Single A-level Mathematicians

Each year a number of students, with a single A-level in mathematics, are admitted to read Mathematics, its joint schools and Computer Science at Oxford . We encourage candidates for these courses to study whatever mathematics is available to them at school, but realise that many students do not have the opportunity to take Further Mathematics, or may have to teach themselves.

Statistics show that single A-level mathematicians are just as successful at Oxford as others; however, the transition to university level maths can be somewhat harder. College tutors often ask such students to do extra reading over the summer before coming to Oxford, and the personalized nature of Oxford's tutorial system is especially suited to deal with the different educational backgrounds of new students.

The Bridging The Gap webpage contains material aimed at facilitating this transition, though this page is still being implemented including copies of the notes produced for previous Bridging Courses. These notes can be bought from the Institute for £10 per copy - the price includes postage to UK addresses. Send a cheque for £10 payable to "The Mathematical Institute, Oxford", together with your address, to "Dr Richard Earl, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB".

In autumn of 2003 a series of classes was run weekly for students with single A-level maths during their first term at Oxford, aimed at making the transition to university level mathematics that much easier. The classes ran weekly on Wednesdays between 4pm and 6pm in weeks 1-7 of Michaelmas term in the Mathematical Institute. The handouts accompanying these classes are below, together with a timetable of the classes:

1. Vectors and Matrices : in (PDF), (PS) formats.
   Algebra of vectors and matrices. 2x2 matrices. Inverses. Determinants. Simultaneous linear equations. Standard transformations of the plane.
2. Techniques of Integration: in (PDF), (PS) formats.
   Integration by Parts. Substitution. Rational functions. Partial fractions. Trigonometric substitutions. Numerical methods.
3. Differential Equations: in (PDF), (PS) formats.
   Linear differential equations with constant coefficients. Homogeneous and inhomogeneous equations. Integrating Factors. Homogeneous polar equations.
4. Complex Numbers: in (PDF), (PS) formats
   Cartesian and polar form of a complex number. The Argand diagram. Roots of unity. The relationship between exponential and trigonometric functions.
5. Induction and Recursion: in (PDF), (PS) formats.
   Using induction in sums and integrals. Further applications. Linear Difference Equations. Ties with Linear Algebra.
6. Taylor Series: (no PDF available)
   Definitions. The Taylor series of standard functions. Convergence issues. Applications in differential equations. Generating Functions.
7. Abstract Algebra: (no PDF available)
   The integers. Prime Numbers. Modular arithmetic. Definition of a group. Examples.