Propositions

• Logics - Mathematical - Conjunction
• Logics - Mathematical - Disjunction
• Logics - Mathematical - Implication
• Logics - Mathematical - Equivalence
• Logics - Mathematical - Negation
• Logics - Mathematical - Inverse, converse and contrapositive
• Logics - Mathematical - Tautology and contradiction

• Negation - Conjunction and disjunction
• Negation - Implication
• Negation - Negation of a proposition

Logics - Applications

• Boolean polynomials - Explanation

Permutations

• Permutations - n things taken r at a time - Without repetition
• Permutations - n things taken r at a time - With repetition
• Permutations - Considering restriction

• Permutations - Objects in different groups
• Permutations - Some alike others different

• Permutations - Circular - Taken all at a time
• Permutations - Circular - Around a thread

Combinations

• Combinations - n things taken r at a time - No repetition
• Combinations - n things taken r at a time - Restrictions
• Combinations - n things taken r at a time - Repetition

• Permutations - Circular - n things taken r at a time
• Combinations - Number of diagonals of a polygon
• Combinations and exponent - Total number - Prime p in n!
• Division - Positive integer

• Combinations - Objects divided - Two groups
• Combinations - Objects divided - Three groups
• Inclusion and exclusion - Principle

Binomial theorem - Integral & rational Index

• Binomial theorem - Integral index - Explanation
• Binomial theorem - General term
• Binomial theorem - Middle term - (x + a)^n
• Expansion of (1 + x)^n - Greatest term
• Expansion of {ax^p + b/x^q}^n - Coefficient of x^k
• Binomial coefficients - Properties

• Binomial theorem - Rational index - Explanation
• Binomial theorem - Expansion - (1 - x)^(- n) - Particular cases
• Expansion of (1 - x)^(p/q)
• Binomial theorem - Approximations

Matrices - Operations and properties

• Matrices - Classification
• Matrix - Order
• Matrix - Elements - Finding
• Matrices - Equality
• Matrices - Multiplication - Scalar
• Matrices - Addition
• Matrices - Subtraction
• Matrices - Multiplication - Theory
• Matrices - Multiplication - General
• Matrices - Multiplication - Using condition of equality
• Matrices - Multiplication - Involving addition and subtraction
• Matrices - Positive integral powers
• Matrices - Transpose
• Matrices - Symmetric and skew symmetric

• Determinants - Minors and cofactors
• Determinants - Expansion
• Matrices - Rank - Using determinants
• Determinants - Properties - General
• Determinants - Multiplication - Method and examples
• Determinants - Differentiation - Method and examples
• Determinants - Application - Area of triangle

• Matrix - Adjoint
• Matrices - Inverse - Using adjoint and determinant
• Matrices - Inverse - Using elementary transformations

• Matrices - Eigen values
• Matrices - Theorem - Cayley Hamilton - Verification
• Matrices - Inverse - Using Cayley Hamilton Theorem

• Linear equations - Solution - Cramer's rule - Two variables
• Linear equations - Solution - Cramer's rule - 'n' variables
• Linear equations - Solution - Matrix method
• Linear equations - Solution - Homogeneous system
• Linear equations - Solution - Gauss Jordan method
• Consistency and inconsistency - Using determinants
• Consistency and inconsistency - Coefficient & augmented matrix