Collegestof Fundamentele Informatica 1

Inhoudsopgave relevante hoofdstukken uit Schaum, onder voorbehoud.
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0. Inleiding

I. Verzamelingenleer

Chapter 1 Set Theory
1.1 Introduction. 1.2 Sets and Elements. 1.3 Universal Set and Empty Set. 1.4 Subsets. 1.5 Venn Diagrams. 1.6 Set Operations. 1.7 Algebra of Sets and Duality. 1.8 Finite Sets, Counting Principle. 1.9 Classes of Sets, Power Sets, Partitions. 		1.10 Mathematical Induction wordt uitgesteld tot bij het toegevoegde onderwerp Recursie.

II. Relaties en Functies

Chapter 2 Relations
2.1 Introduction. 2.2 Product Sets. 2.3 Relations. 2.4 Pictorial Representation of Relations. 2.5 Composition of Relations. 2.6 Types of Relations. 2.7 Closure Properties. 2.8 Equivalence Relations. 2.9 Partial Ordering Relations. 2.10 n-ary Relations.
Chapter 3 Functions and Algorithms
3.1 Introduction. 3.2 Functions. 3.3 One-to-one, Onto, and Invertible Functions. 3.4 Mathematical Functions, Exponential and Logarithmic Functions. 3.5 Sequences, Indexed Classes of Sets. 3.8 Algorithms and Functions. 		3.9 Complexity of Algorithms.

III. Grafen

Chapter 8 Graph Theory
8.1 Introduction, Data Structures. 8.2 Graphs and Multigraphs. 8.3 Subgraphs, Isomorphis and Homeomorphic Graphs. 8.4 Paths, Connectivity. 8.5 The Bridges of Königsberg, Traversible Multigraphs. 8.6 Labeled and Weighted Graphs. 8.7 Complete, Regular, and Bipartite Graphs. 		8.9 Planar Graphs. 8.10 Graph Colorings. 8.11 Representing Graphs in Computer Memory. 8.12 Graph Algorithms. 'Homeomorphic' hoeft niet.
Chapter 9 Directed Graphs
9.1 Introduction. 9.2 Directed Graphs. 9.3 Basic Definitions. 9.5 Sequential Representation of Directed Graphs. 9.8 Graph Algorithms: Depth-First and Breadth-First Searches. 		9.6 Warshall's Algorithm; Shortest Paths. 9.7 Linked Representation of Directed Graphs. 9.9 Directed Cycle-Free Graphs, Topological Sort. 9.10 Pruning Algorithm for Shortest Path.

IV. Bomen

8.8 Tree Graphs.
9.4 Rooted Trees.
Chapter 10 Binary Trees
10.1 Introduction. 10.2 Binary Trees. 10.3 Introduction. 10.4 Representing Binary Trees in Memory. 10.5 Traversing Binary Trees. 10.6 Binary Search Trees. 10.9 General (Ordered Rooted) Trees Revisited. 		10.7 Priority Queues, Heaps. 10.8 Path Lengths Huffman's Algorithm.

V. Recursie en Inductie

3.6 Recursively Defined Functions. 10.5 Traversing Binary Trees. 1.10 Mathematical Induction. 11.3 Mathematical Induction. 		Zie bundel.

VI. Equivalentierelaties

2.8 Equivalence Relations. Modulo rekening 3.4 (Modular Arithmetic) 11.8 Congruence Relation. Aftelbaarheid 3.7 Cardinality. 		Zie bundel.

VII. Talen, Eindige Automaten

Chapter 13 Languages, Grammars, Machines
13.1 Introduction. 13.2 Alphabet, Words, Free Semigroup. 13.3 Languages. 13.4 Regular Expressions, Regular Languages. 13.5 Finite State Automata. 		13.6 Grammars. 13.7 Finite State Machines. 13.8 Gödel Numbers. 13.9 Turing Machines. 13.10 Computable Functions. Zie bundel.