This course on Discrete Mathematics aims to teach students the fundamentals of set theory, relations, functions, and group theory. By the end of the course, students will be able to understand and apply concepts such as reflexive, symmetric, and transitive relations, different types of functions like injective and surjective functions, and algebraic structures like semigroups and monoids. The teaching method involves a detailed syllabus covering various topics with examples to aid in comprehension. This course is intended for individuals preparing for exams like GATE, UGC NET, PSUs, or college/university-level discrete mathematics courses.
Overview
Syllabus
L-0: Discrete Mathematics Syllabus for GATE, UGC NET, PSUs & COLLEGE/UNIVERSITY Exams.
L-1.1: Introduction to Set Theory | Set, Subset, Proper Subset.
L-1.2: Power Set | Set Theory & Algebra.
L-2.1: Relation in Set Theory with examples.
L-2.2: Reflexive Relation with examples | Discrete Mathematics.
L-2.3: How Many Reflexive Relations Possible | Discrete Mathematics Formulas.
L-2.4: Irreflexive Relation with examples | Discrete Mathematics.
L-2.5: Symmetric Relation with examples | Discrete Maths.
Antisymmetric Relation with examples | Discrete Maths.
Asymmetric vs Antisymmetric Relation with examples.
Transitive Relation with examples.
Equivalence Relation in Discrete Mathematics with examples.
Partial Order Relation | POSET in Discrete Mathematics.
Totally Ordered Set in Discrete Mathematics.
Comparison of All Relations | Reflexive,Irreflexive,Transitive, Symmetric,Antisymmetric, Asymmetric.
Introduction to Group Theory | Discrete Mathematics.
Algebraic structure in Discrete Mathematics.
Semigroup in Group Theory | Discrete Mathematics.
Monoid in Discrete Mathematics | Group Theory.
Group in Discrete Mathematics with examples in Hindi.
Abelian Group in Discrete Mathematics with examples.
Function in Discrete Mathematics.
How many Functions Possible | Counting Functions | Discrete Mathematics.
One to One Function (Injection) | Injective Function.
ONTO Function(Surjection) | Surjective Function | Discrete Mathematics.
Bijective Function (Bijection) | Discrete mathematics.
Taught by
Gate Smashers
