MA469 Project Maths-In-Action

MA469 Project

Maths-in-Action Theme Guide 2011-12

Read This First!

1. Register your choices for MA469 Project by Sunday, 30 October 2011 at the latest. 2. This guide contains details of the 6 Maths-in-Action themes offered this year. For each theme you’ll find: • A Synopsis (a short introduction to help you decide) • The Brief (a formal definition of your terms of reference) • Further Information • Sources (a list of books and Web pages) 3. Each theme will be restricted to at most SIX takers (first come, first served). A collaborating pair counts as one taker.

1 Table of Contents

Theme 1. Moving Data Across Networks...... 3

Theme 2. Optimal Vaccination...... 6

Theme 3. The Mathematics of Voting...... 9

Theme 4. Data Compression...... 12

Theme 5. Encryption on the Internet...... 14

Theme 6: The Human Cell ...... 18

2 Theme 1. Moving Data Across Networks

Theme 1. Moving Data Across Networks

Synopsis Each day vast amounts of information are moved electronically around the world: across the Internet, through cell-phone networks, via satellites and along traditional telephone wires. To get from A to B data must be directed along available routes through a given network. How this can be done reliably and economically is a hot topic for engineers and mathematicians alike. The creative interplay of theory and practice continually brings improvements in communications (with faster downloads and cheaper phone calls, for instance). Read more about it at http://plus.maths.org/issue2/dar/index.html, a short informative article by Richard Gibbens and Stephen Turner at the Webby- Award-winning Plus Maths magazine (by the way, issue 15 of the on-line magazine Plus has a tribute to the famous architect of Communications Theory, Claude Shannon, who died in February 2001, aged 84).

Your Brief You must address a coherent selection of the topics in following list, but are free to choose the emphasis you give them. Your work must highlight the connections between theory and practice, between mathematics and the real world. Your brief is: • To find out how messages are routed (i) through mobile `phone networks and (ii) across the Internet. • To discover how speed of connection and volume of traffic can be optimised. • To describe mathematical models of the routing process and measures of the network efficiency. • To describe the mathematical foundations that support these models and measures. • To conjecture how better mathematics and improved technology might interact and lead to greater network efficiency. Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the Course Organiser (either in person or by sending an email to [email protected]).

Further Information A good place to start is the general survey article Modelling Communication Networks, Present and Future (see reference [1] below) by Frank Kelley, an active researcher in the field. The article, based on a memorial lecture he gave to the Royal Society in 1995, begins as follows: Modern communication networks are able to respond to randomly fluctuating demands and failures by allowing buffers to fill, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, large-

3 Theme 1. Moving Data Across Networks scale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow. I recommend two books: 1. Martha Steenstrup [2] is the editor of a collection of 11 chapters by experts in various aspects of routing. The chapters are divided into four parts according to the type of network under consideration: ◦ Circuit-switched networks, like the old physically-switched telephone networks. ◦ Packet-switched networks, where the data packets contend with each other for routes and resources ◦ Fast, broad-band networks, which can accommodate different types of traffic simultaneously ◦ Mobile networks, where A and B are on the move and their connections are passed from one hub to another to maintain contact. 2. The book by Bertsekas and Gallagher [3] covers all aspects of data networks and gives a good idea of the trade-offs between theory and practice. This will help you to understand the problems of routing in the broader context and its 130-page Chapter V is devoted specifically to routing. Interesting URLs are not hard to find. A short readable account of mobile phone networks can be found at http://www.sitefinder.ofcom.org.uk/mobilework.htm The Wikipedia offering at http://en.wikipedia.org/wiki/Cellular_network ends with a good list of internal links.

A good introductory paper (with the mathematics in) by Frank Kelly can be downloaded from http://www.statslab.cam.ac.uk/~frank/mmi.html It is an article in Mathematics Unlimited - 2001 and Beyond, edited byB. Engquist and W. Schmid. Springer-Verlag, Berlin, 2001. pages 685-702,( ISBN: 3540669132).

