Mathematical Modelling Essay

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MATH123 Session 1 Project Essay. Mathematics is the basis of much of modern scientific thought and practice. It provides the key for understanding the nature of science and technology. Mathematics is an integral part of modern civilisation, and many contemporary issues, such as global warming or financial regulation, are complex and can be meaningfully analysed from a quantitative perspective using mathematical models (see, for example, [1]). The development of mathematics to its modern form spans three millennia or more, with contributions from historically diverse cultures and societies. Some of the most important and enduring ideas of mathematics lie in algebra, geometry and calculus. Write an essay, of between 800 and 1200 words, describing the application of mathematical modelling to an appropriate topic of your choice. Your essay should: • Some background as to the nature of the issue or problem that is being addressed • Some detail about the nature of the mathematical model being used • A discussion of the interpretation of the results and conclusions which can be drawn from the mathematical modelling • An assessment of the social, environmental and/or ethical implications of the results and conclusions. • Contain at least four references to published books, journal articles or internet-based materials; however, no more than two of your references should be electronic (i.e. internet-based). This outline of the requirements for the essay also serves as a guide to the correct referencing of material. • Be prepared with a word processing package, and submitted as a paper copy with the downloaded cover page attached. Make sure you sign the declaration. Topics that you might consider researching are the modelling of sea-temperatures, urban population changes, transport planning, taxation or the spread of infectious diseases. Marks will be assigned for each of the points described (the issue or problem, the mathematical model, the results or conclusions, assessment of impacts and references) as well as overall presentation, including style and grammar. Resources for your essay include: • Books and journal articles in the University Library. Section QA21 is particularly useful on the History of Mathematics. Sections QA7 and QA8 are useful for some surveys of Applications of Mathematics, such as linear programming, the travelling salesperson problem, game theory and other ideas described in [2] and [3] , or applications in the natural sciences (biology, ecology,...) described in [4]. A variety of modelling applications appears in the survey [5], and the AIDS epidemic is considered in the journal article [6]. Many other sections also contain books of relevance about topics such as women in mathematics (e.g. [7]), mathematics in ancient cultures (e.g. [8]), important individuals in mathematics (e.g. [9]), or important topics in mathematics (e.g. [10]). • Internet based resources. An example is the MacTutor History of Mathematics Archive, a website hosted at the University of St Andrews [11]. An interesting article on the role of the Black-Scholes equation in financial modelling appeared on the website [12] of The Guardian. The cover sheet for submission of your essay is on the page following the end of the reference section. References [1] http://www.wikipedia.org - search on the term mathematical modelling. . [2] Kline, Morris (editor), Mathematics: an introduction to its spirit and use. WH Freeman and Co. (1979) See chapter VI on applications. [3] Crilly, Tony, Mathematical ideas you really need to know. Quercus (2007) See chapters 45-47 on applications. [4] Builly, Francis and Longo, Guiseppe, Mathematics and the Natural Sciences: the physical singularity of life. Imperial College Press (2010). [5] Korner, Tom, The Pleasures of Counting. Cambridge University Press (1996).

[6] Smith?, R.J., Li,J ., Gordon, R. and Heffernan, J.M., Can we spend our way out of the AIDS epidemic? A world halting AIDS model. BMC Public Health 9
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