Single A-level Mathematicians

Each year a number of students with just a single A-level in mathematics apply to read Mathematics, Computer Science, or joint honours courses 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. If your school or college does not offer Further Mathematics, then you may wish to contact the Advanced Maths Support Programme to see if they can help you learn Further Maths.

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.

The page Bridging the Gap contains material aimed at facilitating this transition. The original notes have now been expanded and revised into a book "Towards Higher Mathematics: A Companion" by Richard Earl, published by Cambridge University Press.

Several years ago, a series of classes was run for students with single A-level maths during their first term at Oxford, aimed at making the transition to university level mathematics easier. The handouts for some of these classes are below:

1. Vectors and Matrices
   Algebra of vectors and matrices. 2x2 matrices. Inverses. Determinants. Simultaneous linear equations. Standard transformations of the plane.
2. Techniques of Integration
   Integration by Parts. Substitution. Rational functions. Partial fractions. Trigonometric substitutions. Numerical methods.
3. Differential Equations
   Linear differential equations with constant coefficients. Homogeneous and inhomogeneous equations. Integrating Factors. Homogeneous polar equations.
4. Complex Numbers
   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
   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.