0
votes
0answers
11 views

difference equations/inequalities in two variables without constant coefficients

I have a linear inhomogeneous difference inequality with variable coefficients. I was wondering if there are any general methods available for solving it. The case where the inequality is replaced by ...
3
votes
4answers
93 views

Book/Article recommendation

I am a first year Math major in the university, this summer I want to self study and go over some specific subjects. Firstly, can someone can give a suggestion for a detailed book/article about the ...
1
vote
1answer
65 views

The relationship between each harmonic numbers

In Knuth's "Concrete Mathematics" in chapter about numbers below equality is given $$H_n = \ln n + \gamma + \frac{1}{2n} - \frac{1}{12n^2} + \frac{\epsilon_n}{120n^4} $$ where $0 < \epsilon_n < ...
14
votes
2answers
304 views

Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling?

8/18/14 Edit: If anyone has a copy of a related reference, then I would be happy to see it. For now, I am accepting the answer below and considering the question answered in the affirmative: Yes. ...
1
vote
4answers
215 views

Discrete Mathematics books for Computer Science Self-study

I am an experienced software developer, want to refresh discrete math back in uni. I am looking for a book that is easy to read, contains more examples, and exercises and solutions for self study ...
0
votes
2answers
43 views

Alternative reference for number of restricted partitions

I am looking for the number of partitions of some number $n$ into $k$ parts. Following the Wikipedia article on partitions, I ended up with Andrew's book [1]. Judging by Google's preview Chapter 3 ...
0
votes
1answer
42 views

“Homotopy theory” on finite topological spaces?

My question concerns finite sets carrying a not-necessarily-discrete topology. I'm wondering if there's an analogue for homotopy theory where the role of $S^n$ is played by some other, finite set. (My ...
3
votes
0answers
42 views

Modular arithmetic - Suggestions to begin

I've always wanted to start studying modular arithmetic to try to solve problems like: $$\text{find } n \in \mathbb{N} : 4n^2 \equiv 1 ~(\text{mod }{10^4})$$ I have a good basis in mathematical ...
3
votes
1answer
162 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”?

Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the constituents of the system to which it applied ...
0
votes
1answer
187 views

Book on discrete mathematics for self study

I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read ...
2
votes
1answer
73 views

Finding the super-mean (NOT the mean) of a set of numbers.

the super-mean is found by grouping pairs of numbers and finding the average successively until there is just one number. For example, $$(1-2-3-4-5) \to ((1+2)/2,(2+3)/2,(3+4)/2,(4+5)/2) \\ ...
1
vote
4answers
1k views

What is the maximum number of pieces that a pizza can be cut into by 7 knife cuts? (NBHM 2005)

I am seeing this question very first time and do not know any formal way to solve it. Which part of mathematics it is related to? What is the maximum number of pieces that a pizza can be cut into by ...
0
votes
3answers
236 views

Book on modular arithmetic

I am searching for some good book which section is devoted to modular arithmetic. I am self learner so I strongly prefer that book has exercises best with answers or solutions. I have CS background ...
0
votes
2answers
68 views

Fact About Equality Proven by Euler in 1748 (Context: Integer Partitions)

I'm currently reading Integer Partitions by Andrews and Eriksson. In the introductory chapter (p.2), there is the following statement: ... The table would have a more efficient design: ...
1
vote
1answer
135 views

Mathematic books

Can anyone recommend good books in which I can find information about interesting sums (like Harmonic number, sum of polynomials etc). The only book in which I found any information was Concrete ...
3
votes
2answers
70 views

Graphs with a polynomial number of shortest paths between any pair of vertices

Let $G$ be a simple undirected graph, and let $s$ and $t$ be two arbitrary vertices of $G$. Even for some rather restricted graph classes, the number of shortest paths between $s$ and $t$ can be ...
0
votes
0answers
32 views

Reference for Body-and-bar or Body-and-hinge frameworks

I'd like a comprehensive reference for the mathematical theory behind body-and-bar and body-and-hinge frameworks (brief intro), possibly with an emphasis on the latter. There are a large number of ...
1
vote
1answer
50 views

discrete mathematics , sequences, characteristic equation

Today in my discrete mathematics class we started combinatorics and also solved some some recurrence relation sequences using the characteristic equation. So my question is can you guys point me to ...
3
votes
3answers
215 views

Any good books on Mathematics and Programming?