Sources 1. Modelling Communication Networks, Present and Future by Frank Kelley. Clifford Paterson Lecture in Philosophical Transactions of the Royal Society of London. Vol 354, No 1707. 437-463 (1996) A postscript version of this lecture can be found at http://www.statslab.cam.ac.uk/~frank/CP/. 2. Routing in Communications Networks by Martha Steenstrup (Editor) 600 pages, Prentice Hall (1995); ISBN 0130107522. 3. Data Networks, 2nd Edition by Dimitri Bertsekas and Robert Gallager, (both MIT) 592 pages, Prentice-Hall (1992) ISBN 0132009161.

4 Theme 1. Moving Data Across Networks

4. Data and Computer Communications (International Edition) by William Stallings 350 pages Prentice Hall (2003); ISBN 0131833111 5. Data Communications and Networks by David Miller, 512 pages, McGraw- Hill/Irwin (2005) ISBN 0072964049

Items 2,3, and 4 on this list are available from the Central Campus Library.

5 Theme 2. Optimal Vaccination

Theme 2. Optimal Vaccination

Synopsis Epidemiology is the branch of medicine that deals with the incidence and transmission of disease in populations, especially with the aim of controlling it. Vaccination is one method of control that has proved effective against diseases caused by viruses and bacteria, but it is expensive and can carry unwelcome risks. It is therefore important for politicians, who take the decisions on whether to implement a vaccination policy, to have an accurate assessment of the costs and benefits. Perhaps the most impressive example of a successful global vaccination policy is the eradication of smallpox in 1980 − see http://choo.fis.utoronto.ca/fis/courses/lis2102/KO.WHO.case.html Interestingly, smallpox has resurfaced in the contemporary context of bio-terrorism: should a new vaccination programme be started, and what level of the population should be vaccinated to prevent a resurgence of the disease? The British foot-and-mouth outbreak in 2001 inspired a lively debate about the pros and cons of vaccination, and the SARS panic in 2003 also raised some interesting epidemiological questions. Currently, the threat of avian ‘flu will continue to exercise official minds over the coming winter. Mathematics and statistics have played a central role in all these questions. Because epidemiology is such a large area, the brief of this project will be focused on vaccination models that predict the level of required to stem an outbreak of a given disease and to protect a population against further occurrences.

Your Brief 1. Your first task is analyse the factors that influence the spread of a given disease: for instance, its virulence (what proportion survive the attack); how it is transmitted (airborne, carried by insects, through physical contact); its infection rate (is one sneeze in a lecture theatre enough to infect everyone?), the protection afforded by previous exposure and by the vaccination; and so on. 2. Your second task is to derive and describe one or more mathematical models that take these factors into account in predicting the level of vaccination required, It is also to assess how accurate and effective these models are, and where appropriate to compare their strengths and weaknesses and to speculate how they might be improved on. 3. Thirdly, you should illustrate your work with plenty of real-life examples, past and present; you should also discuss current issues (political, financial, medical, sociological, demographic) surrounding vaccination. Finally, these three threads should be woven into a coherent and absorbing story that will enthral our open day visitors and engross your fellow MMath students when they come to do a peer assessment.

6 Theme 2. Optimal Vaccination

Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the MiA Course Organiser (either in person or by sending an email to [email protected]).

Further Information There are plenty of general books on epidemiology in the Central Campus Library (their call number is RA651); one such “Epidemiology for the Uninitiated” by D. Coggon, Geoffrey Rose, D.J.P. Barker, published 2003, and a significant number of them address vaccination issues. There is a lot of stuff on the Web too. Type ‘vaccination’ into the web search box at http://www.medbioworld.com/ for 579,000 general articles of current interest! If you want to find articles more closely focused on the brief, the most effective technique to put a few key technical words into the Google search engine; for examples the entry (S-I-S OR S-I-R) models vaccination calls up over 1.340,000 hits, starting with an article by our very own Matt Keeling for PLUS E-zine. A fair number taking you to relevant academic Web resources, and once you get started, you can use the buzzwords to build up a comprehensive collection. A similar process works on Amazon: their advanced search allows you a lot of Boolean options. Incidentally, if you need to consult a book or article not in our library, you can either use Inter-Library loan or ask the MA469 organiser to have it bought for the CC Library on the departmental budget. (Email: [email protected])

