Some simple iterations, which are in fact permutations of integers, lead to challenging questions.

Some simple iterations, which are in fact permutations of integers, lead to challenging questions. For

example, let n be an integer. If n = 3k ± 1 we replace it by 4m ± 1, respectively, and if n = 3k it is

replaced by 2k. E.g., starting from 8 one gets

8 → 11 → 15 → 10 → ...

and so on. We don’t know whether this process yields a cycle or if the sequence goes to infinity.

There are many other open problems based on similar iterated sequences. The aim of the project

is to use a computer to check whether this type of mapping can be used for encryption and data

compression. The project can be done with the help of MatLab

Department of Mathematics requires that written Final Year Project submission should have a maximum length of 70 A4 single sided pages, counting the title page, acknowledgements, etc. In addition to these 70 pages, students must submit an exact copy of their Background and Project Plan submitted in November (as the last appendix which does not count against the 70-page limit) and a computer disc with the electronic copy of the printed submission and all relevant supporting material such as computer programs (with a clear statement of authorship) and/or data (enabling markers to test the various aspects of numerical work, authorship, etc.). Students who submit more than 70 pages will be penalised by 1 mark for every page over the limit. If in danger of submitting a project that is too long, you should consider what the most important themes of your project are, emphasise these, and condense or remove less important material. Also, 70 pages is a maximum, not a requirement: a shorter, but snappier, project is better.
The submission DEADLINE of the project report is 3:30pm Monday 27 March 2017.
The presentation of the report is largely a matter for the student’s discretion, but good presentation is explicitly rewarded in the marking scheme. Students must ensure that sufficient time is available to complete the work and prepare the report. It is usually advisable to complete most of the development work by mid-February so as to leave ample time for the final write-up. All students must use word-processors and submit documents produced on laser printers (or other printers of comparable quality). The text must be on A4 sized paper, written on only one side of the page, using 1 ½ line spacing and type face 12 point in either Times New Roman or Arial fonts. Appropriate margins must be left at the top and bottom and at both edges of all pages; in particular, a left margin of at least 40 mm is necessary to allow for the binding, whilst other margins must be at least 15mm. The opening pages must include a title page, a list of contents with page numbers, and an abstract of about 300 words (you may also include an optional acknowledgements page). These pages should be numbered using Roman numbering. The title page must include the project title; the student’s name and course; the full name of your Department (“Department of Mathematics, College of Engineering, Design and Physical Sciences, Brunel University”); the supervisor’s name (and department/college, if different); and the year of submission. The main body of the text, references, appendices etc. must be numbered normally. Chapter and section headings must be distinguished in a larger font and numbered using a decimal system e.g. 3. Development of ... 3.1 Previous results. Figures must be numbered, have captions and be referenced if they have not been produced by you (e.g., downloaded or scanned), or are the same graphs of results or functions, etc., as in your sources.

Referencing
All references (textbook, papers, websites etc.) must be clearly indicated in the text, and their list set out at the end of the main body of the report, in a standard and consistent manner used in textbooks and/or research papers. References must be precise, e.g., address and date when accessed for a website, or name of the author, publishing data and page if referencing a book, etc., so that interested parties can find the information without effort. In particular, it is important to reference prior results and information properly, so that readers unfamiliar with the subject know where to look for the statement of (non obvious) facts you claim to be true. This applies both for mathematical and non mathematical information, results and even calculations. Good referencing is also an essential part of your demonstration that you understand the subject matter of your project! REFERENCING MUST LEAVE THE READER IN NO DOUBT ABOUT WHAT CONSITUTES YOUR OWN WORK (OR YOUR `SPIN` ON THE MATERIAL) AND WHAT HAS BEEN TAKEN FROM YOUR SOURCES.