# Christopher J. Sangwin

Senior Lecturer

 School of Mathematics The University of Birmingham Edgbaston Birmingham B15 2TT United Kingdom Office: Watson 105 Phone: +44 (0)121 414 6197 Fax: +44 (0)121 414 3389 E-mail: c.j.sangwin@bham.ac.uk Skype: sangwinc

In mathematics we do not appeal to authority, but rather you are responsible for what you believe.
Richard Hamming, American Math Monthly, vol 105 no 7.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
Karl Friedrich Gauss, 1808

On definitions in mathematics. (Goold et. al., (1906) Harmonic Vibrations)

## Research

I am currently a Senior Lecturer in the School of Mathematics. I undertake research in mathematics and in mathematics education.

My educational research currently focuses on using computer algebra systems for assessment of mathematics. A practical outcome of this is the STACK computer aided assessment system. My interest in mathematical notation resulted in a project student, Alex Billingsley, creating the DragMath project.

In 2006 I was awarded a University of Birmingham Teaching Fellowship and a National Teaching Fellowship.

## Teaching

Semester 1 of 2012-2013 session I am teaching the following courses:
• MSM1C Vector Algebra, Elementary Mechanics

## Software Projects

 STACK STACK provides a question type for the Moodle quiz which is specifically designed to enable sophisticated computer-aided assessment in Mathematics and related disciplines, with emphasis on formative assessment. DragMath DragMath is a free "drag and drop" equation editor, written in Java. The editor lets users build up mathematical expressions in a traditional two dimensional way, and then output the results in a correctly formed syntax.

## Some mathematical highlights

 Euler's sum One of my favourite results in mathematics is the following: $1 + \frac{1}{4} + \frac{1}{9} + \cdots = \frac{\pi^2}{6}.$ Leonard Euler's wild and brave explanation is given here. The game of Hex Hex is a connection strategy game for two players. It is simple to learn, great fun to play and has some deep mathematics behind it. Some hex resources. Stacking up dominoes Apparently you can stack up dominoes in balance in the following way To see how click here (PDF). Roller which are not round! Look at the picture below. It shows two `rollers' in the shape of a 50p with a book on top. What will happen to the vertical distance between the book and the table as you roll the book along? Normal vibration modes of a circular membrane Imagine an elastic circular membrane fixed along its circular boundary but otherwise free to vibrate. There are a number of different normal vibration modes which are possible. Click here for more details. The double pendulum A double pendulum consists of two rigid arms that are joined by a low friction bearing. Details are here.

Chris Sangwin's GeoGebra page with some geometry I find interesting.

## Other fun things!

Have you seen

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School of Mathematics
University of Birmingham
Last update: 27 August 2013