This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
2
votes
0answers
40 views
Progress upwards?
I'm looking for a somewhat sequential list of books to learn math beyond calculus at home. I've taken calc 3 and am going further but I'm having a lot of trouble nailing down a real order of things ...
5
votes
1answer
64 views
Applications of representation theory in physics
The notes of a lecture on basic group and representation theory I attended last semester begin with a bit of motivation for the argument. They give the following examples for applications in physics:
...
-1
votes
1answer
63 views
What is combinatorics? How is it related to Ramsey theory? What is the background needed to study it? [closed]
What is combinatorics? How is it related to Ramsey theory? What is the background needed to study it?
When I was reading about Ramsey theory in some reviews on some books, many people mentioned this ...
3
votes
1answer
60 views
Algebra and skills needed for Hatcher
A couple of months ago I asked a professor by e-mail to mentor me on topology during the summer. He advised me to study general topology (Hausdorff spaces, connectedness, compactness) and algebraic ...
-3
votes
1answer
57 views
Books about finite groups construction [duplicate]
The algorithms to construct all finite groups of a given order introduced in :
A millennium project: constructing small groups, Hans Ulrich Besche, Bettina Eick, E.A. O'Brien, Internat. J. Algebra ...
4
votes
0answers
36 views
Second law of thermodynamics as a theorem about state space evolution
I once saw a mathematical explanation of the second law of thermodynamics. The statement was something like this: there is a mapping $f$ from the set of thermodynamic states $S$ to itself, and a ...
17
votes
2answers
164 views
Where can I find good exercises for algebraic geometry that require hard, concrete computation?
I've been studying scheme theory from Hartshorne and Qing Liu for a few months now. (For those who are not big fans of Hartshorne, I have to note that I agree with you: I use it only for exercises.) I ...
2
votes
1answer
47 views
good reading or essay on math
I am a Chinese, who do not have knowledge with university-level mathematics.
I am looking for reading or essay on university-level math (not text which is mainly written the theory).For example, set ...
-5
votes
0answers
92 views
Books to understand the construction of all groups of a specific order [closed]
The algorithms introduced by Besche–Eick (1999) were used to construct (or count) the groups of order up to 2000 in Besche–Eick–O'Brien (2002), yet I find the algorithms somewhat inaccessible.
How ...
2
votes
2answers
65 views
competition math references?
i want to prepare for competition math next years I am searching reference and some book or website about it What resources are available to prepare me for the competition math? if anyone had any ...
2
votes
6answers
62 views
mathematical analysis books for self study [duplicate]
I am looking for mathematical analysis books whose explanation is polite. If they has many familiar example, I will be happier.
I am familiar with set theory, group theory, elementary theory, but am ...
0
votes
0answers
36 views
math book with familiar example [duplicate]
I am looking for the books on linear algebra and analysis(in English). I hope they explain politely and contain many familiar example.
I am not familiar with mathematics except mapping.
2
votes
1answer
34 views
Instead of axiomatizing ordered fields, can we axiomatize just the right half?
Since ordered fields can always be split into two halves whose only common element is $0$, namely $(\leftarrow,0]$ and $[0,\rightarrow),$ I was wondering if we can axiomatize just the right half. Note ...
2
votes
1answer
55 views
How do we know we need the axiom of choice for some theorem?
I have been working through Munkres Topology book and in an exercise he says that there was a theorem he proved in a previous section that relied on the axiom of choice and the task is to find it. I ...
3
votes
3answers
78 views
What does boson-type realization mean?
I have seen several different contexts the expression "boson-type realization", for instance in the study of algebras growth and realization of affine algebras.
To be or not be a boson-type ...
1
vote
0answers
23 views
Specific (algebraic) directions in NCG
Since my initial question (How much algebra is there in Noncommutative Geometry?), I got to study the basics of NCG and I now consider starting a PhD. program in NCG. I read Khalkhali's Basic NCG and ...
1
vote
0answers
24 views
The intuition behind a matrix of a Hamiltonian?
We have derived an elegant partition function for a problem which resembles a quantized model taking the particles to be Bosons. The related Hamiltonian for every $i$th ensemble is there:
...
