Publisher: Princeton University Press (2009)Details: 391 pages, Hardcover
Price: $29.95
ISBN: 9780691135403
Category: General
Topics: Mathematical Physics, Mathematics for the General Reader
Paul J. Nahin
Publisher: Princeton University Press (2009)
Details: 391 pages, Hardcover
Price: $29.95
ISBN: 9780691135403
Category: General
Topics: Mathematical Physics, Mathematics for the General Reader
[Reviewed by Henry Ricardo, on 10/18/2009]
I’ll need a larger thesaurus if I review any more books by Paul Nahin. Once again, he has written a gem of a book, this time a series of “discussions” of various ways in which mathematics and physics are “mutually dependent and mutually illuminating.” The author refers to this as the “mutual embrace.”
The press release from Princeton University Press refers to the author as a “best-selling pop-math author,” but Nahin’s books are not “mathematics for the masses.” Reading MPEQ with comprehension requires a solid understanding of mathematics and physics at the level of a first year science or engineering major at a good college or university. For example, in the Preface, the author poses the problem of showing that
is not zero for t in [0,1]. In total, there are thirty-five such Challenge Problems sprinkled throughout the book.
The Table of Contents reveals the breadth of Nahin’s discussions: Newtonian gravity, air drag, electrical engineering, Fourier series, the zeta function, and probability (both theoretical and Monte Carlo simulation). He provides helpful MATLAB code at various points of the book.
Chapter 13 (“Quilts & Electricity”) does not deal with thermal efficiency on a cold winter’s night. Rather, the author starts with a recreational problem popularized by Sam Loyd and later reproduced and given the name Mrs. Perkins’s Quilt by Henry Dudeney: A square quilt of 169 identical square patches is to be cut into a number of pieces which are themselves square by cutting along the stitch lines (i.e., no cutting through a patch). How can this be done in the fewest number of subsquares? Nahin traces generalizations of this problem up to the 1936-1938 joint work of four undergraduates at Trinity College, Cambridge, including William Tutte (then a chemistry major, eventually a distinguished professor of mathematics in Canada). These young men discovered a completely unexpected, intimate connection between the dissection problem and electrical circuit theory. Nahin illuminates this connection and comments (with a journal reference) that one application of the mathematical problem is the determination of the “best” way to place electronic circuitry on microchips.
Written in Nahin’s usual informal and humorous style (but with admirable rigor when appropriate), Mrs. Perkins’s Electric Quilt will delight all but the “absolutely pure experimentalists, covered with vacuum pump grease and proud of it,…and absolutely pure mathematicians, e.g., those who lust only for a one-page analytical proof of the four-color theorem, or of Fermat’s Last Theorem…” I suspect that even some of these extremists will be captivated by Paul Nahin’s wit and wisdom.
Henry Ricardo (henry@mec.cuny.edu) has retired from Medgar Evers College (CUNY) as Professor of Mathematics, but continues to serve as Governor of the Metropolitan NY Section of the MAA. He is the author of A Modern Introduction to Differential Equations (Second Edition). His linear algebra text will be published in October by CRC Press.