Mathematics undergraduate courses

The purpose of these texts is to ensure that all students start with an appropriate level of knowledge. Revision material and exercises will be provided at the start of the course. You should find this work straightforward, provided that you are familiar with the following:

Basic algebraic processes such as, simplifying and substituting into expressions, expanding brackets and factorisation.

Solution of equations such as, linear, quadratic, simultaneous, inequalities and changing the subject of formulae.

Graphs of simple functions such as, straight line, quadratic, cubic and reciprocal.

• Function Notation, domain and range (or codomain), composite and inverse functions
• Indices and logarithms, the exponential e^x and natural logarithm ln(x) functions
• Functions defined parametrically or implicitly
• Partial fractions
• The Binomial Theorem
• Algebraic division and the Factor Theorem
• Arithmetic and Geometric series. Formulae for nth term and sum of first n terms
• Trigonometric functions (sin, cos, tan, cosec, sec, cot). Addition and double-angle formulae, trigonometric equations and identities, radians, graphs of trigonometric functions
• Differentiation of powers of x, sums, differences, products, quotients, composite functions, exponential, logarithmic and trigonometric functions
• Applications of differentiation to gradients, tangents and normals, maximum and minimum values, rates of change
• Integration of powers of x, sums, differences, exponential and trigonometric functions
• Integration using partial fractions, by substitution and by parts
• Applications of integration to areas and volumes, and to solving simple differential equations
• Vector notation.

The links above can be used as a starting point, and your A-level textbooks will contain more information.To test yourself in these areas have a go at our question sheet (40K PDF). The answer sheet (40K PDF) is also available.

As well as being fully knowledgeable about your A-Level syllabus you can also prepare yourself for a university education by reading some popular science books about the subject. Below are a few you might want to try:

• The music of the primes - Marcus du Sautoy
• The code book - Simon Singh
• Fermat's last theorem - Simon Singh
• An imaginary tale: The story of i [the square root of minus one] - Paul J. Nahin
• `e': The story of a number - Eli Maor
• A history of Pi - Petr Beckmann
• The great mathematical problems - Ian Stewart
• The quantum universe: Everything that can happen does happen - Brian Cox and Jeff Forshaw.

You may also want to acquaint yourself with the following blogs:

• Matheminutes
• Mathblogging.org
• Mathcreation
• Plus magazine

(The opinions expressed in the above blogs are those of the authors of the articles and do not necessarily state or reflect the views of the staff from the University of Surrey).