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Copyright © The University of Birmingham 2012Published in the United Kingdom by The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.All rights reserved. Except as otherwise permitted under the Copyright Designs and Patents Act 1988, no partof the work may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Enquiriesconcerning reproduction outside these terms should be sent to the compiler at the following address:Aslam Ghumra, IT Services, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK.AcknowledgementsWe would like to thank all the people who contributed to this publication. Putting this together pales in comparisonwith the wondrous research they are doing.Most of the work is presented at http://www.bear.bham.ac.uk/CaseStudiesFront cover ‘Fractal Sqaure Root’ created using GIMP.‘The Death of Socrates’ Jacques-Louis David (1748-1825), The Metropolitan Museum of Art, image used for‘Optimal voting rules for two-stage committees’ by Dr Colin Rowat.Photo by Flickr user Mukumbura; used under Creative Commons Attribution license for Chunk Learning andMove Prompting Making Moves in Chess by Dr Andrew Cook.Image of Braid by dow@uoregon.edu for Parallel Computation of Braid Orbits with GAP and SCSCP by GehaoWang.All other images, third party trademarks and service marks are owned by their respective owners.Page i