I've been on google for a while now searching for a good book on mathematics combined with programming, but either the level of math they're starting at is too high or the level of programming is too ...
4
votes
0answers
54 views

Nimber of selective compound games

Background/Definitions. Let $\alpha,\beta$ ordinal numbers. The Hessenberg sum $\alpha \# \beta$ is defined recursively as the smallest ordinal which is $>\alpha' \# \beta$ and $> \alpha \# ...
3
votes
0answers
142 views

Difference between two sets of data points

I'm making a simple calibration of a z-stage, by measuring a number of points in one direction with a constant $\Delta$Z between each sample. Then I reverse the direction and measure the same number ...
7
votes
0answers
190 views

Citation for subset complement result

Let $S = \{s_1, \ldots, s_n\} \subset \{1, \ldots, 2n\}$. Consider two operations on $S$, unfortunately both called complement in different setting: let $A(S) = \{1, \ldots, 2n\} \setminus S$ (set ...
1
vote
1answer
156 views

Where can I learn about solving Big-Oh problems that are written in algebra? [duplicate]

Where can I learn about solving Big-Oh problems that are written in algebra? Such as this $$\sum_{i=1}^{n} (3i + 2n) = O(n^2)$$
4
votes
1answer
79 views

Does a chordal graph with singleton minimal separators have a special name?

Consider a chordal graph $G$. Chordal graphs are precisely the graphs that admit a clique tree representation. A clique tree $T$ has as its vertices the maximal cliques of $G$. Edges in $T$ are ...
4
votes
2answers
1k views

Number Theory Practice Questions

Can anyone please suggest a book or a link to website where I can find Practice questions (and there solutions) on Number Theory. More specifically questions on the following topics: Divisibility ...
0
votes
2answers
345 views

Discrete Math Textbook

For my discrete math class, we are using the textbook Discrete Mathematics and Its Applications, by Rosen. I really like the exercises given at the end of chapters, they are quite challenging at ...
1
vote
1answer
57 views

How to approximate a complex linear homogenous recurrence with constant coefficients with a simple one?

Is there some standard way to approximate a complex linear homogenous recurrence with constant coefficients with a simple one? For example, I might want to approximate $$ ...
1
vote
1answer
248 views

Where can I find (download) a book about basics of discrete mathematics?

I am a beginner in this craft. Do you know where can I download a good book about basics of discrete mathematics?
1
vote
1answer
250 views

What should be in a discrete mathematics book? [closed]

Recently, one of my teacher ask me to help him for writing a book on discrete mathematics book and this book will use in our university for teaching discrete mathematics. The target audience are first ...
2
votes
0answers
317 views

Mathematics in the “ The Art of Computer Programming”

I don't know of this the right place to ask this type of question and hence I apologize (in advance) for any inconvenience. Here is my question: I have studied Concrete Mathematics by Knuth, Graham ...
5
votes
2answers
179 views

Symmetries of a colored cube

Is there a systematic way to find out what all the symmetries of the following cube are? Naturally, rotations and reflections along a diagonal or a plane are taken into account. Of course, by ...
1
vote
0answers
277 views

Augmenting Path Algorithm for Maximum Matching

I have a rather cryptic pseudo code version of the augmenting path algorithm for finding a maximum matching in a bipartite graph in my notes. I m not sure it s correct, and there are some parts that ...
5
votes
1answer
341 views

what textbook would be good as a precursor to discrete mathematics?

I'm about to start a Masters in Software Engineering at university and have not studied/used-intensely anything mathematical for 6 years. I know that computing science makes use of discrete ...
3
votes
1answer
133 views

Looking for an article on general principles of discrete mathematics

In his article 2 cultures Timothy Gowers states that the structure in combinatorics is there in the form of somewhat vague general statements that allow proofs to be condensed in the mind, and ...
11
votes
2answers
9k views

What books do you recommend before 'Concrete Mathematics'?

What book(s) do you recommend before Concrete Mathematics? Is something like "Introduction to discrete Mathematics" enough?
6
votes
5answers
951 views

discrete math book suitable for younger person?

When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens. Does anyone know if there are good books, ...
11
votes
5answers
5k views

Resources/Books for Discrete Mathematics

I am going to a Computer Science Course in University next year. I heard that Discrete Mathematics is whats required for Comp Sci so, I am looking for resources/books that I can read to get started ...
2
votes
2answers
3k views

Free resources to start learning Discrete Mathematics

Can anyone recommend good, free online articles or books to learn Discrete mathematics? When I google'd for them, I came across few resources..but don't know whether they are good to start learning ...
15
votes
2answers
11k views

A comprehensive list of binomial identities?

Is there a comprehensive resource listing binomial identities? I am more interested in combinatorial proofs of such identities, but even a list without proofs will do.
32
votes
7answers
28k views

What is the best book for studying discrete mathematics?

As a programmer, mathematics is important basic knowledge to study some topics, especially Algorithms. Many websites, and my fellows suggest me to study Discrete Mathematics before going to ...
2
votes
5answers
2k views

Where can I find a review of discrete math

I'm looking for course notes and assignments and hopefully some example exams for Discrete Math, I'm taking a placement exam in the subject after having taken it 4 years ago.