While I've been dutifully plugging away at copy edits for *The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse*, Jen-Luc Piquant has been hanging out over at Script Frenzy, which (among other things) randomly generates possible screenplay scenarios for the blockbuster movies of the future. How's this for an elevator pitch: "After crash-landing in the desert, a fallen angel hijacks a bus full of tae bo instructors." Or this: "While lost in a wormhole, a god of the underworld discovers a shocking use for spray cheese." I'm sure wackiness ensues on both counts -- and the one with the tae bo instructors should have some awesome fight choreography.

It's fun playing with Script Frenzy's random generator, but for now I'll leave the screenplays to Jen-Luc and stick with my writerly strengths. The good news is that we're moving into high gear for *The Calculus Diaries,* which will be published August 31. The copy edits are done (with galleys/ARCs imminent), the book has a rudimentary Amazon page, I set up a fan page for it on Facebook, and hey, there's even a nifty cover:

I love the roller coaster imagery with the math-y stuff overlaid (courtesy of the Spousal Unit). It's apt: The entire book is about making the real world your mathematical playground, whether you're shooting craps in Vegas, enjoying the rides at Disneyland (Space Mountain meets vector calculus!), turning your househunting adventure into a multivariable optimization problem, ruminating on Fourier transforms while learning to surf in Hawaii, or expounding on the calculus of the living dead. (Why yes, I'd be happy to show you the derivation for the coming zombie apocalypse. Wait! Come back! Just kidding! Although if anyone's interested, it's covered in Appendix 2.)

Since the book won't be out for a few months yet, I thought now would be an excellent opportunity to highlight some other good math-centric books out there that might appeal to a popular audience. So here's a sampling of books I really enjoyed, in authorial alphabetical order. Feel free to add your own in the comments! And also to buy these other books!

* Math and the Mona Lisa*, by Bulent Atalay. In this erudite-yet-accessible tome, Atalay goes where *The Da Vinci Code* feared to tread: away from paranoid conspiracy theories and into the realm of actual established fact. He explores phi, the "golden ratio," and its sibling, the Fibonacci series, in the context of the mathematical symmetries that can be found in math and art. From Publishers Weekly:

Physics professor Atalay uses as his touchstone Leonardo da Vinci, of whom he says in his prologue: "Had [da Vinci] been able to publish the scientific ruminations found in his manuscripts in his own time, our present level of sophistication in science and technology might have been reached one or two centuries earlier." This assertion sets the buoyant tone for the rest of the book. The author marvels at the symmetries to be found in art and the natural world, discussing the Fibonacci series (0, 1, 1, 2, 3, 5, 8...) and the golden ratio related to it designated by the Greek letter phi (1.618...) with illustrated examples ranging from da Vinci's three portraits of women to the Great Pyramid and the Parthenon.

* The Calculus Wars*, by Jason Bardi. This was one of several books I cite in my own bibliography: an eminently readable historical account of the knock-down, drag-out fight that ensued when Isaac Newton and Gottfried von Leibniz each claimed credit for inventing calculus Per Publishers Weekly:

Those interested in a lucid, nontechnical account of the battle between [Newton and Leibniz] over who invented calculus will welcome science writer and debut author Bardi's cautionary tale. As early as 1665, Newton composed a manuscript detailing his method of calculus with examples, but after his unpleasant experience with a 1672 paper on optics that aroused the ire of Robert Hooke, an eminent member of the Royal Society who accused the younger man of plagiarism, Newton became shy of publishing. Between 1672 and 1676, Leibniz independently discovered calculus, using notation that has since become standard. When Leibniz published his results, Newton's allies rushed to discredit Leibniz in what developed, in Bardi's words, into "the greatest intellectual property debate of all time." [...] Bardi provides a timeless lesson about human pride as he describes the series of misunderstandings and miscommunications that led to the clash between these two great minds, "perhaps the greatest of their day."

