Foundational Mathematics

1. Basic operations with Numbers & Variables
• Addition, subtraction, division and multiplication, insertion and removal of brackets.
• Playing with Fractions and Exponents
2. Simple equations
3. Simultaneous equations
4. Word problems
5. Binomial special products
6. Factoring

Higher Mathematics I

Algebra

1. Complex Numbers
2. Functions and Graphs
3. Linear functions and equations
5. Inequalities
6. Arithmetic and Geometric progressions
7. Logarithms
8. Mathematical Induction
9. The Binomial Theorem
10. Permutations and Combinations
11. Probability
12. Determinants of Orders 2 and 3
13. Systems of Linear Equations
14. Matrices
15. Partial Fractions

Trignonometry

1. Historical Context
2. Angles and Arc Length
3. Reduction to Functions of Positive Acute Angles
4. Variation and Graphs of Trigonometric Functions
5. Solutions of Right Triangles
6. Practical Applications
7. Basic Relationships and Identities
8. Reduction to Functions of Positive Acute Angles
9. Trigonometric Functions of Two Angles
10. Sum, difference and Product formulas
11. Inverse Trigonometric Functions
12. Trigonometric Equations

Higher Mathematics II

Coordinate Geometry

1. The Straight Line
2. The Circle
3. The Parabola
4. The Ellipse
5. The Hyperbola
6. Transformation of Coordinates
7. Points in Space, Planes
8. Polynomial Equations

Calculus I

1. Functions
2. Limits and Continuity
3. Derivatives
4. Implicit Differentiation
5. Tangents and Normal Lines
6. Mean Value Theorem
7. Maxima and Minima
8. Curve Sketching
9. Differentiation of Trigonometric Functions
10. Related Rates
11. Differentials

Calculus 2

1. The Anti-derivative
2. The Definite Integral
3. Applications of Integrals I -- Area and Arc Length
4. Applications of Integrals II -- Volumes
5. Techniques of Integration
6. Applications of Calculus
7. Series and Convergence
8. Taylor and MacLaurin Series
9. Partial Derivatives
10. Vector Analysis