-3
votes
2answers
72 views
linear algebra books with many examples [duplicate]
I am looking for books on linear algebra written in English that explain thing clearly and contain many good examples.
I don't possess a very in-depth knowledge of mathematics. Also, it's alright if ...
-2
votes
0answers
44 views
set theory books with many examples [closed]
I am looking for linear algebra books that can explain thing clearly and contain many good examples to help me understand the math.
I don't possess a very in-depth knowledge of mathematics. Also, ...
1
vote
2answers
62 views
mathematical analysis books with many examples [duplicate]
I am looking for analysis books that can explain thing clearly and contain many good examples to help me understand the math.
I don't possess a very in-depth knowledge of mathematics. Also, it's ...
3
votes
1answer
84 views
+100
Book on Geometry (GRE Math Subject Test)?
I don't believe that this is a duplicate of any question that is on this site.
I am currently searching for a geometry textbook which covers (at least) material for the GRE Math Subject Test. I have ...
0
votes
0answers
53 views
References for basic level Differentiable Manifolds and Lie Groups
I an undergraduate math student with a decent background in abstract algebra. I am looking forward to studying Lie groups this summer...I want some you to suggest good references for the following ...
3
votes
0answers
41 views
Where can I find a good introduction to quaternions (plus dual quaternions)?
Math people:
I am looking for a good book, monograph, or paper presenting the fundamentals of quaternions, and dual quaternions, if possible. I am trying to read some engineering papers that assume ...
3
votes
0answers
30 views
Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas?
Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas?
It seems that it have a big gap between this graduate textbooks and the easier ones.
2
votes
1answer
60 views
Prerequisites for understanding Borel determinacy
I have just learned that Gale-Stewart game is determined for open and closed sets, so naturally I'm interested to understand Borel determinacy which seems to be on a totally different level. What's ...
3
votes
1answer
69 views
Ultrafilters - when did it start?
I am writing a paper on some of the applications of ultrafilters, especially the ones on $\mathbb{N}$. I thought that it would be interesting to include some information about how the concept got ...
1
vote
1answer
39 views
Permutations and Combinations reference request
I have an exam on Wednesday on Permuations and Combinations and while I understand most of the concepts, I find it difficult to apply it to the questions because I haven't done many practice ...
1
vote
3answers
57 views
Generalization of Holder inequality
On this wiki page, one can see that
$$\|fg\|_r\leq \|f\|_p\|g\|_q,$$
when
$$\frac{1}{r} = \frac{1}{p} + \frac{1}{q}, \ p,q\in(0,\infty].$$
I have two questions,
is the statement true?
If so, is ...
2
votes
1answer
82 views
maths required to complete project euler
What math's will help one complete all if not most of project Euler questions? Last I've attempted project Euler I could not understand the questions/vocabulary, etc., and could only complete a few ...
1
vote
0answers
43 views
solutions to $f(y) = n(n + 1) \ldots (n + m - 1)$
I was reading a paper about solutions to $f(y) = P(m)$, where $f(y) \in \mathbb Z[y]$ and $P(m) = n(n + 1) \ldots (n + m - 1)$ is a product of $m$ consecutive integers ...
4
votes
1answer
51 views
$\Delta u = \operatorname{div}f \ \ \mbox{in} \ \ B_1, f \in L^2 \Rightarrow \nabla u \in L^2$
I'm looking for results like, If $f \in L^p$
and
$$
\begin{array}{rclcl}
\Delta u & = & \operatorname{div}f & \mbox{in} & B_1\\
u&=&0& \mbox{on}& \partial B_1
...
2
votes
0answers
21 views
Inverting a discrete linear transformation
Consider the transformation from the set $\{a_n\}_{n=0}^N$ to the set $\{p_j\}_{j=0}^N$: $$ p_j = \sum_{n = 0}^Na_n\phi_n(x_j)$$ where $\{\phi_n(x)\}_{n=0}^N$ is a set of basis functions (linearly ...
-2
votes
0answers
24 views
all of the references in Theory of computation [closed]
I am seeking for all of the formal definition of Turing machine in all of the books.
Now I need any reference of theory of computation that I read those.
any answer of you could help me...