* A Tour of the Calculus*, by David Berlinski. This is pretty much the classic popular book on the subject, recommended to me by several regular commenters at the cocktail party. The prose can be a bit pedantic, unfocused, and overly florid at times, and some non-mathy readers won't care for the inclusion of equations in the text. (Once I really got into the calculus, I found his inclusion of the equations quite helpful, but as a casual reader, I probably would have skipped them.) There are some excellent explanations, some lovely turns of phrases, and one charming chapter on continuity using a stroll around the city of Prague as a metaphor. Berlinski later annoyed atheists with *The Devil's Delusion*, and wrote a follow-up calculus book I've yet to read: *Newton's Gift: How Sir Isaac Newton Unlocked the System of the World*. Here's a take on *A Tour of the Calculus*, courtesy of Booklist:

Even those who flailed through calculus class sense the power and perfection of that branch of mathematics, and Berlinski rekindles the interest of lapsed students in this pleasing excursion through graphs and equations. Berlinski's goal is to explain the mystery of motion and the area and volume of irregular shapes, issues that gave rise to Leibnitz and Newton's invention of calculus. He makes his points one concept at a time, but not so dryly as asking and answering, "What is a function?" No, ... Berlinski tangibly grounds the abstract notions, so that attentive readers can ease into and grasp the several full-blown proofs he sets forth, as of the mean-value theorem. Though the math-shy won't necessarily jump to the blackboard to begin differentiating and integrating polynomial equations, Berlinski's animated presentation should tempt them to sit forward and appreciate the elegance of calculus--and perhaps banish recollections of its exam-time terrors.

* The Unknowns: A Mystery*, by Benedict Carey. I met Carey last year when we were both instructors at the Santa Fe Science Writing Workshop (good times, y'all). He's a reporter with *The New York Times*, and happens to really like math, which is what inspired him to write this Young Adult novel about a couple of kids in a small not-quite-town called Adjacent (get it?) who must rely on mathematical clues to solve their hometown mystery. Per Booklist:

Math is the key to solving the mystery in this fast-paced adventure about a group of seventh-grade misfits who discover secrets surrounding the energy plant next to their trailer park. After their teacher disappears, the kids stumble across mysterious clues that she left behind. Di, Tom, and three more classmates band together, and their sleuthing takes them through claustrophobic man-made tunnels, secret underground workstations, and horrifying mountains of trash before they finally expose a team of powerful and corrupt grown-ups. Computers are part of the detective work: essential clues are on the teacher’s flash drive, and the details about how the kids crack the code and get the password will hook young readers. Science and math buffs will love the equations and charts, but even those bored by the technical details will be swept up in the fast talk and exciting action.

* The Unfinished Game: Pascal, Fermat and the 17th Century Letter that Made the Modern World*, by Keith Devlin. I found this book incredibly useful while writing my chapter on probability. I used the game of craps, courtesy of the New York, New York casino in Vegas, but Devlin's book provided some excellent historical anecdotes about how probability theory developed over the years (blame wealthy and titled patrons with gambling addictions -- even Galileo dabbled in the subject). Per Publishers Weekly:

Prior to the development of statistics in the late seventeenth and eighteenth centuries, even rationalists were convinced that no human could speculate on the future. Devlin ... shows us how that belief was transformed through the 1654 correspondence between mathematicians Blaise Pascal and Pierre de Fermat. Devlin uses the critical letter from Pascal to Fermat in which he discusses "the problem of points"-that is, how to determine the probable outcome of a game of chance-as a framework for a history of probability theory and risk management, fields which now dominate our social, political and financial lives. Devlin interweaves the specific issues discussed in that famous letter with the work of other mathematicians, like the London businessman John Graunt, whose ingenious, groundbreaking work analyzing London parish death records helped predict a breakout of bubonic plague and essentially founded the science of epidemiology. Devlin also introduces the remarkable Bernoulli family, eight of whom were distinguished mathematicians, and the Reverend Thomas Bayes, whose formula has enabled the calculation of risk in a variety of fields.

* The Numbers Behind NUMB3RS: Solving Crime with Mathematics*, by Keith Devlin and Gary Lorden. It won't surprise regular readers to know I'm a huge fan of the TV series, *Numb3rs*. In fact, one of my very first blog posts at the cocktail party reported on a AAAS session on *Numb3rs*, featuring co-creators Cheryl Heuton and Nick Falucci, and star David Krumholtz. Don Eppes (Rob Morrow) is a practical-minded FBI agent intent on catching the bad guys by any means necessary to ensure the safety and security of America and its citizens. Charlie Eppes (Krumholtz) is the quintessential absent-minded professor, a mathematical genius whose precociousness earned him tenure at a prestigious California institute -- loosely based on CalTech -- at the ripe old age of 26. The two brothers are repeatedly thrown together when Charlie's math skills turn out to be critical to helping Don solve the crime *du jour*. In the process, they develop a growing appreciation for their respective strengths, and realize how well they complement each other.

Devlin teams up here with one of the show's technical consultants, Caltech's Gary Lorden, to explore some of the underlying mathematical concepts in more detail than can be realistically achieved in the weekly episodes. It's an entertaining and engaging read. And hey, if you're not already a fan, why not check out Seasons 1 through 5, now available as a DVD boxed set? Surely you could spare a couple of weeks for marathon viewing sessions.

