# Mathematics in Everyday Life

This is not the first book on mathematics in everyday life. Some of there are truly recreational and are addressing a general motivated layperson like for example *Raising public awareness of mathematics* (E. Behrends et al) or *Figuring it out - Entertaining encounters with everyday math* (N. Crato), and there are many other examples. Some are more recreational and collect tricks, games, history and anecdotes, some others embed the mathematics in a novel where the story becomes more important. At the other side of the spectrum you find the true lecture notes that include many applications and examples.

The present book is different. It is intended to be a book with everyday illustrations of applications of mathematics intended to accompany introductory mathematics courses for a beginning university student. Thus it contains the application part, outside of the volume with the (more) theoretical lecture notes which will normally contain all the definitions, theorems, and proofs. It is somewhat similar to *Everyday Calculus* (by O.E. Fernandez) although the latter is just illustrating and does not provide exercises for the student as in Haig's book which is also broader, not restricted to only calculus. The content is organized by application domain (finance, economics, dynamics, sports, social sciences, gaming, and gambling). The mathematics involve a cross section of what the students will get in traditional classes (calculus, differential equations, probability, linear algebra, combinatorics,...). The applications usually have just one mathematical component i.e., as a rule they don't mix different mathematical disciplines. Each of the seven chapters give many examples that are worked out and each one ends with a rather extensive set of exercises for the student to solve. Most problems are numerical or computational, occasionally an exercise asks for a proof. They stay within the same complexity of the examples given in the chapter. No solutions are provided though. For the reader who is interested in further reading some references are provided. Besides an appendix with general useful mathematical facts at the end of the book, some chapters also have an appendix attached which elaborates somewhat deeper on a technical matter.

To give an idea of the applications covered, I will give some examples from the different chapters. The first chapter has financial applications that are mostly involved with interest computation. Annual percent rate (APR), compound interest, the 72 rule (it takes about 72/p years to double the capital with an interest rate of p), investing, loan, taxes,...

Differential equations in the second chapter are derived but are restricted to first and second order. Solution methods are analytic, not numerical. Models are given for physical problems, but also the Lotka-Volterra model for predator-prey simulation.

The sports and games chapter is rather extensive and covers almost many different sports (tennis, rugby, snooker, darts, athletics, golf, soccer) but also tournament design. For example the optimal place in the rugby field to kick the ball towards the poles, where to hit a snooker ball, the chance of scoring a soccer penalty depending on the chances of the player aiming left or right and the keeper diving left or right, what is best during golf: consistency or a flamboyant game with risky shots? etc.

Chapter 4 on business applications involves stock control, delivery of goods, human resource management, check digits, promotion policy, investment and profits,... Several examples involve linear programming problems, so the simplex method to solve such problems is explained.

Among social science applications we find voting techniques, the Arrow paradox, the Simpson paradox, the problem of false positives in medical applications, how to measure social inequality in a population, etc.

Also TV games problems are considered, discussing questions such as when to make a highly rewarding risky rather than a less rewarding save decision, of course the classic Monty Hall problem is one of them,... Several British TV shows are scrutinized in this way. Most will not be familiar to non-British readers, but the situation is explained and the problem (usually involving probabilities) is clarified before a solution strategy is given.

The last chapter involves gambling: lottery, roulette, horse racing, and card games. Of course probability is here the main mathematical ingredient. For readers who are particularly interested in this chapter, I can recommend to read more on these sports gambling strategies in L.A. Math: Romance (J.D. Stein) although there it is framed in a bit more "playful" environment.

The book could be appealing to non-student-but-motivated-hobbyists, but I guess there are lighther and more amusing alternatives that are better suited. The content invites to really work on the topics that were presented. So for students and their instructors, this gives a wealth of ideas for practical sessions that are intended to work with the theory from the mathematics courses in a practical environment.

**Submitted by Adhemar Bultheel |

**13 / Mar / 2016