Sources For a popular history of the subject, try Patrick Pead’s paperback “Vaccination Rediscovered: New Light in the Dawn of Man's Quest for Immunity” Timefile Books, 2006, ISBN-13: 978-0955156106 Anderson, R.M., May, R.M., “Infectious Diseases of Humans”, Oxford University Press (1991). Ball, F.G., Lyne, O.D., Optimal Vaccination Policies for Stochastic Epidemics among a population of households, Mathematical Biosciences, Vol. 177 (2002), pp.333-354 Beutals, et al., An economic evaluation of universal pertussis vaccination in Italy, Vaccine, Vol. 17 (1999), pp. 2400-2409 Busenberg, S., Cooke, K. “Vertically Transmitted Diseases”, Springer-Verlag (1993) Capasso, V. Mathematical Structures of Epidemic Systems, Spinger- Verlag (1993) Keeling, M. “Mathematical Epidemiology Course Lecture Notes”, University of Warwick (2002). Kermack, W., McKendrick, A. A contribution to the mathematical

7 Theme 2. Optimal Vaccination theory of epidemics, Proceedings of the Royal Society, Vol. 115 (1927). Müller, J. Optimal Vaccination Strategies – For Whom? Mathematical Biosciences, Vol. 139, pp.133-154 (1997) Murray, J. “Mathematical Biology” (Volume I), Springer-Verlag (2002). Ögren, P., Martin, C.F., Vaccination Strategies for epidemics in highly mobile populations, Applied Mathematics and Computation, Vol. 127 (2002), 261-276. Roberts, M.G., Tobias, M.I., Predicting and preventing measles epidemics in New Zealand: application of a mathematical model. Epidemiology and Infection Vol. 124 (2000), 279-287.

8 Theme 3. The Mathematics of Voting

Theme 3. The Mathematics of Voting

Synopsis The history of elections shows that unexpected results are more common than you might imagine, whatever voting system is used. The 2000 US presidential election was widely perceived to have had an unsatisfactory outcome. There are many different voting systems, and most have been tried out somewhere. One of the main theoretical results is a theorem due to the 84-year-old Kenneth J. Arrow, a Stanford professor who won the Nobel Prize for Economics in 1972. Arrow’s Theorem shows paradoxically that under fairly natural assumptions there is no fair voting system (apart from a dictatorship!). The mathematics used to study voting systems is relatively new and research in the field is very much alive; there is scope for original work here, even at the MMath level. For a quick introduction to the subject, I suggest you look at Keith Devlin’s MAA column last November at http://www.maa.org/devlin/devlin_11_00.html

Your Brief 1. To analyse the different types of voting systems and the principles that underpin them, giving examples of institutions and countries that use them and presenting illustrations of the conflicting outcomes they can produce. 2. To describe and evaluate the mathematics associated with voting theories, in particular Arrow’s Theorem, Gibbard-Satterthwaite’s Theorem, McKelvey’s Theorem and the recent results of Donald Saari, William Zwicker, and others working in the field. (Warning: Some of the proofs of these theorems in the literature are couched in the terminology of social scientists ; they appear clumsy, obscure, and confused. Students who just copied them undigested into their scholarly report got low marks. You will be expected to grasp the essentials the proofs and reformulate them using the mathematical notation and concepts you have learnt as an undergraduate. They are much easier than they seem but getting to the heart of them will call for some creative energy on your part.) 3. To debate the conflicting claims for the voting systems you have discussed and their underlying assumptions. Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the MiA Course Organiser (either in person or by sending an email to [email protected]).

Further Information A good place to start is an article entitled “Making Sense out of Consensus” by Dana Mackenzie in Siam News in October 2000 (Volume 33/Number 8). She briefly explains some of the standard categories of voting systems: • First past the post

9 Theme 3. The Mathematics of Voting

• The Borda Count • The Condorcet Criterion • Approval Voting • The single transferable vote and highlights the controversy between Saari and Brams. Next you might like to read book Basic Geometry of Voting (see [3] below). Alternatively, you could start with one of the two easier books cited in [1] and [2] if they are available. Finally, Professor Saari’s following home page promises a list of his paper: http://www.math.uci.edu/~dsaari/ Although the models used to analyse voting (‘social choice functions’ in the jargon of sociologists) are strongly combinatorial, there are useful geometrical viewpoints that allow visualisation. A good starting point for this geometrical approach is the prize- winning article entitled “The Instability of Democratic Decisions” by Philip D. Straffin Jnr., which can be found in the April 2002 issue of Math Horizons.

