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Mathematics in everyday life. (English)
Cham: Springer (ISBN 978-3-319-27937-4/pbk; 978-3-319-27939-8/ebook). ix, 159~p. (2016).
The motivation for this book was to construct a mathematics module that encouraged first-year 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. Each chapter ends with a collection of exercises, which are an integral part of the book. The author do not indicate whether an exercise is expected to be routine, or quite tricky; lack of that knowledge is exactly the position mathematician find themselves in when confronted with a problem to solve. The Chapter 1 “Money" consists of 7 sections: 1.1.~Interest; 1.2.~Present value and APR; 1.3.~Mortgage repayments: annuities; 1.4.~Investing; 1.5.~Personal finance; 1.6.~More worked examples; 1.7.~Exercises. In this Chapter, the author examines the concept of interest, developing the Rule 72, mortgage repayments, personal finance the ideas of present value and annual percentage rate (APR), and shows how to calculate mortgage repayments or annuity receipts over different periods. In Chapter 2 “Differential equations" with Sections 1‒4 (What they are, How they arise; First order equations; Second order equations with constant coefficients; Linked systems; Exercises) the author consider only straightforward first or second order ordinary differential equations and how particular types problems can be solved by standard methods. The author seeks to model changes in population size, or the path of a projectile, or the escape of water down a plughole, or rowing across a river, an linked systems, with applications to predator-prey equations, and models for the spread of epidemics or rumors, with Exercises on topics such as carbon dating, cooling of objects, evaporation of mothballs, mixing of liquids and Lanchester’s square law about conflicts. Chapter 3 “Sport and games" with Sections 1‒9 (Lawn tennis; Rugby; The snooker family; Athletics; Darts; Tournament design; Penalty kicks in soccer; Golf: flamboyance versus consistency; Exercises) explains how mathematical methods can give pointers to good tactics for games won in a variety of sports and games, such as lawn tennis, rugby, snooker, athletics, darts, soccer, golf, ice-skating. For the investigation of this problems such branches of mathematics, as geometry, trigonometry, vector algebra, and the theory of differential equations, logic, probability theory, zero-sum games can be applied. Chapter 4 “Business applications" with Sections 1‒9, such as Stock control, Linear programming, Transporting goods, Jobs and people, Check digits, Hierarchies in large organizations, Investing for profits, Exercises begins by analyzing how a retail outlet can minimize its overall costs in ordering and holding stock, and then show to set up and solve problems as linear programming, with applications to diets, producing the right quantities of goods at minimum cost, transporting materials from several sources to different destinations as cheaply as possible, and even allocating nurses to shifts, or obtaining the optimal allocation of lecturers to different modules in universities. Chapter 5 “Social sciences" consider 6 sections: Voting methods; Voting dilemmas; Simpson’s paradox; False positives; Measuring inequality; Exercises. The mathematical properties of the variety of methods used in different countries and organizations to vote for their legislatures or executives in examined with copious examples to illustrate the merits and problems that arise. Chapter 6 “TV game shows" consists 12 sections, such as: Utility; Monty Hall’s Game; The Price Is Right; Pointless; Two Tribes; The Million Pound Drop; Deal or No Deal; the Weakest Link; The Colour of Money; Who Wants to be a Millionaire? Other shows; Exercises. It may surprise many people how often mathematical ideas arise in popular TV game shows, either in pointing the way towards good tactics, or simply adding to the viewer’s enjoyment. The general idea of the utility of a sum of money, rather than its actual amount, has a strong influence on whether a contestant will play safe, or take a riskier but potentially more rewarding path. Chapter 7 “Gambling" contains the following Sections 1‒7: Introduction; Lotteries; Roulette; The horse racing family; Card games; Premium bounds. The author point out that the term odds is ambiguous, either relating to the true probability an event occurs, or to the payout price offered by bookmakers. The UK National Lottery changed its format in 2015; comparisons are made between the old and new formats, with well-organized counts central to analyzing both. When examining roulette, it is draw parallels between differential equations and difference equations, and show how similar are the methods used in both fields ‒ a link between discrete and continuous mathematics. The Appendix contains several formulae, techniques and approximations.
Reviewer: Irina V. Konopleva (Ul’yanovsk)
Classification: A80 M10 I70
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