Tagged Questions
4
votes
0answers
58 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 ...
9
votes
1answer
109 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 ...
7
votes
1answer
335 views
Practical Tips: Mathematical research and discoveries [closed]
How to behave when you have the feeling of 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 ...
3
votes
1answer
80 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 ...
43
votes
17answers
1k 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
53 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
61 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
102 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 ...
4
votes
2answers
130 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 ...
0
votes
1answer
76 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 ...
16
votes
19answers
754 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
112 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
...
5
votes
6answers
340 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
121 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
209 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
88 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 ...
4
votes
1answer
149 views
Help me get hyped about lattices
I own a small book on Lattice theory published by Dover. Unfortunately, since I bought it almost a year ago, I have gotten nowhere in its study.
What I am asking for are freely available papers that ...
1
vote
1answer
90 views
a question on countable discrete set
Let $X$ be Hausdorff and $C$ is countable discrete in $X$ and $x \in cl(C)$.
Does there exist a subset $D$ of $C$ such that $x \in cl(D)$ and there is a point-finite family $\{U_n\}$of open sets ...
5
votes
3answers
244 views
Fun but appropriate Christmas gift to give influential professors.
Inspired by this question...
Background
A friend and I have been meeting informally with a retired professor to do math on a weekly basis for several semesters now. He is a dear mentor to both of ...
106
votes
35answers
7k views
Fun but serious mathematics books to gift advanced undergraduates.
I am looking for fun, interesting mathematics textbooks which would make good studious holiday gifts for advanced mathematics undergraduates or beginning graduate students. They should be serious but ...
9
votes
4answers
438 views
recommending books for intro to diff. geometry
I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, stoke's thm, dRham chomology, ...
2
votes
1answer
120 views
Examples of Eilenberg-type Swindles
I am compiling a list of 'swindles' in the style of the Eilenberg-Mazur swindle. I've already got some swindles in K-theory, the Mazur Swindle and the proof of the Cantor–Bernstein–Schroeder theorem. ...
4
votes
1answer
75 views
Problem books in different languages
I simply love problem books in mathematics, though you have to know how to use them properly. I think they are useful to me because most of time I study on my own. I'm thinking here at MSE, since we ...
9
votes
2answers
266 views
problem books in functional analysis
There are many excellent problem books in real analysis.I'm looking for a problem book in functional analysis or a book which contains a lot of problems in functional analysis (Easy and hard problems) ...
6
votes
3answers
158 views
Simple problems that can be carried around in your head
What are some problems that can easily be carried around in your head and require no need of ink and paper? Problems like irrationality of $\sqrt2$ or infinitude of primes or Gauss's first initiation ...
1
vote
0answers
115 views
A rigorous book (or preferrably set of notes) on classic multivariable calculus-analysis?
This is different to (Theoretical) Multivariable Calculus Textbooks as I want a classical treatment of line and surface integrals without the notion of a differential form.
Prerequisites: Paths, ...
1
vote
2answers
297 views
Books that every undergraduate should read [closed]
Reference requests are common. However, I wish to make this a list of books which every undergraduate,majoring in mathematics should own or at least read.It may be a bit subjective.
Please include 1 ...
29
votes
6answers
714 views
Original works of great mathematicians
In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that...
For ...
9
votes
11answers
437 views
A list of books for discovering mathematics using computer software
I'm searching for books that allow one to discover/experiment with mathematics by using computer environments such as Mathematica/Magma/Magma/Pari-GP, etc.
Until now, I discovered these:
...
12
votes
9answers
422 views
What are the math challenges websites?
I know two websites that offer some challening puzzles for programming, Project Euler (PE has something about math, but I feel it's more about programming) and Code-Golf.
Can you recommend me some ...
2
votes
4answers
360 views
Undergraduate Topology Books [duplicate]
Possible Duplicate:
best book for topology?
Introductory book on Topology
I have been charged with ordering some topology books for our library. The books must be intended for ...
10
votes
2answers
362 views
References on Linear Algebraic Groups/Lie Theory
I am currently doing a course on Lie groups, Lie Algebras and Representation theory based on Brian Hall's book of the same name. We should cover upto chapter 4/5 in this book by the end of the ...