Sources 1. Chaotic Elections! A Mathematician Looks at Voting, by Donald G. Saari. American Mathematical Society, 2001. Paperback, 159 pp, $23.00. ISBN 0- 8218-2847-9. This is well-written semi-popular book was probably commissioned in response to the 2000 US presidential election. 2. Decisions and elections : explaining the unexpected, by Donald G. Saari, Cambridge University Press, 2001, Paperback, 240 pp, £13-95. ISBN 0521004047. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated. 3. Mathematics and Politics : Strategy, Voting, Power and Proof (Textbooks in Mathematical Sciences) by Alan D. Taylor. Springer Verlag (1995) ; ISBN: 0387943919. Starts from a very elementary base and focuses on the conceptual aspects of mathematics in the context of important real-world questions in politics and social science. 4. Basic Geometry of Voting by D.G. Saari Springer-Verlag (1995); ISBN: 3540600647 The complexities of voting theory are explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results.

10 Theme 3. The Mathematics of Voting

5. International Encyclopaedia of Elections, Macmillan 2000 (in library?) might be worth following up if it can be located. 6. Handbook of game theory with economic applications (Vol 3) Elsevier, 1999. – ISBN 0444894284 This reference book contains a couple of surveys that may be relevant. 7. Public choice II by Dennis C. Mueller Cambridge University Press, (1989) (in the series Cambridge surveys of economic literature) ISBN 0521370833. 8. Arrow, Sen and Suzumura have edited two volumes of the Handbook on Social Choice and Welfare, containing chapters on voting procedures. The first volume (ISBN: 0444829148) came out in 2002 and the second (ISBN: 0444508945) in July this year. Brams and Fishburn contributed a comprehensive chapter on voting procedures. Ask the Social Sciences librarian for further information. 9. The Web site http://mathforum.com/t2t/faq/election.taco has a lot of stuff on the mathematics of elections (mainly in an American context). 10. There is a huge a huge alphabetical bibliography of articles on choice (including most of Donald Saari’s output on voting) at http://www.maxwell.syr.edu/maxpages/faculty/jskelly/S.htm#2703

11. See in particular many papers by William Zwicker at http://www.math.union.edu/people/faculty/publications/zwickerw.html and by Steven Brams listed in his CV -- click ‘research interests’ for a pdf-file at http://www.nyu.edu/gsas/dept/politics/faculty/brams

12. A course on applied maths with a section on voting theory can be found at http://www.ctl.ua.edu/math103/

Click the link The Mathematics of Voting in the left-hand menu.

11 Theme 4. Data Compression

Theme 4. Data Compression

Synopsis Surfing the Internet can be a slow business, with tedious delays while Web pages download over a 56K modem and frustrating waits for streamed sound or video to buffer. Broadband Internet access is a partial solution but so also is efficient data compression. Five years ago 50 CDs were needed to hold a digitized 2-hour film, but now it will all fit onto a single digital versatile disk (DVD). Again mathematics has come to the rescue. Different compression techniques are used for each of the following types of data: • Text • Sound and music (audio data) • Single images (static graphics) • Video (moving graphics) The aims of this project are • to find out why this is so, and • to study the mathematics behind one of the compression techniques For a popular introduction, you might try to consult “Wavelets”, an article by Gilbert Strang in the American Scientist, 82 (1994) 250-255 downloadable as item 104 from http://www- math.mit.edu/~gs/papers/papers.html Strang has a link to Recent Wavelet Papers on his home page

Your Brief 1. To compare the four types of data formats listed in the Synopsis above, explaining briefly why they call for different methods of compression and how these methods work. 2. To describe in greater depth the compression methods that are available for ONE of the above data types, to explore the mathematics that underlies them, and to explain why the methods are successful. 3. (Optional) To discuss new ideas and alternative methods of compression now being developed and what limits to compression there are. Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the Course Organiser (either in person or by sending an email to [email protected]).

