Archive for the 'Mathematics' Category

A Tour of the Calculus, by David Berlinski

SEL Books: QA303 .B488 1995

I wish my instructors had assigned this book those many years ago when I was taking calculus. My grades may have risen above C’s. I learned to take derivatives, but I never really understood the concepts behind the formulas I was working.

If reading a book on calculus sounds dry and dull, you may be pleasantly surprised. This book is written for the general public. And aside from his acumen in mathematics, Berlinski is a gifted writer. Don’t take my word for it; read a bit of his prose for yourself:

Before the seventeenth century, everything is squid ink and ocean ooze and dark clotted intuitions; but afterward, a strange symbolic system erupts into existence and floods the intellectual landscape with a hard flat nacreous light. Communing with the powers of the night and the dark undulating rhythms that flow across the sky, the mathematician—of all people!—emerges as the unexpected master of those symbols, the calculus his treasure chest of chants and incantations, fabulous formulas, wormholes into the forbidden heart of things.

This book combines a history of calculus with a primer on its concepts. Aside from the Appendix, which contains proofs, the book contains few formulas and a few graphs. It is full of stories used to illustrate otherwise difficult concepts.

It is that most wonderful of textbooks—one that conveys a lot of useful information and entertains along the way.

(Originally published in Connections, May 2006)

Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age, by Steven Levy

SEL Books: QA76.9.A25 L49 2001

This book immerses you into the world of codes, code-breaking, and encryption. Though it is a non-fiction, investigative work, Crypto reads like a novel. It is a compelling and enjoyable read.

What the author accomplishes here is to convey not only how fascinating is the tale of encryption, but also to emphasize the importance of it in our daily lives. What is at stake here is no less than the protection of our personal and collective data. As we become increasingly dependent on the Internet, we become increasingly vulnerable to theft—both financial and personal. I heard recently that identity theft reached an all-time high in 2005, and that data thefts from large, ostensibly secure, organizations is on a steep rise.

While this book is not a primer for protecting yourself, it certainly succeeds in explaining the importance of encryption in our lives. It does so by entwining several branches of the story—a history of encryption, Whitfield Diffie’s personal battle to protect individual’s personal data, and the fearless battle of a number of code rebels to wrest encryption from the government in order to protect individual privacy.

This is a wonderful book about an important subject. I’d place it on the shelf labeled “Must Read.”

Steven Levy also wrote Insanely Great: The Life and Time of the Macintosh, the Computer that Changed Everything (SEL Books: QA 76.8 .M3 L487 1994).

(Originally published in Connections, January 2006)

Innumeracy : Mathematical Illiteracy and Its Consequences, by John Allen Paulos

SEL: Books QA 93 .P38 1988

Illiteracy is a huge issue in America, but what about innumeracy? This book was published in 1988, yet today it is as relevant as ever. Our confused responses to numbers result in much more dire consequences than low scores on a grade report. Widespread innumeracy leaves us vulnerable to clever statistical manipulations by politicians, interest groups and the media. And misunderstanding numbers results in panic about statistically negligible dangers (terrorism) while we neglect protecting ourselves from less terrifying but more probable dangers (heart disease). The book is short (135 pages) and easy reading; and you’ll thank yourself for reading it during your next encounter with the news media.

The Central Library collection has a few more books by John Allen Paulos that I haven’t yet read, though I certainly intend to read everything by this entertaining and enlightening author. A Mathematician Plays the Stock Market (Central: HG4515.15 .P38 2003), I Think, Therefore I Laugh : An Alternative Approach to Philosophy (Central: BC 71 .P38 1985) and Mathematics and Humor (Central: PN6149.P5 P3).

I have also read and recommend two more books by Dr. Paulos that are not available at UTA. A Mathematician Reads the Newspaper, which reveals the ways statistics are used (and abused) in the media and how we can educate ourselves to read between the lines, and Once Upon a Number : The Hidden Mathematical Logic of Stories, which connects numbers and narrative, illustrating how stories contain numeric logic and how numbers are meaningless without some sort of narrative to give them context.

(Originally published in Connections, April 2005)

Mind Over Matter : Conversations with the Cosmos, by K.C. Cole

SEL: Books Q162 .C584 2003

This book is a collection of columns by LA Times science writer K.C. Cole. Each essay discusses current scientific issues and philosophies in relation to topics like politics, art, literature, and daily living.

Cole captures the essence of how science and mathematics play an important role in our everyday lives. Scientific chapter titles like “Eclipse,” “Calibrations,” “Patterns,” “Resistance” and “Time” live adjacent to the more esoteric “Beethoven and Quantum Mechanics,” “Love and Bosons,” “Play” and “Apocalypse Soon.”

I have also read and recommend two more books by K.C. Cole: The Universe and the Teacup : The Mathematics of Truth and Beauty, (SEL: Books QA 36 .C65 1998), which reveals how integral mathematics is in our everyday lives, and The Hole in the Universe : How Scientists Peered over the Edge of Emptiness and Found Everything (not available at UTA), which contains the fascinating history of the concept of nothing—the vacuum, the void, and the number zero.

Also by Cole in the UTA collection is Sympathetic Vibrations: Reflections on Physics as a Way of Life, (SEL: Books QC 21.2 .C62 1985).

(Originally published in Connections, March, 2005)