* Logicomix: An Epic Search for Truth*, by Apostolos Doxiadis. The science blogosphere started raving about this book last year (at least that's when it crossed my consciousness), and the Spousal Unit has been hoarding our household copy, so I haven't had a chance to read it yet. But the Spousal Unit loved it, and so does pretty much anybody else who enjoys this sort of thing, so I have high hopes for the reading experience. Per Publishers Weekly:

An ambitious full-color exploration of the life and ideas of philosopher and mathematician Bertrand Russell, the book meticulously interconnects Russell's life, the timelessness of his ideas and the process of creating the book. While a comic about the quest for the foundations of mathematics may seem arduous, it is engrossing on many levels; the story moves, despite heavy philosophical and technical information, as the images, dialogue and narration play off each other. ... One of the most prominent themes is the conflict and symbiosis between madness and logic. The fear of madness haunts Russell because of childhood trauma, as he neurotically pushes himself toward what he conceives of as its opposite, a system for certainty. Inventive, with both subtle and overt narrative techniques, the comic form organizes the complex ideas into a simpler system, combining to form a smart and engaging journey through the ambiguity of truth.

* The Complete Idiot's Guide to Calculus*, by Michael W. Kelley. Okay, this is less of a popular book and more a supplementary textbook to help high school students get through calculus, and it's definitely not for rank beginners. Frankly, when I first dipped a toe into the murky waters of the subject, Kelley's book was a bit beyond me; he might want to re-title it *The Half-Wit's Guide to Calculus*. But once I got the basic concepts down and needed to seriously start grappling with the actual math, this book proved an invaluable resource. And I just discovered that Kelley has another book called *The Humongous Book of Calculus Problems for People Who Don't Speak Math*. According to the jacket copy: "The best-selling author of *The Complete Idiot’s Guide to Calculus *has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear." Huzzah! I just ordered it myself.

* The Manga Guide to Calculus*, by Hiroyuki Kojima. This is just one in an entire math and science series from No Starch Press. From the book jacket: "Noriko is just getting started as a junior reporter for the Asagake Times. She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye." Of course, Noriko soon figures out that calculus isn't for math nerds anymore: she use it to understand patterns in the real-world that are relevant to the hard-hitting journalist she aspires to do (probability, supply and demand curves, even the density of a Japanese liquor known as Shochu). I had a lot of fun perusing this book. If *The Calculus Diaries* has a manga soul mate out there, this could definitely be a contender. If only it had been written by a fellow mathephobe....

* The Golden Ratio*, by Mario Livio. I read this in conjunction with Atalay's book above, since taken together they tell you everything the lay reader needs to know about the golden ratio. From Publishers Weekly:

Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Livio carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls "Golden Numberists." This is an engaging history of mathematics as well, addressing such perennial questions as the geometric basis of aesthetic pleasure and the nature of mathematical objects. Useful diagrams and handsome illustrations of works under discussion are amply provided.

* Math Doesn't Suck* and *Kiss My Math*, by Danica McKellar. The actress best known as Winnie from *The Wonder Years* is also an accomplished mathematician, and a few years ago she decided to share her hard-earned wisdom with young girls who might be struggling with (or afraid of) their math classes. The first covers the basics of middle school math (fractions, decimals, percents and so forth), while *Kiss My Math* helps prepare girls for pre-algebra, and I believe she has a third book on algebra proper due any day now. McKellar has been criticized in some circles for her unapologetic, blatantly "girly" approach to all things math: her examples focus on shopping ("You can never have too many shoes"), boy troubles, sharing with siblings, even a math "horoscope," along with *Cosmo*-style personality quizzes. But the criticism is a little unfair: I have teenaged nieces and believe, McKellar is speaking their language, plus she offers her own personal stories and those of other girls to serve as role models/inspiration. Buried amidst all that sugar is quite a lot of practical mathematical advice. I originally bought the books for my nieces, but despite the deliberately juvenile tone, *Kiss My Math*, in particular, actually turned out to be useful when I had to sharpen my own sadly atrophied algebra skills (along with geometry and trig) in preparation for delving into calculus. Everything we learn in math class is supposed to be prepare us for calculus and beyond, after all. I can't wait for McKellar's take on calculus.

