28 September
Dr Richard Walters of the School of Mathematics, University of Bristol, visited Abbey College Cambridge on 28 September to conduct a seminar for 25 of our Further Mathematics students minded to apply to read Mathematics, Engineering, Physics or Natural Sciences at Russell Group universities. 

The seminar was made up of 3 sessions of about 1.5 hours each.  The sessions comprised a short teaching element, a student activity main part, and a debrief.

Session 1 introduced the day.  It presented a version of Maclaurin, using it to expand binomials, trigonometrical functions and e^x.  The debrief dealt with some of the issues encountered, such as factorials from repeated differentiation, and the need for radian measure.

Session 2 dealt with the required results from session 1 and went on to show how the series could be used to find accurate values of e and roots; it also discussed convergence speed.  The activity required students to complete any unfinished tasks, and to find values of roots and reciprocals without a calculator, hence demonstrating what a calculator does.  It required students reconcile the series obtained for sin x, cos x and e^x using complex numbers and to use their results to obtain double angle formulae.

Session 3 dealt with synthesis and inductive thinking.  The activity asked students to find roots of unity and to consider the arctan function as a method of deriving a series for pi.

As part of each session, Dr Walters explained the way in which the work covered and the skills demonstrated impinged on UCAS applications.

Friday 1 October
Dr John McWilliams of the Faculty of Engineering, University of Bristol, visited Abbey College Cambridge to offer consultancy for 12 of our students minded to apply to read Engineering at Russell Group universities.  He dealt with all Engineering disciplines and offered advice on the construction of UCAS applications.