Further Information A good place to start your reading is the chapter 27 on Data Compression in the online book (see [9] below) found at the following URL http://www.dspguide.com/pdfbook.htm

12 Theme 4. Data Compression

Sources 1. The 2005 paperback Fundamental Data Compression by Ida Mengyi Pu (Butterworth-Heinemann, ISBN-13: 978-0750663106) is well reviewed as a good introduction on Amazon. 2. The World according to Wavelets by Barbara Burke Hubbard (2nd Edition) A.K. Peters (1998) ISBN 1-56881-072-5 (review in Notices of AMS, Vol 46, No 9, pp 1059-61). ISBN:1568810725 (Main Library call number QA 404.H8) A formidable attempt to write a book for non-mathematicians about wavelets, the branch of mathematics that underlies most effective image compression. 3. Introduction to Data Compression (2nd Edition) by Khalid Sayood, Morgan Kaufmann Publishers (2000) ISBN 1558605584 (Main Library call number QA 77.4.S2) This book attempts to cover the whole spectrum of data compression and strikes a good balance between theory and practice. 4. Data Compression: The Complete Reference (2nd edition) by David Salomon, Springer-Verlag (2000) ISBN: 0387950451 (Main Library call number QA 77.4.S2) 5. Managing Gigabytes : Compressing and Indexing Documents and Images (Morgan Kaufmann Series in Multimedia Information and Systems) (2nd Edition) by Ian H. Witten, et al Morgan Kaufmann Publishers (1999) ISBN: 1558605703 (Main Library call number QA 79.3.W4) 6. Compressed Image File Formats: JPEG, PNG, GIF, XBM, BMP by John Miano, Addison-Wesley (1999) ISBN: 0201604434 (Main Library call number QA 79.3.M4) 7. Computer Speech: Recognition, Compression, Synthesis by Manfred. R. Schroeder Springer-Verlag(1999); ISBN: 3540643974 8. The Data Compression Book by Mark Nelson and Jean-Loup Gailly, M & T Books (1996); ISN: 1558514341. (Main Library call number QA 77.4.N3) This book focuses on the computer programs that implement various kinds of compression and contains large sections of C code. Its final Chapter 13 is devoted to Fractal Image compression 9. The Scientist and Engineer's Guide to Digital Signal Processing by Steven W. Smith, an on-line book which can be downloaded free at http://www.dspguide.com On the Web: There is loads of stuff on the Web. For instance, there is a dedicated site at http://www.data-compression.com/index.shtml and you’ll find a big page of Wavelet links at http://www.cosy.sbg.ac.at/~uhl/wav.html The Sept-03 issue (Vol 50 No 8,) of the Notices of the American Mathematical Society has an interesting cover article on Wavelets and Matrix Factorizations.

13 Theme 5. Encryption on the Internet

Theme 5. Encryption on the Internet

Synopsis Have you ever worried about making a credit card purchase on the Internet in case some clever hacker intercepts your details and runs up a huge debt on your card? Just how safe are the encryption methods used in such transactions? The answer is: • sending your card number to the site server is pretty safe, but • how it is stored and passed from the server to the merchant is not always safe When the lock icon in your browser window indicates a secure connection with the server, a protocol called Secure Sockets Layer (SSL) comes into play to transmit your card number and other confidential information to the site server. Under this procedure, your browser randomly chooses a large integer N which it sends to the server encoded with highly-secure asymmetric public key encryption. The server then decodes this integer and uses it as the secret key for a faster conventionally-encoded transmission of your card number and other personal details needed for the transaction. Until fairly recently, the level of public-key encryption allowed by the US government in browsers exported to foreign countries (e.g the United Kingdom) was 40-bits, which yields over a million million possible values for the encryption key N. However, this can be broken with a roomful of Pentiums in an average of 15 hours, as was demonstrated by Damien Doligez and others is 1995 (see http://pauillac.inria.fr/~doligez/ssl). Moreover, the cost of such an operation is a sufficient deterrent against hacking one credit card transaction. Microsoft and other US browsers now offer world citizens the option of 128-bit 128 38 public-key encryption. This option yields 2 ≈ 10 possible values for the integer N and makes breaking it well beyond the realms of current feasibility, at least until quantum computing becomes a reality.

