Sets - Basic concepts

Sets - Definition and representation

• Sets - Types
• Sets - Finite and infinite
• Subsets - Definition and explanation
• Sets - Union and intersection
• Sets - Complement
• Sets - Difference
• Sets - Algebra - Explanation
• Sets - Venn diagrams - Explanation
• Sets - Cartesian Product

Sets - Relations - Introduction

Relations - Algebra

• Relations - Domain, range and inverse
• Relations - Types
• Relations - Equivalence
• Relations - Equivalence classes and partition

Sets - Functions - Domain, range & types

Sets - Mappings

• Functions - Domain and range
• Functions - Types
• Functions - Relation
• Functions - Inverse
• Functions - Composite
• Functions - Binary operations

Group theory - Binary operation

Group theory - Algebraic structure

• Group theory - Binary operations - Properties
• Group theory - Group - Properties
• Group - Finite and infinite - Order
• Group - Abelian
• Group - Cube roots and fourth roots of unity
• Group - Non abelian
• Group - Modulo - Addition
• Group - Modulo - Multiplication
• Group - Semigroup
• Group - Residue classes
• Group - Subgroups

Group theory - Permutations

• Group theory - Permutations - Algebra
• Group theory - Permutations - Product and composition
• Group theory - Permutations - Inverse

Vectors

Vectors - Properties

• Vectors - Properties - Classification

Vectors - Basic operations

• Vectors - Basic operations - Addition
• Vectors - Basic operations - Subtraction
• Vectors - Basic operations - Multiplication - By scalar
• Vectors - Division formula - External & internal

Vectors - Linear combinations

• Vectors - Linear combinations - Dependent & independent set
• Vectors - Linear combinations - Collinearity
• Vectors - Linear combinations - Coplanarity

Vectors - Representation

• Vectors - Distance between two points
• Vectors - Direction ratios & direction cosines

Vectors - Geometrical elements

• Vectors - Line - Equation
• Vectors - Plane - Equation
• Vectors - Point of intersection - Lines

Vectors - Product - Two vectors

• Product - Two vectors - Scalar
• Vectors - Angle between
• Vectors - Parallelism - Condition
• Vectors - Projection - Orthogonal
• Vectors - Work done
• Vectors - Product - Problems - Geometrical
• Vectors - Product - Problems - Triangle
• Vectors - Plane - Vector equation
• Vectors - Product - Two vectors - Vector
• Vectors - Unit - Perpendicular to two vectors
• Vector areas
• Vectors - Moment

Vectors - Product - Three and four vectors

• Product - Triple - Scalar
• Volume - Parallelopiped
• Volume - Tetrahedron
• Skew lines - Shortest distance
• Vectors - Coplanarity - Condition
• Product - Triple - Vector
• Reciprocal system
• Vectors - Product - Four vectors