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
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
3.6 Binomial Theorem
3.7 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