id: 06541819
dt: b
an: 2016d.00082
au: Haigh, John
ti: Mathematics in everyday life.
so: Cham: Springer (ISBN 978-3-319-27937-4/pbk; 978-3-319-27939-8/ebook). ix,
159~p. (2016).
py: 2016
pu: Cham: Springer
la: EN
cc: A80 M10 I70
ut: general mathematics; mathematical models in the life
ci:
li: doi:10.1007/978-3-319-27939-8
ab: 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.
rv: Irina V. Konopleva (Ul’yanovsk)