Beata Fałda, Lech Gruszecki ISBN: 9788377029640 Pages: 250 Format: B5 (hard cover) Year: 2014 Language: English
SPIS TREŚCI
Introduction
1 Logical and set theoretical preliminaries 1.1 Introduction to the classical twovalued statement calculus 1.2 Formal introduction to the classical statement calculus 1.3 Elements of manyvalued statement calculus 1.4 Classical predicate calculus 1.5 Sets and their properties
2 Relations and functions 2.1 Relations and their properties 2.2 Relations between the elements of finite sets 2.3 Equivalence relations 2.4 Order relations 2.5 Functions and their properties
3 Set of natural numbers and induction 3.1 Set of natural numbers. Defining by induction 3.2 Recursive functions 3.3 Application of recursion: finitestate automata and their languages
4 Lattices, Boolean algebras and Boolean functions 4.1 Lattices and their properties 4.2 Boolean algebras 4.3 Boolean expressions and functions
5 Finite sets and methods of counting their elements 5.1 Introduction to combinatorial methods 5.2 Basics of combinatorics  formal approach 5.3 Binomial and polynomial coefficients 5.4 InclusionExclusion Principle 5.5 Pigeonhole Principle (Dirichlet Drawer Principle)
6 Partitions and permutations. Stirling and Bell Numbers 6.1 Counting partitions 6.2 Factorizations of numbers 6.3 Permutations 6.4 Special numbers
7 Main concepts of the graph theory 7.1 An informal introduction to the graph theory 7.2 Basic definitions of graph theory 7.3 Connectivity of graphs
8 Graph traversal 8.1 Euler Graphs 8.2 Hamiltonian Graphs 8.3 Weighted graphs
9 Trees and digraphs 9.1 Basic concepts of tree theory 9.2 Spanning trees 9.3 Digraphs
10 Counting graphs. A few selected problems
11 Modular arithmetic 11.1 Basic properties of the divisibility relation on the set of integers 11.2 Congruences and their basic properties 11.3 Elements of number theory
12 Graphs in economic sciences 12.1 Traveling Salesman Problem 12.2 Maximum flow problem 12.3 Event networks
Bibliography
