Discrete Mathematics with Its Applications to Economics

Beata Fałda, Lech Gruszecki
ISBN: 978-83-7702-964-0
Stron: 250
Format: B5 (oprawa twarda)
Rok wydania: 2014


SPIS TREŚCI

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 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