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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