Decision theory and discrete mathematics

Discrete Mathematics Number theory

The focus of this entire note is on positive integers. I will start by the basic notion of divisibility. We say that a divides b, or a is a divisor of b, or b is a multiple of a, if there exists an integer m such that b = am We also denote this by a | b (a divides b). If a is not a divisor of b, the we write a | b, but we can still talk about division by a with a remainder r. Given any two inte...

Discrete Mathematics and Probability Theory

Discrete mathematics - applied combinatorics and graph theory

No wonder you activities are, reading will be always needed. It is not only to fulfil the duties that you need to finish in deadline time. Reading will encourage your mind and thoughts. Of course, reading will greatly develop your experiences about everything. Reading discrete mathematics applied combinatorics and graph theory is also a way as one of the collective books that gives many advanta...

Limit theory of discrete mathematics problems

Limit theory means an advanced analysis of the asymptotic behavior of discrete problems when some finite parameter tends to infinity. Namely, we are looking for limits of finite problems for which we can prove that the solutions of the finite problems converge to the solution of the limit problem. We show this simple but powerful technique on three problems: the Manickam–Miklós–Singhi Conjectur...

Interpreting Set Theory in Discrete Mathematics: Boolean Relation Theory

Wqo theory = well quasi ordering theory, is a branch of combinatorics which has proved to be a fertile source of deep metamathematical pheneomena. In wqo theory, one freely uses some overtly set theoretic arguments. They are definitely noticeable, although they come fairly early in the interpretation hierarchy. Way before, say, ZFC. A qo (quasi order) is a reflexive transitive relation (A,£). A...