integers. I also don't know how fraction manipulation works. What reference books can I read that can help for ...
2
votes
1answer
103 views

Reference Request - Early Calculus Papers

Question: I am looking for good references on the early calculus papers. Optimally, I want emphasis on the mathematics itself and I want that mathematics to be translated into modern terminology and ...
1
vote
0answers
44 views

Repository of functions which do not have elementary integrals [duplicate]

If there is some function and I suspect that the primitive function cannot be expressed using elementary functions, I would like to have some argument that there indeed is no such expression. One ...
1
vote
2answers
63 views

Introductions to posets on algerbaic structures (Everything I need to know about them)

I need a good and complete introduction to Tree-like orders and partial orders on algebraic structures with one operations. I accept basic texts too. I'm looking for free online texts mostly because ...
2
votes
0answers
42 views

Good topologies on $\mathcal{P}(X)$

Let $X$ be a topological space, and let $\mathcal{P}(X)$ (resp. $\mathcal{P}_0(X)$) be the set of all subsets of $X$ (resp. the set of all non empty subsets of $X$). Finally, let ...
0
votes
1answer
43 views

What are some good introductory textbooks on Sieve Theory?

I fail to find a duplicate. If it exists, please give me the link and close the question accordingly. As the title suggests, I am looking for recommendations on introductory books to Sieve Theory. ...
2
votes
0answers
34 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
1
vote
0answers
33 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
5
votes
2answers
137 views

Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
1
vote
2answers
141 views

Recommendation for Number Theory Textbook

. Greetings, every mathematicians! I'm a foreigner (meaning English is not my first language) and an undergraduate student. I'm currently studying linear algebra, set theory and have already studied ...
0
votes
1answer
42 views

Overview of game theory

I have a good high school math background, and I am interested in game theory, so I wanted to know something more about it, but I found very technical things or wikipedia. I am looking for something ...
4
votes
3answers
336 views

Most inspirational mathematical books [closed]

I would like to know which books on mathematics (from university texts to divulgative pop-math books) inspired you the most. My choice is Spivak's Calculus, which is, IMHO one of the most ...
2
votes
3answers
132 views

University-level books focusing on intuition?

I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors). While in high school they usually don't study, or are not interested, etc., in ...
0
votes
2answers
47 views

What is list of common integral that have no closed form?

What is list of common integral that have no closed form? It's diffucult for me to google it for some reason.
3
votes
1answer
138 views

Hard problems book in linear algebra

Could you suggest me a book where I can find hard problems in Linear Algebra for an undergraduate student? Thanks in advance.
0
votes
1answer
133 views

Most “beautiful” presentations of the basic proofs for vector spaces?

I am familiar with the standard proofs presented in textbooks for stuff like linear independence/dependence, the dimensions of common vector spaces, any basis for a vector space V must be linearly ...
2
votes
1answer
281 views

Lecture Notes in Real Analysis

I understand that this question was partially addressed here but I would like to have a question dedicated to just real analysis. I am looking for both elementary real analysis (advanced calculus type ...
4
votes
2answers
114 views

Theorems that have proofs from the outside of the original field of math

I would like to know more examples of theorems, which "belong to one field of math", but their proofs are from the "outside of the field". I am mostly interested in proofs that are not too long ...
6
votes
2answers
127 views

Sources of Elementary Number Theory Problems

I am looking for sources of interesting and challenging problems that would suitably accompany an honors level introductory number theory course. What are some good sources for interesting elementary ...
17
votes
3answers
283 views

Results in graph theory proved using other areas of math, and vice versa

I'm curious about learning graph theory, as it seems to pop up in some unexpected places. In order to get a partial feel for the subject, I was wondering if anyone could point me to some survey ...
2
votes
2answers
64 views

when is a ring a free module over a subring?

