Mathematics in Everyday Life – 1st Edition
Book Preface
The motivation for this book was to construct a mathematics module that encouraged firstyear university students to appreciate the diverse ways in which the mathematics they already knew, or were just about to learn, can impact on everyday occurrences. The applications discussed here will give students further practice in working with calculus, linear algebra, geometry, trigonometry and probability, thus supporting other modules. The chapters are largely independent of each other, and within most chapters, sections are often selfcontained, giving teachers freedom in selecting topics to their taste. All in all, there is likely to be more material than would be covered in a onesemester course. Readers are assumed to have a background roughly equivalent to singlesubject Mathematics at Alevel in the UK.
In many degree courses, students have the opportunity, or even the obligation, to write an extended essay on a mathematical topic of their choice. They will find a range of ideas here, in the set exercises as well as the formal text, and references to more substantial accounts.
Mathematics has many applications: it is unrealistic to expect one book to do more than give a representative sample of them. My selection runs from the obviously practical, such as how to calculate mortgage repayments, or schedule nurses to cover hospital wards, to amusing ways in which mathematical ideas can give pointers to tactics in TV Game Shows, or influence the scoring systems in sporting events. We see how simple differential equations can model bacterial growth, mixing liquids, emptying baths, evaporating mothballs, and the spread of epidemics; when looking at darts, roulette and how people progress through hierarchical organisations, we use combinatorics, logic, difference equations, and calculations with matrices and vectors. The variety of voting systems in use throughout the world is inevitable, given Kenneth Arrow’s “Impossibility Theorems”—that no system can be constructed that satisfies all among a simple list of desirable properties! Mathematics is versatile: and discovering the unusual places where it provides insights or answers is enjoyable.
Contents
1 Money.
2 Differential Equations
3 Sport and Games
4 Business Applications
5 Social Sciences
6 TV Game Shows
7 Gambling
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March 13, 2016 
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