* The Drunkard's Walk*, by Leonard Mlodinow. Probably one of the most readable accounts of randomness, probability, statistics, and so forth you're ever likely to encounter. Mlodinow makes the mathematical concepts crystal clear, even to a reader like me, whose eyes tend to glaze over then things get too technical. That's probably because he tells such terrific stories. This book has one of the most detailed and colorful accounts of Cardano, who invented the concept of the sample space, for example, as well as an excellent summary explication of the problem of points (the focus of Devlin's *Unfinished Game*). Per Publisher's Weekly:

Mlodinow, a visiting lecturer at Caltech ... leads readers on a walk through the hills and valleys of randomness and how it directs our lives more than we realize. Mlodinow introduces important historical figures such as Bernoulli, Laplace and Pascal, emphasizing their ideas rather than their tumultuous private lives. Mlodinow defines such tricky concepts as regression to the mean and the law of large numbers, which should help readers as they navigate the daily deluge of election polls and new studies on how to live to 100.

* Innumeracy* and *A Mathematician Reads the Newspaper*, by John Allen Paulos. Paulos is a professor of mathematics at Temple University, as well as a regular contributor to such esteemed publications like *The New York Times* and *Newsweek. Innumeracy,* first published in 1988, is his *j'accuse* to a public he feels has remained too long ignorant to math, and indifferent about their own ignorance. And you know, it's a valid point. He can be a tad bit curmudgeonly at times, but it's usually with a wryly humorous twist. Per the jacket copy:

Why do even well-educated people understand so little about mathematics? And what are the costs of our innumeracy? John Allen Paulos argues that our inability to deal rationally with very large numbers and the probabilities associated with them results in misinformed governmental policies, confused personal decisions, and an increased susceptibility to pseudoscience of all kinds. Innumeracy lets us know what we're missing, and how we can do something about it. Sprinkling his discussion of numbers and probabilities with quirky stories and anecdotes, Paulos ranges freely over many aspects of modern life, from contested elections to sports stats, from stock scams and newspaper psychics to diet and medical claims, sex discrimination, insurance, lotteries, and drug testing.

The second book is Paulos' "irreverent investigation of the often faulty use of statistics and fact in newspaper articles." If you're one of those people who groans inwardly and experiences repeated "face palm" moments when perusing your daily paper or watching broadcast news, Paulos is a kindred spirit. But you know, being a mathematical smarty-pants didn't save him from losing a bunch of money in the stock market. He learned from the experience, though, and the result is yet another book, published in 2004, that is probably also worth a gander:* A Mathematician Plays the Stock Market*.

* Zero: The Biography of a Dangerous Idea*, by Charles Seife. I've known Seife for more years than I care to admit, since we were both regularly covering meetings of the American Physical Society. This book is proof that lightning can strike on a science writer's first foray into book writing. It's well nigh flawless (and garnered a PEN award as evidence of that perfection): clear, succinct yet elegant prose laying out the history of the number 0, why it's so important, and most importantly, why the non-scientific among us should care. One of the first books I ever read that made me want to know more about the fascinating history of math. Per Publishers Weekly:

Seife takes readers on a historical, mathematical and scientific journey from the infinitesimal to the infinite. With clever devices such as humorously titled and subtitled chapters numbered from zero to infinity, Seife keeps the tone as light as his subject matter is deep. By book's end, no reader will dispute Seife's claim that zero is among the most fertile--and therefore most dangerous--ideas that humanity has devised. Equally powerful and dangerous is its inseparable counterpart, infinity, for both it and zero invoke to many the divine power that created an infinite universe from the void. ... In addition to offering fascinating historical perspectives, Seife's prose provides readers who struggled through math and science courses a clear window for seeing both the powerful techniques of calculus and the conundrums of modern physics: general relativity, quantum mechanics and their marriage in string theory. In doing so, Seife, this entertaining and enlightening book reveals one of the roots of humanity's deepest uncertainties and greatest insights.

* The Witch of Agnesi*, by Robert Spiller. This is part of a series of murder mysteries by Spiller, a math teacher turned novelist; other titles include *A Calculated Demise: The Hypatia Murders* and *Irrational Numbers*. His protagonist is Bonnie Pinkwater, a widowed high school math teacher who finds herself getting involved in investigating murder after murder in tiny East Plains, Colorado. There's not a whole lot of mathematical discussion in these, but there is a bit of math-y history, and Pinkwater is a terrific, feisty character. My only quibble is after three books (with more on the way), it kind of strains credibility that such a small town has such a high murder rate. The corpses keep piling up, and sometimes they are the corpses of Pinkwater's young students.

