Discrete Mathematics and Graph Theory
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Follow on Instagram for UpdatesDiscrete Mathematics and Graph Theory Syllabus — Unit-wise Content
The official GTU curriculum for Discrete Mathematics and Graph Theory (subject code BE04000261) as prescribed for AI & DS · Semester 4 divides the course into 5 units, covering 86 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (BE04000261)Unit 1 Propositional Logic
- statements & notation
- truth values
- statement formulas & truth tables
- well-formed formulas
- equivalence of formulas
- duality law, tautological implications
- Predicate Logic: Definition of predicates
- statement functions
- predicate formulas
- free & bound variables
- the universe of discourse
- valid formulas & equivalences
Unit 2 Set Theory
- Basic concepts of set theory like inclusion
- Cartesian product
- power set
- Counting and Combinatorics: Basic counting principles
- permutations and combinations
- binomial coefficients and the binomial theorem
- Pigeonhole principle
- inclusion-exclusion principle
- Recurrence relations: Definitions and simple examples only
Unit 3 Functions
- Basic concepts of functions like domain
- composition of functions
- inverse of functions
- Algebraic Structures: Algebraic structures with one binary operation- semigroup
- normal subgroup
- homomorphic subgroups
- Lagrange’s theorem
- congruence relation and quotient structures
- Algebraic structures with two binary operation- Ring
- integral domain and field (definitions and simple examples only)
Unit 4 Relations
- binary relation
- universal relation
- void relation
- intersection, and complement operations on relations
- properties of binary relations in a set: reflexive
- anti-symmetric relations
- partition and covering of a set, equivalence relation
- equivalence classes
- compatibility relation
- maximum compatibility block
- composite relation
- converse of a relation
- transitive closure of a relation R in set X Partial Ordering: Definition
- simple or linear ordering
- totally ordered set (chain)
- frequently used partially ordered relations
- representation of partially ordered sets
- Hesse diagrams
- least & greatest elements
- minimal & maximal elements
- least upper bound (Supremum)
- greatest lower bound (Infimum)
- Well-ordered partially ordered sets (Posets)
- Lattice as Posets
- modular and complemented lattices
- Boolean and pseudo Boolean lattices (definitions and simple examples only)
Unit 5 Graphs
- adjacent nodes
- directed and undirected edge
- directed graph
- undirected graph
- Initiating and terminating nodes
- loop (sling)
- distinct edges
- parallel edges
- simple graph
- weighted graphs
- Isolated nodes
- null graph
- isomorphic graphs
- total degree of a node
- Subgraphs: definition
- Converse (reversal or directional dual) of a digraph
- Path: Definition
- paths of a given graph
- length of path
- Simple path (edge simple)
- elementary path (node simple)
- Cycle (circuit)
- elementary cycle
- Reachability: Definition
- Properties of reachability
- the triangle inequality
- Reachable set of a given node
- Program Name: Bachelor of Engineering Level: UG Subject Code: BE04000261 Subject Name: Discrete Mathematics and Graph Theory Node base
- examples Connectedness: Definition
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