Your Brief 1. To describe the various encryption techniques used (now and in the past) for the secure transmission of data, in particular over the Internet, and to compare their merits on speed, reliability and vulnerability to attack. 2. To analyse fully the mathematics behind public key cryptography, to explain why it is effective, and to discuss theoretical efforts to break it. 3. To look at recent developments promising even greater security for future Internet transactions, both at the theoretical level (e.g. using algebraic geometry) and at the practical level (e.g using quantum-based transmission techniques). Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the Course Organiser (either in person or by sending an email to [email protected]).

14 Theme 5. Encryption on the Internet

Further Information This whole area is a wonderful blend of mathematics and computing with a rich past. In recent years it has evoked a lively political debate between government and civil libertarians, and the heated controversies are certain to be cranked up a few notches by recent events in the USA. At the centre of modern cryptography are RSA codes, named after Rivest, Shamir and Adleman, who invented them. They depend for their strength on the difficulty of factorising large numbers (with say at least 140 decimal digits) into products of primes, and they exploit the discrete logarithm and exponential functions for encoding and decyphering. Other methods are currently being developed that arise from difficult problems in Algebraic Geometry and Algebraic Number Theory. New technologies that exploit the quantum effects are now at the research stage. For an entertaining popular account of the history and recent developments in the area, you might like to read Simon Singh’s The Code Book. For details see his Web site http://www.simonsingh.com/The_Code_Book.html where you might like to click on the “Cipher Challenge” link to find out who won the £10,000 prize for the first person to break the10 coded messages listed in the end of his book. The book is good readable journalism but beware a number of factual inaccuracies (see the review of Singh’s book by Jim Reeds in the Notices of the American Mathematical Society, Vol 47 (2000), pages 369-372).

Sources

1. Towards a Quarter of a Century of Public Key Cryptography, a collection of survey articles edited by Neal Koblitz. A special double issue (2/3) of volume 19 of the international journal Designs, Codes, and Cryptography published by Kluwer in 2000. This overview contains some readable state-of-the-art accounts of the mathematics behind various public-key codes. 2. A Course in Number Theory and Cryptography (2nd Edition) by Neal Koblitz, Springer-Verlag (1994); ISBN 3540942939. (Main Library call number QA241.K6.) A more leisurely textbook presentaton of the mathematics behind public-key codes (the author’s profits go towards buying books for universities in Vietnam, Nicaragua and El Salvador). 3. Factorization and Primality Testing by David M. Bressoud, Springer-Verlag (1989); ISBN: 3540970401. (Main Library call number QA242.B7.) A well-written undergraduate textbook on the mathematics of factorization, which plays a central part in public-key RSA codes. 4. Number Theory and Cryptography edited by J.H. Loxton, Cambridge University Press (1990); ISBN: 0521398770. (Main Library call number QA77.3.N8.) A collection of articles presented to a conference held in Sydney in 1989.

15 Theme 5. Encryption on the Internet

5. Cryptological Mathematics by Robert Lewand, The Mathematical Association of America(2000); ISBN: 0883857197 This introduction to the mathematics of cryptology is written at an elementary level, suitable for beginning undergraduatess, with careful explanations of all the concepts used. Challenging computer programming exercises are also included, and the book includes historical background on some of the founders of the subject. 6. Introduction to Cryptography by Johannes Buchmann, Springer-Verlag (2001); ISBN: 0387950346 This book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundations. Several exercises are included following each chapter. 7. Personal Encryption Clearly Explained by Pete Loshin, AP Professional (1998); ISBN: 0124558372. (Main Library call number QA77.3.L6.) A non-technical description of the practical aspects of secure transmission of digital data. 8. Applied Cryptography by Bruce Schneier, John Wiley (1996); ISBN: 0471128457 (Main Library call number QA77.3.S2.) From the Preface: “This book gives you the tools to protect your own privacy; cryptography products may be eclared illegal, but the information never will be.” It contains the C cource code for 10 algorithms discussed in the book (the accompanyiing CD is missing by US government decree). It also has one and a half thousand references. 9. Cracking DES published by the Electronic Frontier Foundation; ISBN 1565925203 (Main Library call number QA77.3.E5.) The Data Encryption Standard (DES) ws published by the US governernment in 1975. This book describes a machine that will crack code written to this standard (and briefly discusses the interesting politics behind it). 10. Chinese Remainder Theorem: Applications in Computing, Coding, and Cryptography by C.Ding, D.Pei, and A. Salomaa, World Scientific (1996); ISBN: 9810228270. (Main Library call number QA242.D2.) An interesting collection of applications of the Chinese Remainder Theorem. 11. Contemporary Cryptography by Rolf Oppliger, Artech House Publishers (2005); Hardcover (510 pages): ISBN: 1580536425. Comprehensive and academic, well reviewed on Amazon: “Dr. Oppliger's book draws a balance between the computer scientist approach who is looking to implement a secure communications protocol, and the mathematician who is interested in the theoretical concepts. …” The Internet: There is a magnificent range of stuff on the Web. For instance … • the elementary account of public key cryptography (PKC) at http://www.livinginternet.com/i/is_crypt_pkc.htm