* Quicksilver*, by Neal Stephenson. Book 1 in Stephenson's justly lauded Baroque Cycle. *Snow Crash* remains my all-time favorite Stephenson novel, but this one might run a close second. How can you go wrong with a riveting historical thriller/mystery centered on who gets credit for inventing calculus? It's a weighty tome, and a firmer editorial hand would have helped some of the more cloying sections, but on the whole, it's an impressive achievement, and I have every intention of reading the other two books in the cycle, once my insane schedule permits. Per the Amazon review:

The novel, divided into three books, opens in 1713 with the ageless Enoch Root seeking Daniel Waterhouse on the campus of what passes for MIT in eighteenth-century Massachusetts. Daniel, Enoch's message conveys, is key to resolving an explosive scientific battle of preeminence between Isaac Newton and Gottfried Wilhelm Leibniz over the development of calculus. As Daniel returns to London aboard the Minerva, readers are catapulted back half a century to recall his years at Cambridge with young Isaac. Daniel is a perfect historical witness. Privy to Robert Hooke's early drawings of microscope images and with associates among the English nobility, religious radicals, and the Royal Society, he also befriends Samuel Pepys, risks a cup of coffee, and enjoys a lecture on Belgian waffles and cleavage-—all before the year 1700. In the second book, Stephenson introduces Jack Shaftoe and Eliza. "Half-Cocked" Jack recovers the English Eliza from a Turkish harem. Fleeing the siege of Vienna, the two journey across Europe driven by Eliza's lust for fame, fortune, and nobility. Gradually, their circle intertwines with that of Daniel in the third book of the novel.

* Geek Logik*, by Garth Sundem. This is one of those one-off whimsical humor books, but in the case of *Geek Logik*, Sundem wants to show people like me how to use the principles of basic algebra to "take the guesswork out of life" -- and foster critical thinking skills. I found it quite helpful, actually, because one of the trickier aspects of writing *The Calculus Diaries* was figuring out how to translate my real-world questions into the more rigorous form of a mathematical equation. Sundem uses humor to show you how to do this for questions like, "Should I call in sick," "Should I join a gym," "Do I have a snowball's chance in hell with her," and "How many beers should I have at the company picnic?" (Regarding the latter, the Spousal Unit and I seriously discussed including a segment on the calculus of inebriation -- but then we got, um, distracted by the experiment involving lots of cocktail sampling and wine tasting. We suspect it would take the form of an exponential decay curve, though.) Apparently you can even devise an algebraic equation to determine whether or not to get a tattoo. Bonus: there's a little working calculator embedded in the cover. Sundem followed up with *The Geek's Guide to World Domination: Be Afraid, Beautiful People*.

And there you have it: lots of lovely reading material to keep you busy until *The Calculus Diaries* comes out in the fall. It's a math, math, world out there, people, with numbers and geometry to be found everywhere in nature, as this gorgeous movie by Cristobal Villa (via Eterea Studios) makes clear:

I would add Loren Graham's lovely little book- Naming Infinity- about set theory and Russian religious mysticism in the 19th and 20 th century

Marvin

Posted by: marvin thalenberg md | March 28, 2010 at 11:31 PM

I'd add that it is worth reading almost anything by Marcus du Sautoy. Says Amazon: "Marcus du Sautoy has been named by the Independent on Sunday as one of the UK's leading scientists, has written extensively for the Guardian, The Times and the Daily Telegraph and has appeared on Radio 4 on numerous occasions. In 2008 he was appointed to Oxford University's prestigious professorship as the Simonyi Chair for the Public Understanding of Science, a post previously held by Richard Dawkins" and "Mesmerising, articulate, fluent, funny and personable, [du Sautoy] is also absolutely passionate about mathematics, with a burning desire to make the rest of us as excited as he is about its problems, its patterns and its beauty." I especially enjoyed Finding Moonshine: A Mathematician's Journey Through Symmetry.

Posted by: Keith | March 30, 2010 at 03:24 AM

you've left out many of my favorite math writers: Keith Devlin, Martin Gardner, Clifford Pickover, Calvin Clawson... and my single favorite book, "How Mathematicians Think" by William Byers

Posted by: Arj | March 30, 2010 at 08:27 PM

...my baaaad... you've got Devlin in there, just not the particular volumes of his I most enjoy!

Posted by: Arj | March 30, 2010 at 08:29 PM

Great post! Just a small comment, I share your view on Stephenson's 'Snow Crash', but calling 'Quicksilver' his 2nd best? Did you miss 'Cryptonomicon'? atb :: lieven.

Posted by: lieven | April 29, 2010 at 12:17 PM