Beata Fałda, Lech Gruszecki ISBN: 978-83-7702-616-8 Pages: 204 Format: B5 (hard cover) Year: 2012 Language: English
TABLE OF CONTENTS
Introduction
1 Logical and set theoretical preliminaries 1.1 Introduction to the classical two-valued statement calculus 1.2 Formal introduction to the classical statement calculus 1.3 Elements of many-valued 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: finite-state 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 Inclusion-Exclusion 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 graph theory 7.1 An informal introduction to 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
Bibliography
|