16 Theme 5. Encryption on the Internet

• The article at the Web address http://www.pbs.org/wgbh/nova/decoding/web.html has the basic stuff on Internet encryption. The author of this article, Richard E. Smith, has written a book Internet Cryptography, Addison-Wesley-Longman (1997). • An article called “Are Secure Internet Transactions Really Secure?” by Stephen Mencik at http://www.jsweb.net/paper.htm explains why in practice Internet shopping is not always secure (small firms receive the credit card details via unencrypted emails).

17 Theme 6: The Human Cell

Theme 6: The Human Cell Synopsis This theme marshals forces from vast areas of contemporary science, above all from biology, mathematics and statistics, and computer science. Our current view on the functions of the cell is based on the double helix of DNA (the human genome) in its nucleus, selected expression of its genes, their transcription of messenger RNA, and finally translation into the proteins that carry out a myraid of different tasks to keep us alive and well. Most appealingly, the study of the human cell promises us understanding and control of pathology, and offers the tantalising prospect of victory over disease, perhaps ultimately the philosopher’s stone of everlasting life. If you are a beginner and want to get an up-to-date understanding of what’s happening currently in this exciting field, I suggest you start by reading the nine tutorials on the Science primer Web page of the US National Center for Biotechnology Information at http://www.ncbi.nlm.nih.gov/About/primer/index.html, clicking first on the title Molecular Genetics. The essays are well written and fully accessible to the novice; they take about an hour of concentrated reading altogether.

Your Brief Because of the breadth of the subject area, this is the most open-ended of this year’s themes. I propose that you choose one of the three following topics: 1. DNA sequencing 2. DNA microarrays (or DNA chips, as they are sometimes called) 3. Protein analysis In each case, for your scholarly report you should introduce enough background to make your account accessible to your target audience (fellow MMath students who know no more about the subject than you did when you started). Above all, you must highlight the role mathematics plays in research and applications (for this purpose, mathematics can be interpeted broadly to include statistics and theoretical computer science). And, if you wish, you can add your own twists of history and speculation to make your story interesting and engrossing. Important: This brief will be strictly adhered to when assessing your work. If you wish to deviate from it, you must apply to the Course Organiser (either in person or by sending an email to [email protected]).

Further Information There is a great deal of useful information on the World Wide Web. I list just a few sites below, and from them you will be able to navigate easily to many more. Search engines like Google will take you deeper as you learn new key words, acronyms, and phrases to pursue. Of course, you should be selective and canny about what you read and believe. The URLs are divided loosely into the six categories, but there is considerable overlap.

