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Mathematics in Civilization

H. L. Resnikoff and R. O. Wells
Dover Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Underwood Dudley
, on

In 1973, when this book was first published, the number of courses with titles like “Mathematics for the Liberal Arts” was at or near a relative maximum, as was the number of textbooks for them. Both numbers subsequently declined, but I think that they have increased from whenever their post-1973 relative minimums occurred.

I haven’t kept up with the field, so I went to Google to see what was happening. The first mathematics for the liberal arts textbook that I found had three authors, more than 1000 pages of text, and a retail price in excess of $200. Its first chapter was on sets, its second was on logic, and a later one was on systems of linear equations and inequalities. Its table of contents looked ghastly and I have pity for the students who have had to undergo the unliberating experience of having to plow through it, even though homework can be done online. It is in its eighth edition!

I was so dispirited that I looked no further, though there are (there must be) better texts. The one by Resnikoff and Wells is superior by at least 1.5 orders of magnitude, and maybe more. The question is, is it still useful as a text?

Like other living things, textbooks are born, flourish (or not), and die. Their lifetimes are typically short, though some exceed the mean by several standard deviations. G. B. Thomas’s Calculus, born in 1952, still carries on, though it has become a brand, or an industry, with at least three other authors at one time or another supplying life support. Birkhoff and Mac Lane’s A Survey of Modern Algebra (1941) has slipped below the one millionth place on Amazon’s list of best sellers but has not yet passed away.

Resnikoff and Wells ranks even lower on Amazon than Birkhoff and Mac Lane and so it may be old, wrinkled, and feeble before its fiftieth birthday. The reason is that fashions change. Resnikoff and Wells has long sections on navigation and cartography. I found them fascinating, but the subjects are no longer in style. The book contains quite a bit of calculus. One of the purposes of liberal arts courses these days is to avoid calculus.

There are problems, many of them good. (The population of Houston is increasing more rapidly than the population of the United States. If the rates of increase don’t change, when will the population of Houston be equal to the population of the US? Will the rest of the country then be empty?) There are solutions, to both odd and even numbered ones, in the back.

There are fifty pages of supplements “to include events in mathematics since 1985” but contain, since the book is not a history book, only a few more miscellaneous topics and a picture of an obsolete Hewlett-Packard pocket calculator. They also contain typographical errors (one page has two of them) and inconsistencies — single quotes instead of double quotes, mathematicians’ names in small capitals — that a copy editor should have taken care of.

The authors write well, present an amazing amount of information (including a family tree of thirteen mathematical Bernoullis — how many can you name?) and assume familiarity with, though not necessarily great facility in, algebra, including logarithms, and trigonometry. The book is, I think, still usable as a text, though it would take an instructor of strong will and self-confidence to adopt it and fly in the face of current fashion.

Even if its days as a text are over, the book is well worth reading for its own sake. People other than students in courses can stand to have their horizons broadened, and Mathematics in Civilization can do it. Dover Publications deserves credit for keeping it before the public.

Woody Dudley used to teach, in the days when this book first appeared, a section of the Mathematics in the Liberal Arts course now and then. It was fun, but students discovered that it didn’t satisfy any requirements and it disappeared from the curriculum.

The table of contents is not available.