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Outline of discrete math semester autumn 2014

Functions

 Functions Defined on General Sets
Finite State Automata,
 One-To-One, Inverse Functions,
 the Pigeonhole Principle

 Efficiency of Algorithms

Real Valued Functions of Real Variable and Their Graphs, 
O-Notations, 
Efficiency of Algorithms-I, 
Efficiency of Algorithms-II 

Boolean Algebra 

Basic Definition, 
Basic Theorems and Properties of Boolean Algebra,
Boolean Functions, 
Canonical and Standard Forms,
Logic Operations 

 Introduction of Mathematical Reasoning 

Logical Form & Logical Equivalence, Conditional Statements, 
Valid and Invalid Arguments,
Digital Logic Circuits, Number Systems and Circuits for Additions, 
Predicates and Quantified Statements, 
Arguments with Quantified Statements 

Number Theory and Mathematical Induction 

 Introduction, Rational Numbers,
 Divisibility, 
Division into Cases and the Quotient Remainder Theorem, 
Algorithms,
 Sequences, 
Principles of Mathematical Induction, 
Correctness of Algorithms 

 Set Theory 

 Basic Definitions,
 Properties of Sets, 
The Empty Set, 
Partitions, 
Power Sets,
 Boolean Algebra, 
Russell’s Paradox and Halting Problem 

Counting Techniques 

Counting and Probability, 
Possibility Trees and Multiplication Rule,
 Counting Elements of Disjoint Sets,
 Counting Subsets of a Set 

Recursion 

Recursively Defined Sequences, 
Solving Recurrence Relations by Iteration 

 Graphs

 Introduction, Paths and Circuits, 
Matrix Representation of Graphs, 
Isomorphism of Graphs