
06109138
b
2015b.00758
Bindner, Donald
Erickson, Martin J.
Hemmeter, Joe
Mathematics for the liberal arts.
Hoboken, NJ: John Wiley \& Sons (ISBN 9781118352915/hbk; 9781118371787/ebook). xii, 411~p. (2013).
2013
Hoboken, NJ: John Wiley \& Sons
EN
I15
F15
A30
history of mathematics
mathematics for nonmathematicians
calculus
number theory
This very nicely written text provides a concise introduction to mathematics history and an easily accessible overview of some fundamental mathematical concepts. Presented in the first part ``an overview of the history of mathematics" can be successfully used as an independent text for the corresponding course, as well as an excellent source of complementary historical information for a wide range of an undergraduate mathematics courses. Starting with mathematics of the ancient world, Chapters 1 to 3 cover Middle Ages, the Renaissance and conclude with the recent developments. Contrary to many texts on the history of mathematics, this book has a great deal of nicely selected exercises illustrating mathematical concepts and ideas relevant to historical environment at the time they were introduced. The second, mathematical part of the text covers two areas of mathematics selected by the authors as major  calculus and number theory. The way fundamental mathematical concepts are introduced definitely suits the purpose of teaching liberal arts students. Chapter 4 (Calculus) starts with the explanation of physical and geometric meanings of the derivative of a function, continues with the formal differentiation rules leading to applications in optimization and economics. The concept of Riemann integral is then introduced and some of its properties and applications are studied. Special attention is paid to the analysis of the exponential growth and its important applications in reallife problems. Infinite sums are discussed in the end of this chapter. The topics explored in Chapter 5 (Number theory) include divisibility, irrational numbers, greatest common divisors, primes, relatively prime integers, Mersenne and Fermat primes. The fundamental theorem of arithmetic, Diophantine equations, Pythagorean triples, modular arithmetic, congruences and Fermat's last theorem are also briefly discussed here. The reader will find in the end of the book two appendices with answers to selected exercises, suggestions for further reading, as well as useful index. This book is warmly recommended both as an informative text on history of mathematics and as a delicate introduction to mathematics for liberal arts students.
Yuriy V. Rogovchenko (Kristiansand)