0
votes
0answers
4 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
23 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
121 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
108 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
27 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 ...
3
votes
3answers
108 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 ...
1
vote
3answers
94 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
39 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.
2
votes
1answer
88 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
107 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 ...
1
vote
0answers
144 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
98 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
110 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 ...
16
votes
2answers
261 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
54 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
75 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
229 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
175 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?
28
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
152 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
148 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 ...
39
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
88 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
179 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
545 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
82 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
771 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
217 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
220 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
281 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 ...
4
votes
0answers
93 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
163 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
893 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
311 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 ...
9
votes
1answer
441 views

Practical Tips: Mathematical research and discoveries [closed]

How to be when you are working on something innovative? What to do if there is a chance (even the $1\%$) that your work is leading you to something original? For example what have I do if I ...
3
votes
1answer
129 views

Worst category with first isomorphism?

I am no expert in category theory, but from VIII of Algebra: Chapter 0 I learnt that In an abelian category every $A\xrightarrow{\phi}B$ can be decomposed into \begin{equation}A\twoheadrightarrow ...
58
votes
20answers
4k views

The Best of Dover Books (a.k.a the best cheap mathematical texts)

Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books ...
2
votes
0answers
73 views

Books similar to “Primes of the form $x^2+ny^2$”

Are there any other books which are similarly to the book "Primes of the form $x^2+ny^2$"? Basically, I want a book which starts with a very important classical problem ( in this case which primes can ...
4
votes
2answers
114 views

Foundation on Diophantine Analysis and Number Theory

I want to read particularly about diophantine Analysis and Elementary Number Theory from a novice level. The books which I found on net: A Guide to Elementary Number Theory by Underwood Dudley ...
5
votes
1answer
116 views

Differences in worlds with and without $\aleph_0<|S|<2^{\aleph_0}$

Paul Cohen told us that whether or not there is $S$ with \begin{equation} \aleph_0<|S|<2^{\aleph_0} \end{equation} cannot be decided within ZFC, and hence it is reasonable to work in two ...
6
votes
2answers
307 views

Counterexamples in algebra

I got the feeling that whenever a subject gets so sophisticated that Zorn's lemma is needed, a book of counterexamples in that subject would probably benefit researchers/ students a lot. Zorn's ...
1
vote
1answer
254 views

Is there a list of all known Sophie Germain prime numbers?

Is there a list of all known Sophie Germain prime numbers available anywhere for download? I found a small list from OEIS and the top 20 biggest of such primes, but I can't find a list that would ...
18
votes
19answers
1k views

Elementary books by good mathematicians

I'm interested in elementary books written by good mathematicians. For example: Gelfand (Algebra, Trigonometry, Sequences) Lang (A first course in calculus, Geometry) I'm sure there are many other ...
4
votes
1answer
131 views

What other math fields wouldn't require learning a huge amount of material in advance?

From An Introduction to the Theory of Surreal Numbers: [...] Thus the reader has the opportunity which is all too rare nowadays of getting to the surface and tackling interesting original ...
11
votes
6answers
2k views

List of problem books in undergraduate and graduate mathematics

I would like to know some good problem books in various branches of undergraduate and graduate mathematics like group theory, galois theory, commutative algebra, real analysis, complex analysis, ...
0
votes
1answer
215 views

Functional Analysis - Where to go from here?

The short version of this question is this: I like functional analysis and want to learn more. I've taken a class on it and I've read the books by Brezis and Conway. Where can I go from here? Do ...
1
vote
1answer
695 views

what is the most traditional abstract algebra textbook? and [Linear algebra & Abstract algebra] [closed]

I have listed 3 textbooks i have in my mind to buy Herstein - Topics in Algebra Artin - Algebra Lang - Undergraduate Algebra Unlike Lang's Algebra is the most traditional abstract algebra text for ...
-2
votes
4answers
114 views

Noetherian and Artinian rings (reference) [closed]

I started to study localization of rings and Noetherian and Artinian rings. Do you know any good references for these subjects? I'm using the one by Atiyah and Mcdonald. Is there another one? Thank ...
25
votes
1answer
692 views

Counterexample Math Books

I have been able to find several counterexample books in some math areas. For example: $\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted $\bullet$ Counterexamples in ...