Mathematics

Course summary

Why might anyone support mathematics and wave its flag? First, because mathematics is demonstrably useful: one cannot find the price of a financial derivative, understand quantum mechanics or plot the position of a star without it. Secondly, the study of mathematics is, inter alia, an introduction to the apparatus of argument: anyone can profit from learning about premises, conclusions, necessary and sufficient conditions, the law of the excluded middle and entailment. Thirdly, because it has intrinsic value: solving puzzles and problems is satisfying, and mathematics is full of them. In sum, mathematics is not the preserve of the mathematician alone: the list of its advocates is long, catholic and illustrious, and you would do well to add yourself to it. Paper 1. Pure Mathematics [9MAO/01] 1. Proof. 2. Algebra & functions. 3. Coordinate geometry in the x-y plane. 4. Sequences & series. 5. Trigonometry. 6. Exponentials & logarithms. 7. Differentiation. 8. Integration. 9. Numerical methods. 10. Vectors. Paper 2. Pure Mathematics [9MAO/02] 1. Proof. 2. Algebra & functions. 3. Coordinate geometry in the x-y plane. 4. Sequences & series. 5. Trigonometry. 6. Exponentials & logarithms. 7. Differentiation. 8. Integration. 9. Numerical methods. 10. Vectors. Paper 3, section A. Statistics [9MAO/03] 1. Statistical sampling. 2. Data presentation and interpretation. 3. Probability. 4. Statistical distributions. 5. Statistical hypothesis testing. Paper 3, section B. Mechanics [9MAO/03] 6. Quantities and units in mechanics. 7. Kinematics. 8. Forces and Newton’s laws. 9. Moments.