Discrete Mathematics
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Discrete Mathematics Syllabus — Unit-wise Content
The official GTU curriculum for Discrete Mathematics (subject code 3140708) as prescribed for Common · Semester 4 divides the course into 5 units, covering 96 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 (3140708)Unit 1 Set Theory
- Basic Concepts of Set Theory: Definitions
- Equality of Sets
- Cartesian product
- The Power Set, Some operations on Sets
- Venn Diagrams
- Some Basic Set Identities Functions: Introduction & definition
- value of a function
- Composition of functions
- Inverse function
- Identity map, condition of a function to be invertible
- Inverse of composite functions
- Properties of Composition of functions
- Counting: The Basics of Counting
- The Pigeonhole Principle
- Permutations and Combinations
- Binomial Coefficients
- Generalized Permutations and Combinations
- Generating Permutations and Combinations
Unit 2 Propositional Logic
- Statements & Notation
- Truth Values
- Statement Formulas & Truth Tables
- Well-formed Formulas
- Equivalence of Formulas
- Duality Law, Tautological Implications
- Examples Predicate Logic: Definition of Predicates
- Statement functions
- Predicate Formulas
- Free & Bound Variables
- The Universe of Discourse
- Valid Formulas & Equivalences
Unit 3 Relations
- Binary Relation
- Universal Relation
- Void Relation
- Intersection, and Complement Operations on Relations
- Properties of Binary Relations in a Set: Reflexive
- Anti-symmetric Relations
- Relation Matrix and Graph of a Relation
- 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 Members
- Minimal & Maximal Members
- Least Upper Bound (Supremum)
- Greatest Lower Bound (infimum)
- Well- ordered Partially Ordered Sets (Posets)
- Lattice as Posets
- distributive Subject Code: 3140708 w.e.f
- AY 2018-19 modular and complemented lattices Boolean and pseudo Boolean lattices
- (Definitions and simple examples only) Recurrence Relation: Introduction
- Recurrence Relation
Unit 4 Algebraic Structures
- Algebraic structures with one binary operation- Semigroup
- normal subgroup
- group Permutations
- homomorphic subgroups
- Lagrange’s theorem
- Congruence relation and quotient structures
- Algebraic structures (Definitions and simple examples only) with two binary operation- Ring
- Integral domain and field
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
- Node base
- Connectedness: Definition
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