This is a set of notes for MAT203 Discrete Mathematical Structures. The notes are designed to take a Second-year student through the topics in their third semester. This set of notes contains material from the first half of the first semester, beginning with the axioms and postulates used in discrete mathematics, covering propositional logic, predicate logic, quantifiers and inductive proofs. It also covers set theory elements such as the De Morgans theorem, functions and relations.
| Board | KTU |
| Scheme | 2019 New Scheme |
| Year | Second Year |
| Semester | S3 Computer Science |
| Subject | MAT 203 | Discrete Mathematical Structure Notes |
| Credit | 4 Credit |
| Category | KTU S3 Computer Science |
KTU S3 CSE Discrete Mathematical Structure Notes (2019 Scheme)
Module 1
Module 1 - Syllabus
Fundamentals of Logic: Mathematical logic - Basic connectives and truth table, Statements, Logical Connectives, Tautology, Contradiction. Logical Equivalence - The Laws of Logic, The Principle of duality, Substitution Rules. The implication - The Contrapositive, The Converse,The Inverse.
Logical Implication - Rules of Inference. The use of Quantifiers - Open Statement, Logically Equivalent – Contrapositive, Converse, Inverse, Logical equivalences and implications for quantified statement, Implications, Negation.
Module 1 - Notes
Module 1 Discrete Mathematical Structure | MAT 203 PDF (SET 1) Notes
Module 1 Discrete Mathematical Structure | MAT 203 PDF (SET 2) Notes
Module 2
Module 2 - Syllabus
Fundamentals of Counting Theory: The Rule of Sum – Extension of Sum Rule. The Rule of Product - Extension of Product Rule. Permutations. Combinations. The Binomial Theorem (without proof). Combination with Repetition. The Pigeon hole Principle. The Principle of Inclusion and Exclusion Theorem (Without Proof) - Generalization of the Principle. Derangements.
Module 2 - Notes
Module 2 Discrete Mathematical Structure | MAT 203 PDF (SET 1) Notes
Module 2 Discrete Mathematical Structure | MAT 203 PDF (SET 2) Notes
Module 3
Module 3 - Syllabus
Relations and Functions: Cartesian Product - Binary Relation. Function – domain, range-one to one function, Image- restriction. Properties of Relations- Reachability Relations, Reflexive Relations, Symmetric Relations, Transitive relations, Anti-symmetric Relations, Partial Order relations, Equivalence Relations, Irreflexive relations.
Partially ordered Set – Hasse Diagram, Maximal-Minimal Element, Least upper bound (lub), Greatest Lower bound(glb) ( Topological sorting Algorithm- excluded). Equivalence Relations and
Partitions - Equivalence Class. Lattice - Dual Lattice, Sub lattice, Properties of glb and lub , Properties of Lattice, Special Lattice, Complete Lattice, Bounded Lattice, Completed Lattice, Distributive Lattice.
Module 3 - Notes
Module 3 Discrete Mathematical Structure | MAT 203 PDF (SET 1) Notes
Module 3 Discrete Mathematical Structure | MAT 203 PDF (SET 2) Notes
Module 4
Module 4 - Syllabus
Generating Functions and Recurrence Relations: Generating Function - Definition and Examples, Calculation techniques, Exponential generating function. First-order linear recurrence relations with constant coefficients – homogeneous, non-homogeneous Solution. Second-order linear recurrence relations with constant coefficients, homogeneous, non-homogeneous Solution.
Module 4 - Notes
Module 4 Discrete Mathematical Structure | MAT 203 PDF (SET 1) Notes
Module 4 Discrete Mathematical Structure | MAT 203 PDF (SET 2) Notes
Module 5
Module 5 - Syllabus
Algebraic Structures: Algebraic system-properties- Homomorphism and Isomorphism. Semigroup and monoid – cyclic monoid, sub semigroup and sub monoid, Homomorphism and Isomorphism of Semigroup and monoids. Group- Elementary properties, subgroup, the symmetric group on three symbols, The direct product of two groups, Group Homomorphism, Isomorphism of groups, Cyclicgroup. Rightcosets - Leftcosets. Lagrange’s Theorem
Module 5 - Notes
Module 5 Discrete Mathematical Structure | MAT 203 PDF (SET 1) Notes
Module 5 Discrete Mathematical Structure | MAT 203 PDF (SET 2) Notes
KTU S3 CSE Related Links
| KTU S3 CSE Syllabus | Click Here |
| KTU S3 CSE Study Notes | Click Here |
| KTU S3 CSE Reference Textbook | Click Here |
| KTU S3 CSE Previous Year Solved Questions | Click Here |
| KTU S3 CSE Study Materials | Click Here |
Other Related Links
| MAT 203 - Discrete Mathematical Structures | Click Here |
| CST 201 - Data Structures | Click Here |
| CST 203 - Logic System Design | Click Here |
| CST 205 - Object-Oriented Programming Using Java | Click Here |
| MNC 202 - Sustainable Engineering | Click Here |
| HUT 200 - Professional Ethics | Click Here |
| EST 200 - Design and Engineering | Click Here |
| CSL 201 - Data structure LAB | Click Here |
| CST 203 - Object-Oriented Programming Lab (In Java) | Click Here |
