# Discrete Structures

 Course Code : ULZ0361 Author : uLektz University : General for All University Regulation : 2017 Categories : Computer Science Format : ePUB3 (DRM Protected) Type : eBook

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Description :Discrete Structures of ULZ0361 covers the latest syllabus prescribed by General for All University for regulation 2017. 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 SETS AND PROPOSITIONS, RELATIONS AND FUNCTIONS

1.1 Sets and Propositions: Principle of Inclusion and Exclusion, Mathematical induction, oppositions

1.2 Logical Connectives, Conditionals and Biconditionals, Logical Equivalences, Predicate Calculus, Quantifiers, Theory of inference, Methods of proof

1.3 Relations and Functions: properties of binary relations, Closure of relations

1.4 Warshall’s algorithm, Equivalence relations, Partial ordering relations and lattices, Chains and antichains, Functions

1.5 Composition of Functions, Invertible Functions, Recursive Functions, Pigeonhole principle

###### UNIT - II NUMERIC FUNCTIONS AND GENERATING FUNCTIONS, RECURRENCE RELATIONS AND RECURSIVE ALGORITHMS

2.1 Numeric Functions and Generating Functions: Discrete Numeric functions, Generating Functions

2.2 Recurrence Relations and Recursive Algorithms: Recurrence relations, Linear recurrence relations with constant coefficients, Solution of recurrence relations by the method of generating functions

2.3 Divide and conquer algorithms

###### UNIT - III GROUPS AND RINGS, BOOLEAN ALGEBRAS

3.1 Groups and Rings: Groups and subgroups, Cosets and Lagrange’s theorem

3.2 Codes and Group codes, Error detection and correction using Group codes

3.3 Isomorphism, Homomorphism and normal subgroups, Rings, Integral domains and Fields

3.4 Boolean Algebras: Lattices and algebraic systems, Principle of duality, Distributive and complemented lattices

3.5 Boolean functions: Boolean expressions, Simplification of logic expressions using Karnaugh Map, Design and Implementation of Digital Networks, Switching Circuits

###### UNIT - IV GRAPHS AND TREES

4.1 Graphs and Trees: Basic terminology, Digraphs and relations, representation of Graphs, operations on graphs

4.2 Paths and circuits, graph traversals, shortest path in weighted graphs, Eulerian paths and circuits

4.3 Hamiltonian paths and circuits, Traveling sales person’s problem

4.4 Planar graphs, Graph Coloring

4.5 Trees, Rooted trees, Binary search trees, Spanning trees, Minimum spanning trees, Kruskal’s Algorithm, Prim’s Algorithm