-3
votes
1answer
143 views
What is a good list of more than 20 math books for functional equation with 200+ pages of each [closed]
What is your good list of more than 20 math books for functional equation with 200+ pages of each? And not very specific book with very complicated/very sophiscated topic for mathmatician please!
It ...
0
votes
2answers
135 views
Resources for IMO
I am seeking an online resource or any book where I can find the questions of International Mathematical Olympiad questions chapter wise eg Number Theory problems grouped together.
Like this site ...
47
votes
21answers
4k 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 ...
11
votes
4answers
823 views
Good exercises to do/examples to illustrate Seifert - Van Kampen Theorem
I have just learned about the Seifert-Van Kampen theorem and I find it hard to get my head around. The version of this theorem that I know is the following (given in Hatcher):
If $X$ is the ...
12
votes
5answers
466 views
Can the order of learning be changed?
I have been advised by many people to learn from scratch. So I decided to learn it. But I have the following questions in my mind.
Can we skip "the Trinity" and learn something else directly? ("the ...
13
votes
4answers
635 views
Best books in the genre “______ for Mathematicians”
I once heard someone (perhaps from someone famous -- anyone have a citation?) say that there ought to be a series of books called "__ for Mathematicians," each one of which would explain a different ...
2
votes
1answer
68 views
Inequalities involving some common functions
I often see the following inequality is used over and over again
$$
1−x⩽e^{−x}
$$
for $x \in \mathbb{R}$, for proving or deriving various statements.
As a layman, I haven't seen this inequality ...
31
votes
7answers
2k views
Open math problems which high school students can understand
I request people to list some moderately and/or very famous open problems which high school students,perhaps with enough contest math background, can understand, classified by categories as on ...
4
votes
1answer
211 views
Unrivaled math classics that would be of practical benefit to the upcoming generation?
I'm often impressed that top mathematicians in a given field seem to have not only a knowledge of the "state of the art" of their subfield, but also a knowledge of the history of the field and thus ...
21
votes
5answers
1k views
Famous papers in algebraic geometry
I'm reading the Mathoverflow thread "Do you read the masters?", and it seems the answer is a partial "yes".
Some "masters" are mentioned, for example Riemann and Zariski. In particular, a paper by ...
4
votes
1answer
527 views
A list of basic integrals
I am in need of a list of basic integrals for my upcoming ODE test,
I have searched on Math.SE for a post that might help but I didn't find such a post.
When I write 'basic' I don't necessarily mean ...
0
votes
0answers
60 views
All known ways to calculate $\int_{-\infty}^\infty \exp(-x^2/2)$? [duplicate]
Possible Duplicate:
Proving $\int_{0}^{+\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$
I want to collect all known ways how to compute
$$\int_{-\infty}^\infty \exp(-x^2/2) = ...
2
votes
1answer
155 views
List of important and influential publications in logic
Wikipedia surprisingly does not contain a good list. Under philosophy of mathematics it is rather vacant too. A graduate level list is here, but I was curious more about the most influential papers. ...
5
votes
1answer
85 views
Simplest nontrivial example repository
I've often wondered if it would be feasible to have a searchable online database of worked out "first nontrivial examples". Users could upload their examples to the database and these could be ...
1
vote
2answers
85 views
What is the list of theorem that are able to find out a sequence is converge or not?
A sequence is called converge if for every next term of the sequence is getting closer to the limit of a number.
What is the list of theorem that are able to helping to find out a sequence is converge ...
4
votes
2answers
181 views
Formulae for PDEs : Commuting derivatives and/or integrals
Many times I come across some new formula being used to work with and/or reduce partial differentials. As kleingordon said, these things are mysteriously not taught anywhere(atleast in physics ...
9
votes
8answers
536 views
Reference for general-topology
Though there are several posts discussing the reference books for topology, for example best book for topology.
But as far as I looked up to, all of them are for the purpose of learning topology or ...
4
votes
0answers
221 views
Structuralist slogans
I am afraid to make a bad impression by misusing this forum but I am looking for as-many-as-possible mathematically inspired formulations and references to one (sometimes vague) idea. The idea is ...