Let $S \subset R$ be rings, $S$ not necessarily an ideal of $R$, and $S \neq R$. Is there anything that can be said about when $R$ is free as an $S$-module?
2
votes
1answer
112 views

Book about elementary geometry , triangles, circles … [duplicate]

Currently, I'm studying a little about geometry and I was trying to find out some good book about it on internet, however I didn't find anything that I thought nice to me or what I really expected to ...
2
votes
3answers
395 views

Book with lots of geometry theorems

I want to study geometry and was looking for some book that has lots of theorems and covers almost all Euclidean geometry that is needed for High School and Maths Olympiads. Thanks.
3
votes
1answer
211 views

Best book ever on Galois theory (and differential galois theory) [closed]

Which is the single best book for Galois theory (that includes differential Galois theory) that everyone who loves pure Mathematics should read?
27
votes
20answers
2k views

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 ...
6
votes
2answers
178 views

List of (pre-graduate level) exercises

I am about to get my undergraduate degree in (pure) mathematics, but I feel like I'm ill prepared to go through a graduate program. This is why I'm looking for texts like this one ...
2
votes
1answer
190 views

Best book to learn Affine Geometry?

I'm going to learn Affine plane as well as affine Geometry. Unfortunately, my text book (not in English) is not good at all, so please recommend some book you think it's good for self-learning (and ...
41
votes
13answers
5k views

Interesting math-facts that are visually attractive

To give a talk to 17-18 years old (who have a knack for mathematics) about how interesting mathematics (and more specifically pure mathematics) can be, I wanted to use nice facts accompanied by nice ...
1
vote
0answers
90 views

What is a good source of problem-solving type problems?

I am not looking for contest problems where there is a clever trick or a standard approach, I am looking for more creative and open-ended problems such as this , and I am not looking for questions ...
4
votes
1answer
188 views

List of proofs of non-trivial theorems which were unnoticed to be wrong for at least a few years

For example, the Weber's proof of Kronecker–Weber theorem. I would like to know such proofs. It seems to be important for me to remember that a widely accepted proof might be wrong.
19
votes
4answers
556 views

What newer mathematics fields helped to solve or solved problems from older fields of mathematics?

I usually have a more or less formed template of conversation to talk with people about mathematics, It's importance, methods, history, etc. I've been for some time interested in newer fields of ...
5
votes
0answers
87 views

Classes of groups known to be realizable (IGP)

A finite group $G$ of order $n$ is said to be realizable (over $\mathbb{Q}$) if there exists a Galois extension $L/\mathbb{Q}$ such that $\mathrm{Gal}(L/\mathbb{Q})=G$. I'm curious what classes of ...
3
votes
1answer
876 views

Recommended maths book for beginner to study in computer science

I am going to study computer science next year. I am afraid I can't handle the mathematics in the university because I only know some basic mathematics, such as set theory, simple probability, simple ...
1
vote
1answer
263 views

Practice Problem Books

The Analysis I/II/III (Differentiation and Continuity/Sequence and Series/Integration) published by AMS. The first one is this. It's a problem-solution book. I found it excellent because of the ...
1
vote
1answer
268 views

what is the best book to study contour integration?

what is the best book or website to study contour integration ? I find in some question answer using contour integration but I can't understand how they do that so is there any help ?
3
votes
5answers
323 views

Geometry books with beautiful diagrams

What are some geometry books with particularly beautiful diagrams? Old or new. Could be on 'standard' material or specialised on one particular topic. Something for the connoisseur of mathematical ...
5
votes
0answers
104 views

What are some great graduate textbooks with solutions in the back to the problems?

I can think of Aubin's A Course in Differential Geometry, as well as Knapp's books. Any other great ones you know of? Especially in the GSM series from AMS (blue and yellow covers).
4
votes
0answers
184 views

Good examples of proofs in mathematics exemplary of creative reasoning [closed]

Just what the title says. I'm not looking for any proofs that require specialized knowledge past the very fundamentals of real analysis. I'm looking for proofs for important results (don't have to be ...
6
votes
7answers
1k views

Guides/tutorials to learn abstract algebra?

I recently read up a bit on symmetry groups and was interested by how they apply to even the Rubik's cube. I'm also intrigued by how group theory helps prove that "polynomials of degree $\gt4$ are not ...
11
votes
1answer
355 views

List videos of interesting courses at the doctoral level.

Many mathematics departments has provided video lessons their courses (usually one semester) that are offered in their doctoral programs in mathematics. Most often these courses total average of 26 ...