# KTU S3 Discrete Mathematical Structures Notes 2019 scheme

Are you a student studying the MAT203 DCS Discrete Mathematical Structures course materials under the
KTU S3 CSE curriculum? Feeling lost or confused with your mat203 notes? These notes are designed in a unique way based on the KTU scheme and previous year questions. It naturally guides you from basic concepts to test-taking strategies. The main focus of these discursive lecture notes is that to build up your concepts first then only you will be in a position to solve any type of question.

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)

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### 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 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 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 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 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 2) Notes

Discrete mathematics forms the foundation for much of modern computer science. While some of the specific concepts may be foreign, discrete math is a part of our daily lives. By better understanding discrete mathematics, you will be able to improve your problem-solving skills, develop new algorithms, and create more efficient code.

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