# JNTUH CSE-AIML CS310PC: DISCRETE MATHEMATICS SYLLABUS

Prerequisites: An understanding of Mathematics in general is sufficient.
Course Objectives
 Introduces the elementary discrete mathematics for computer science and engineering.
 Topics include formal logic notation, methods of proof, induction, sets, relations, graph theory,
permutations and combinations, counting principles; recurrence relations and generating functions.
Course Outcomes:
 Ability to understand and construct precise mathematical proofs
 Ability to use logic and set theory to formulate precise statements
 Ability to analyze and solve counting problems on finite and discrete structures
 Ability to describe and manipulate sequences
 Ability to apply graph theory in solving computing problems
UNIT – I
The Foundations: Logic and Proofs: Propositional Logic, Applications of Propositional Logic,
Propositional Equivalence, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference,
Introduction to Proofs, Proof Methods and Strategy.
UNIT – II
Basic Structures, Sets, Functions, Sequences, Sums, Matrices and Relations Sets, Functions, Sequences & Summations, Cardinality of Sets and Matrices Relations, Relations and Their Properties, n-ary Relations and Their Applications, Representing Relations, Closures of Relations, Equivalence Relations, Partial Orderings.
UNIT – III
Algorithms, Induction and Recursion: Algorithms, The Growth of Functions, Complexity of Algorithms Induction and Recursion: Mathematical Induction, Strong Induction and Well-Ordering, Recursive Definitions and Structural Induction, Recursive Algorithms, Program Correctness
UNIT – IV
Discrete Probability and Advanced Counting Techniques: An Introduction to Discrete Probability,Probability Theory, Bayes’ Theorem, Expected Value and Variance Advanced Counting Techniques: Recurrence Relations, Solving Linear Recurrence Relations,Divide-and-Conquer Algorithms and Recurrence Relations, Generating Functions, InclusionExclusion, Applications of Inclusion-Exclusion
UNIT – V
Graphs: Graphs and Graph Models, Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest-Path Problems,Planar Graphs, Graph Coloring.Trees: Introduction to Trees, Applications of Trees, Tree Traversal, Spanning Trees, Minimum
Spanning Trees

## CSE-AIML

SEMESTER SUBJECT CODE SUBJECT Lession Plan Lecturer Notes & Question Bank SYLLABUS
II-I CS304PC Computer Organization and Architecture
III-I Information Retrieval Systems(PE2)