Discrete Mathematics (3140708) Syllabus :
Syllabus
1 Set Theory , Functions and Counting
Set Theory : Basic Concepts of Set Theory: Definitions, Inclusion, Equality of Sets,
Cartesian product, The Power Set, Some operations on Sets, Venn Diagrams, Some
Basic Set Identities
Functions : Introduction & definition, Co-domain, range, image, value of a function;
Examples, surjective, injective, bijective; examples; Composition of functions,
examples; Inverse function, Identity map, condition of a function to be invertible,
examples; 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
2 Propositional Logic and Predicate Logic
Propositional Logic: Definition, Statements & Notation, Truth Values, Connectives,
Statement Formulas & Truth Tables, Well-formed Formulas, Tautologies,
Equivalence of Formulas, Duality Law, Tautological Implications, Examples
Predicate Logic: Definition of Predicates; Statement functions, Variables,
Quantifiers, Predicate Formulas, Free & Bound Variables; The Universe of Discourse,
Examples, Valid Formulas & Equivalences, Examples
3 Relations, Partial ordering and Recursion
Relations : Definition, Binary Relation, Representation, Domain, Range, Universal
Relation, Void Relation, Union, Intersection, and Complement Operations on
Relations, Properties of Binary Relations in a Set: Reflexive, Symmetric, Transitive,
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, Examples, 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), Wellordered Partially Ordered Sets (Posets). Lattice as Posets, complete, distributive modular and complemented lattices Boolean and pseudo Boolean lattices. (Definitions
and simple examples only)
Recurrence Relation: Introduction, Recursion, Recurrence Relation, Solving,
Recurrence Relation
4 Algebraic Structures
Algebraic structures with one binary operation- Semigroup,
Monoid, Group, Subgroup, normal subgroup, group Permutations, Coset,
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.
5 Graphs
Graphs : Introduction, definition, examples; Nodes, edges, adjacent nodes, directed
and undirected edge, Directed graph, undirected graph, examples; Initiating and
terminating nodes, Loop (sling), Distinct edges, Parallel edges, Multi-graph, simple
graph, weighted graphs, examples, Isolated nodes, Null graph; Isomorphic graphs,
examples; Degree, Indegree, out-degree, total degree of a node, examples; Subgraphs:
definition, examples; Converse (reversal or directional dual) of a digraph, examples;
Path: Definition, Paths of a given graph, length of path, examples; Simple path (edge
simple), elementary path (node simple), examples; Cycle (circuit), elementary cycle,
examples;
Reachability : Definition, geodesic, distance, examples; Properties of
reachability, the triangle inequality; Reachable set of a given node, examples, Node
base, examples;
Connectedness : Definition, weakly connected, strongly connected,
unilaterally connected, examples; Strong, weak, and unilateral components of a graph,
examples, Applications to represent Resource allocation status of an operating system,
and detection and correction of deadlocks; Matrix representation of graph: Definition,
Adjacency matrix, boolean (or bit) matrix, examples; Determine number of paths of
length n through Adjacency matrix, examples; Path (Reachability) matrix of a graph,
examples; Warshall’s algorithm to produce Path matrix, Flowchart.
Trees: Definition, branch nodes, leaf (terminal) nodes, root, examples; Different
representations of a tree, examples; Binary tree, m-ary tree, Full (or complete) binary
tree, examples; Converting any m-ary tree to a binary tree, examples; Representation
of a binary tree: Linked-list; Tree traversal: Pre-order, in-order, post-order traversal,
examples, algorithms; Applications of List structures and graphs
| Syllabus | Download |
|---|---|
| Discrete Mathematics | Click Here |
Discrete Mathematics- IMP Question (Solved) :
| Materials | Download |
|---|---|
| Question Bank By Amiraj College | Click Here |
Chapter-Wise Darshan Institute PPTs/Notes :
| Units | Download(Notes) | Download(PPT) |
|---|---|---|
| Discrete Mathematics (All Chapter Notes) | Click Here | - |
| Set theory, Functions and Counting(Notes) | Click Here | Click Here |
| Propositional Logic and Predicate Logic(Notes) | Click Here | Click Here |
| Relations, Partial ordering and Recursion(Notes) | Click Here | Click Here |
| Algebraic Structures(Notes) | Click Here | - |
| Graph Theory(Notes) | Click Here | Click Here |
Discrete Mathematics Old Papers :
| Year(Winter/Summer) | Question Paper |
|---|---|
| Winter 2020 | Click Here |
| Winter 2021 | Click Here |
| Summer 2020 | Click Here |
| Summer 2021 | Click Here |
Discrete Mathematics Books :
| Books | Download |
|---|---|
| Technical Book All Chapter | Click Here |
| Discrete Mathematics by Atul Prakashan | Click Here |
| Discrete Mathematics by Mc Graw Hill | Click Here |
| Discrete Mathematics Structures | Click Here |
| Discrete Mathematics By Kenneth H. Rosen | Click Here |
| Discrete Mathematics by T. Veerarajan | Click Here |
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