Discrete Structure

SECI1013 Discrete Structure introduces us to the principles and applications of discrete structure in the field of computer science. At the end of the course, we are able to use set theory, relations and functions to solve computer science problems, analyze and solve problems using recurrence relations and counting methods, apply graph theory and trees in real world problems and use deterministic finite automata finite state machines to model electronic devices and problems.

1. SYLLABUS

Chapter	Title
1	SET THEORY & LOGIC 1.1 Set Theory - Set and Subset - Operations on Sets 1.2 Propositions, Conditional Propositions and Logical Equivalences 1.3 Quantifiers - Basic Quantifiers - Nested Quantifiers 1.4 Proof Techniques - Direct Proof - Indirect Proof
2	2.1 Relations - Digraph - Matrices of Relations - Characteristics of Relations - Equivalence Relations - Partial Orders 2.2 Functions - One-to-one, Onto, Bijection, Inverse functions - Composition - Recursive Algorithm 2.4 Recurrence Relation - Sequences - Solving Recurrence Relation
3	COUNTING METHODS & PROBABILITY 3.1 Basic Principles 3.2 Permutations 3.3 Combinations 3.4 Pigeonhole Principle (First, Second, third Form) 3.5 Discrete Probability Theory - Discrete Probability Theory - Bayes' Theorem
4	GRAPH THEORY 4.1 Graph Definition and Notations 4.2 Representation of Graphs 4.3 Isomorphism of Graphs 4.4 Path and Cycles 4.5 Euler Cycles 4.6 Hamiltonian Cycles 4.7 Dijkstra's Shortest Path Algorithm 4.8 Trees - Terminology and Characterizations of Trees - Rooted Trees - Binary Trees - Tree Traversals - Spanning Tree
5	FINITE AUTOMATA 5.1 Deterministic finite automata 5.2 Finite state machines

Discrete Structure

1. SYLLABUS

2. Assignment 1

3. Assignment 2

4. Assignment 3

5. Reflection