# Discrete Mathematics

 Course Code : ULZHS0127 Author : uLektz University : General for All University Regulation : 2013 Categories : Arts and Science Format : ePUB3 (DRM Protected) Type : eBook

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Description :Discrete Mathematics of ULZHS0127 covers the latest syllabus prescribed by General for All University for regulation 2013. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT I:THE LANGUAGE OF LOGIC

1.1 Propositions - Logical Equivalences - Quantifiers - Arguments - Proof Methods

1.2 The Language of Sets: The Concepts of a Set - Operations with Sets - Computer Operations with Sets - The Cardinality of a Set - Recursively Defined Sets

1.3 Functions: The concept of Functions - Special Functions - Properties of Functions - The Pigeonhole principle - Composite Functions - Sequences and the Summation Notation

###### UNIT II:RELATIONS

2.1 Boolean Matrices - Relations and Digraphs - Computer Representations of Relations - Properties of Relations

2.2 Operations on Relations - Transitive Closure - Equivalence Relations - Partial and Total Ordering

2.3 Lattices & Boolean Algebra: Lattices as Partially Ordered Sets - Properties of Lattices - Lattices as Algebraic Systems - Sub lattices - Direct Product and Homomorphism - Boolean Algebra and Boolean Functions

###### UNIT III:ALGEBRAIC STRUCTURES

3.1 Algebraic Systems - Semigroups and Monoids - Groups - Subgroups and Homomorphism - Cosets and Lagrange‘s theorem - Normal Subgroups

3.2 Combinatorics: The Fundamental Counting Principles - Permutations - Derangements

3.3 Combinations - Permutations and Combinations with Repetitions - The Binomial Theorem - The Generalized Inclusion- Exclusion Principle

###### UNIT IV:INDUCTION AND ALGORITHMS

4.1 The Division Algorithm - Divisibility Properties - Non decimal Bases - Mathematical Induction - Algorithm Correctness

4.2 The Growth Functions - Complexity of Algorithms

4.3 Recursion: Recursively Defined Functions - Solving Recurrence Relations - Generating Functions - Recursive Algorithms - Correctness of Recursive Algorithms - Complexities of Recursive Algorithms

###### UNIT V:GRAPHS

5.1 Computer Representation of Graphs - Isomorphic Graphs - Paths,Cycles and Circuits - Eulerian and Hamiltonial Graphs - Planar Graphs - Graph Coloring - Digraphs and Weighted Digraphs - Dags, DFS and BFS Algorithms

5.2 Trees - Spanning Trees - Minimal Spanning Trees - Kruskal‘s and Prim‘s Algorithm