# 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
I MA101BS Mathematics – I Click Here
I CS103ES Programming for Problem Solving Click Here
I AP105BS Applied Physics Lab Click Here
I CS106ES Programming for Problem Solving Lab Click Here
II MA201BS Mathematics – II Click Here
II EE203ES Basic Electrical Engineering Click Here
II CH206BS Engineering Chemistry Lab Click Here
II EN207HS English Language and Communication Skills Lab Click Here
II EE208ES Basic Electrical Engineering Lab Click Here
II-I MA313BS Mathematical and Statistical Foundations Click Here
II-I CS304PC Computer Organization and Architecture
II-I CS307PC Data Structures Lab Click Here
II-I CS312PC Python Programming Lab Click Here
II-I MC309 Gender Sensitization Lab Click Here
II-II CS416PC Formal Language and Automata Theory Click Here
II-II CS404PC Database Management Systems Click Here
II-II CS412PC Object Oriented Programming using Java Click Here
II-II CS406PC Operating Systems Lab Click Here
II-II CS407PC Database Management Systems Lab Click Here
II-II CS408PC Java Programming Lab Click Here
II-II MC409 Constitution of India Click Here
III-I Design and Analysis of Algorithms Click Here
III-I Introduction to Data Science(PE1) Click Here
III-I Information Retrieval Systems(PE2)