18 Theme 6: The Human Cell

Glossary http://www.ornl.gov/TechResources/Human_Genome/glossary/glossary.html#dna General Tutorials http://www.warwick.ac.uk/telri/Bioinfo/home.htm (Warwick’s online course) http://www.research.ibm.com/journal/sj/402/swope.html (IBM Research Journal) http://123genomics.homestead.com/files/learning.html http://csm.jmu.edu/biology/monroejd/amcp/genome2.html Institutions http://www.research.ibm.com/compsci/compbio/ (IBM research group) http://researchweb.watson.ibm.com/bioinformatics/ (IBM research group) http://mips.gsf.de/ http://www.ncgr.org/ Sequencing http://www.research.ibm.com/journal/sj/402/headgordon.html http://www.nature.com/nature/supplements/collections/humangenome/index.html Microarrays http://www.ncbi.nlm.nih.gov/About/primer/microarrays.html http://ihome.cuhk.edu.hk/~b400559/book_mray.html#Microarray (book list) http://research.nhgri.nih.gov/microarray/index.html http://www.nature.com/genomics/post-genomics/microarrays.html Proteomics http://www.cryst.bbk.ac.uk/education/AminoAcid/overview.html http://www.cse.ucsc.edu/research/compbio/ismb99.handouts/KK185FP.html#c6 http://www.techfak.uni-bielefeld.de/bcd/Curric/ProtEn/contents.html http://www.research.ibm.com/journal/sj/402/duan.html http://www.research.ibm.com/journal/sj/402/liu.html http://www.research.ibm.com/journal/sj/402/wang.html

Books Because the field relatively new and fast-developing, the latest research will not have reached the textbooks yet. You might therefore want to be adventurous and read some articles in the learned journals, such as the online IBM research journal linked to above. In any case, type some key words into the Amazon book search engine, noting that, with your tutor’s signature on the form, you can use the Inter-Library Loan scheme to get books and copies of articles that are not in the University’s periodicals collection.

19 Theme 6: The Human Cell

I begin with two books with serious mathematical content relevant to the theme: 1. “Biological Sequence Analysis” by R. Durbin, S. Eddy, A. Krogh and G. Mitchinson. Cambridge University Press, 1998. Paperback 356 pages. ISBN 0521629713. 2. “Mathematics of Genome Analysis” by J.K. Percus. Cambridge University Press, 2002. Paperback 139 pages. ISBN 0521585260. There now follows a list of books which I haven’t been able to look at and therefore cannot vouch for. I suggest you go to the publisher’s Web site, or to an Internet bookshop like Amazon, to read more about them. 3. “Discovering Genomics, Proteomics, and Bioinformatics” by A. Malcolm Campbell and Laurie J. Heyer. Addison Wesley & Benjamin Cummings, just published Sept 2002. Paperback 410 pages. ISBN 0805347224. A first textbook for upper-level undergraduate and first-year graduate students which combines integrated Web exercises with a problem-solving approach to train students in basic hands-on genomic analysis. Features include an inquiry approach to give students hands-on practice and buid on problem-solving skills, students learn to use databases and how to extract pertinent information. "Math Minutes" supply brief tutorials that reveal the math behind the biology. 4. “DNA Microarrays and Gene Expression” by Pierre Baldi and G. Wesley Hatfield. Cambridge University Press, 2002. Hardcover 230 pages. ISBN 0521800226. 5. “Introduction to Proteomics: Tools for the New Biology” edited by D.C. Liebler. Humana Press Inc, 2002. Paperback 210 pages. ISBN 0896039927. An introduction to proteomics, which is currently the hottest thing in the biological sciences as it enables scientists to study the protein complement of the genome. It refers to studying the functions of many proteins at one time, as opposed to how research was conducted in the mid-90's where the technology did not enable the study of the entire protein system. From this, one is able to develop a systematic overview of the way a genome functions and the role it plays in health and disease. 6. “Protein Evolution” by Laszlo Patthy. Blackwell Science, 1999. Paperback 240 pages. ISBN 0632047747. 7. “Protein Structure, Stability and Folding” edited by Kenneth P Murphy. Humana Press Inc,2001. Hardback 264 pages. ISBN 0896036820. 8. “Protein Structure Prediction: Methods and Protocols” by D Webster. Humana Press Inc, 2000. Hardback 300 pages. ISBN 0896036375. 9. “DNA Microarrays” edited by David Bowtell and Joseph Sambrook. Cold Spring Harbor Laboratory Press, 2002. Paperback 375 pages. ISBN 0879696257.

20 Theme 6: The Human Cell

10. “Microarray Gene Expression Data Analysis – A Beginner's Guide” by Helen Causton, Alvis Brazma, John Quackenbush. Blackwell Science, 2003 (paperback, 176 pages). ISBN 1405106824. 11. Beyond the Genome-The Proteomics Revolution” by Fred Askari and Emilia Askari. Prometheus Books. 2003 (hardcover, 300 pages). ISBN 1591020190.