Pure mathematics

This is the foundation course on which subsequent, university level pure mathematics is based.

Topics covered

• Logic, Proof and Sets: Mathematical statements and proof. Some basic logic. Quantifiers and proof by contradiction. Set notation and operations on sets.
• Algebra: Polynomial division. The factor and remainder theorems. Solving polynomial equations. The relationship between the roots of a polynomial and its coefficients. Partial fractions. The binomial theorem.
• Trigonometry: Trigonometric functions and the Pythagorean identities. The compound angle formulae. Using trigonometric identities to simplify and evaluate trigonometric expressions. Solving trigonometric equations.
• Calculus: Differentiating implicitly defined functions. Integration by substitution. Integration by parts. Using trigonometric identities and partial fractions in integration.
• Differential Equations: Separable and linear first‐order differential equations with some applications.
• Coordinate Geometry: Conic sections. Tangents and normals. Parametric equations and using them to find gradients.
• Vectors: Vector addition and scalar multiplication. The dot product and the angle between two vectors. The vector equation of a straight line. Normal vectors and planes. The Cartesian and vector equations of a plane.

Learning outcomes

If you complete the course successfully, you should be able to:

• Use the concepts, terminology and methods covered in the course to solve mathematical problems
• Solve unseen mathematical problems involving understanding of these concepts and applications of these methods
• See how mathematics can be used to solve problems in economics and related subjects
• Demonstrate knowledge and understanding of the underlying mathematical principles.

Assessment

Unseen written exam (Two-hour 15 minutes).