Algebra & Arithmetic

Algebra is the study of mathematical symbols and the rules for manipulating these symbols. Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them - addition, subtraction, multiplication and division.

3. Algebra

3.3. Partial Fractions

• Partial Fractions

3.4. Permutation & Combination

• Factorial
• Fundamental Principles of Counting
• Concept of Permutations
• Permutations of Objects Not All Distinct
• Permutations When Objects Can Repeat
• Circular Permutations
• Combinations
• Properties of Combinations

3.5 Mathematical Induction

• Principle of Mathematical Induction

3.6 Binomial Theorem

• Binomial Theorem

3.7 Quadratic Equations

• Quadratic Equations

3.8 Sequences and Series

• Progressions
• Arithmetic Progression
• Geometric Progression
• Harmonic Progression
• Means of Progressions

3.9 Complex Numbers

• Complex Number System
• Algebraic Operations of Complex Numbers
• Conjugate of Complex Number
• Modulus of Complex Number
• Geometrical Representation
• Polar Form of Complex Number
• Exponential Form of Complex Number
• Cube Roots of Unity
• De Moivre’s Theorem
• Roots of Complex Number

4. Matrices and Determinants

4.1 Matrix

• Introduction to Matrix
• Order or Size of Matrix
• Types of Matrices
• Equality of Matrices
• Transpose of Matrix
• Scalar Multiplication of Matrix
• Negative of Matrix
• Addition & Subtraction of Matrices
• Matrix Multiplication
• Algebraic Properties of Matrices

4.2 Determinants

• Introduction to Determinants
• Minors and Co-factors
• Singular and Non-singular Matrices
• Properties of Determinants
• Product of Determinants

4.3 Applications of Matrices & Determinants

• Adjoint of Matrix
• Inverse of a Matrix
• Rank of a Matrix
• Matrix Inversion Method

5. Vector Algebra

• Introduction to Vectors
• Types of Vectors
• Addition of Vectors
• Resolution of Vector
• Direction Cosines
• Direction Ratios
• Scalar or Dot Product
• Vector or Cross Product