Each year a number of students, with a single A-level in mathematics, apply 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. You may want to get in touch with the Further Maths Support Programme, to see if they can help you take Further Maths to AS or A2 level if your school does not offer it.
Statistics show that single A-level mathematicians are just as successful studying 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.
Bridging the Gap contains material aimed at facilitating this transition. 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, Andrew Wiles Building, Radcliffe Observatory Quarter, Oxford, OX2 6GG".
Additionally, several years ago 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 handouts accompanying these classes are below:
- Vectors and Matrices
Algebra of vectors and matrices. 2x2 matrices. Inverses. Determinants. Simultaneous linear equations. Standard transformations of the plane.
- Techniques of Integration
Integration by Parts. Substitution. Rational functions. Partial fractions. Trigonometric substitutions. Numerical methods.
- Differential Equations
Linear differential equations with constant coefficients. Homogeneous and inhomogeneous equations. Integrating Factors. Homogeneous polar equations.
- Complex Numbers
Cartesian and polar form of a complex number. The Argand diagram. Roots of unity. The relationship between exponential and trigonometric functions.
- Induction and Recursion
Using induction in sums and integrals. Further applications. Linear Difference Equations. Ties with Linear Algebra.
- Taylor Series (no pdf available)
Definitions. The Taylor series of standard functions. Convergence issues. Applications in differential equations. Generating Functions.
- Abstract Algebra (no pdf available)
The integers. Prime Numbers. Modular arithmetic. Definition of a group. Examples.