2
votes
4answers
92 views
Introductory books on complex analysis? [duplicate]
I'm a senior in my undergrad. years of college, and I haven't taken Complex Analysis yet.
I have taken Real Analysis I (covered properties of $\mathbb{R}$, set theory, limits of sequences and ...
2
votes
1answer
58 views
Are there any perfect numbers which are also powerful?
Powerful numbers are discussed in this paper by R. A. Mollin and P. G. Walsh.
Wikipedia has more information.
In particular, note that OEIS A001694 does not seem to contain any (even) perfect ...
2
votes
0answers
23 views
Condition for for Manifolds dual to functions
What is the condition (locally compact/paracompact/Hausdorff/second countable?) for the following familiar statement:
The category of (finite dimensional smooth) manifolds is contravariant ...
0
votes
1answer
28 views
A reference to learn about duality
I am interested in learning about duality in convex optimization. I am looking for something to read which is:
Reasonably short.
Fairly self-contained (if it is a chapter in a textbook, I would ...
5
votes
3answers
138 views
Self teaching Galois Theory
At uni, I did a module in group theory which I really enjoyed. I also did one on number theory which had aspects of rings and fields in it and I enjoyed learning this. Now that I have finished uni, I ...
4
votes
2answers
50 views
Possible typo in Bogachev's Measure Theory
I've a problem with the definition of a measure space in Bogachev's Measure Theory. The author (Definition 1.3.2, p. 9) assumes a measure to be a countably additive set function defined on an algebra ...
4
votes
3answers
69 views
Notes about evaluating double and triple integrals
I'm searching notes and exercises about multiple integrals to calculate volume of functions, but the information I find in internet is very bad. Can someone recommend me a book, pdf, videos, ...
0
votes
2answers
30 views
Error estimation for spline interpolation
Can you please indicate a reference for the proof of the fact that the error when interpolating a $C^4$ function by a cubic spline is bounded by $Ch^4\sup_{[x_{i},x_{i+1}]} |f''''(x)|$?
3
votes
1answer
49 views
Is this equality in a double category true?
Caveat: This is a utterly trivial question from a person who always learned to manipulate diagrams in a double category "from the ground"; I'll be glad even if you simply address me to any source ...
0
votes
0answers
42 views
the title of books and publication year
I am a Japanese so I may make some grammatical mistakes.
There are some books whose name are same but publication year are different.Is almost same the content of these books?
And, can I read the ...
3
votes
2answers
45 views
$\Delta u = f, f \in L^q \Rightarrow u \in W^{2,q}$ References
I'm looking for references for the following theorem. I will very grateful
Theorem: [Calderón Zigmund] If $u$ is a solution of
\begin{equation}
\Delta u = f \quad \mbox{in} \quad B_2
...
2
votes
0answers
51 views
General questions on measure spaces
Let $X$ be a set and $\mathcal{A}$ a sigma-algebra on $X$. Two measures are said to belong to the same class iff. they have the same null sets.
Together with every measurable map between measure ...
4
votes
0answers
50 views
+50
Interpolation method
I am researching about different interpolation methods, and their pros and cons. Please help me to understand ideas behind Gaussian interpolation method. Although, I looked at different papers for ...
1
vote
0answers
90 views
I hear that Dover books are cheap, but old and useless - is this correct? [closed]
I do not live in English-speaking world. I'm sorry if my sentences are difficult to read.
I hear that Dover books are cheap, but old and useless. Is this correct?
Also I plan to buy some books, ...
0
votes
0answers
29 views
Text suggestion for linear algebra and geometry
I want to study more linear algebra over the summer, specifically relating it to geometry. I was originally going to read Shafarevich's Linear Algebra & Geometry, after a recommendation, but it ...
4
votes
2answers
104 views
What is Ramsey Theory ? what is its own importance in maths?
3 days ago , i had a discussion with a close friend who studies physics - still a student - .
and i was telling her about the biggest known numbers in maths , so i told her about numbers such googol ...
1
vote
0answers
27 views
References for basics of Piecewise-Deterministic Markov Processes
I am looking for introductory/pedagogical material to Piecewise-Deterministic Markov Processes (see http://en.wikipedia.org/wiki/Piecewise-deterministic_Markov_process) (For the moment I am interested ...
