These are brief notes on an eclectic set of books--suitable for high-school and gifted middle-school students-- that I think will interest my friends and math / science teachers (the categories are not mutually exclusive). This list consists of books I happened to run across in my unsystematic search for good reads. None of them are textbooks, but almost all are useful for enrichment material. I have not hesitated to mention a few clinkers to avoid. Adult science and math aficionados will also enjoy most of them (you are an aficionado, I am a junkie).

Only abbreviated references are given (author, title) since with today's computers, it is very easy to find the rest of the information--including the price if the book is currently available. Try Amazon.com, for example, or your own library's computer. I do not think year of publication is important in determining the value of a book; many of the old or middle-age ones are unjustly forgotten in the spate of new releases. The books reviewed here range from the middle 1800s to manuscripts I've read in preprint and which are just coming out.

Faraday, Michael. The chemical history of a candle

Yes, THE Michael Faraday. With a preface by William Crookes (yes, that William Crookes). Written in 1861, this book is as delightful today as it must have been then. He gets a prodigious amount of basic science out of some relatively simple and rather clear experiments, many of which are readily duplicated. Topics such as the products and nature of combustion, that water is made of hydrogen and oxygen, and many others are touched on and well-illuminated (by candlelight).

Boys, C.V. Soap Bubbles and the forces which mould them

Today's students may not topple with laughter when the experiment requires the author to tip a candle so that "the falling grease will just fall on the edge of the candlestick and splash on to the carpet" because our students have not been taught, from an early age, that one must always hold a candle upright and to never spill candle wax on the carpet. On the other hand, it is at just this angle that the shadow of the base of the candlestick makes a parabola on the wall. Even if not all the humor survives from 1902, the cleverness, directness, and simplicity of the experiments and the wealth of science they uncover are undimmed. A delightful book, scant in page count and easily digested.

Bitter, Francis. Magnets, The education of a physicist.

Bitter writes, "Let me tell you something of what I learned, and why it fascinated me." And he does, with charm and at a level that youngsters can follow. Bitter (after whom the magnetics lab at MIT is named) made many fundamental discoveries about magnetism, but his career was varied. We read of the earth's magnetic field, how he helped keep magnetic mines from blowing up ships in World War II, and of the magnetism of the nucleus of the atom. This is a small book, dated 1959, quickly read, but rich in personality and well-presented science.

Casti, John. Five golden rules

A look at some major issues in modern mathematics. Only for the very talented student who wants to strike out beyond the normal course matter, it is readable because it mostly talks about some very exciting mathematics rather than actually having the math there. Covers the minimax theorem of game-theory fame, the Brouwer fixed-point theorem (topology), and the Halting problem, among other topics. Also good for teachers who want a feel for some major mathematical developments of the 20th century, in case some bright kid asks.

 Dewdney, A.K. 200% of nothing

John Allen Paulos popularized the term "innumeracy" and a number of books have followed showing the consequences of not understanding basic mathematics (including Paulos's own "A mathematician reads the newspaper"). This is the best and most readable of those I've seen. A math-grokking sixth-grader will find little over her head here. Especially good for parents. Students who like to critique what they see and read will get lots of ammo here, ammo especially useful for shooting down specious advertising claims.

 Dewdney, A.K. Yes, we have no neutrons

One of the best ways to get to understand something is to see how it fails. In solving problems we look for edge conditions, and we only learn how strong a toothpick is by breaking a few. Dewdney helps us understand sound science by looking at broken science; not confusion but cold fusion; not fraud but Freud. He tells the tales well, the book is entertaining, and the overall picture of science as a self-correcting enterprise is well presented. "Yes, we have no neutrons" is a good book to read alongside of all those stories where the end result is a Nobel prize, rather than an ignoble footnote. Students will love the way the good guys trip up the bad guys.

Stein, Sherman. Strength in Numbers

A very good book on various empowering mathematical topics. The book strays a bit much into questions of pedagogy for the young student, but there are many chapters that, taken by themselves, make great short readings. The book is well-written, requiring no math background beyond the most elementary of algebra and some comfort with exponents, and perhaps a bit more than that toward the end of the book (but, of course, you are going to use only selected chapters). A few elementary proofs are presented very clearly, and their impact is explained. My favorite part is where Stein shows that lots of great art and the pyramids etc. were not based on the golden ratio, as is so often claimed. I argued that very point in class once to a teacher who believed otherwise, and who couldn't follow my statistical demonstration. If only I'd had this book then. Small oops: the St. Louis arch is not a catenary.

 Peterson, Ivars. The jungles of randomness

A set of loosely connected essays on various mathematical (and sometimes non-mathematical) topics that is simple in its approach and comprehensible in its treatment of randomness, chaos, gambling, and the like. By chance (so to speak), the preprint of this book arrived when I was working with two seventh-graders building electronic oscillators. However, the oscillators tended to lock onto certain relative frequency pairs. The book's chapter on coupled oscillators, whether mechanical, electronic, or even thousands of fireflies in the jungle, was just the explanation they needed.

 Trefil, James. A scientist at the seashore

Covering tides and many other littoral phenomena, both physical and biological, the book will help the young reader better understand waves, how sailboats work, and other topics about where solids and liquids meet on our planet. Most of the book is fine, unfortunately, chapter 11 is very wrong: Trefil just does not understand lift and even gets the direction a ball turns due to its spin wrong (complete with an explanation of why it has to be the way he says it is!). I look forward to having some students read this chapter and then try to explain why a spinning ball (a beachball makes the effects clearly visible in class) turns the "wrong" way. This chapter is valuable as an object lesson that you can't believe everything you read in books, you've got to keep a scientist's skeptical eye open at all times.

 McMahon, Thomas and Bonner, Tyler. On size and life

Reminiscent of the classic "On growth and form" by D'arcy Thompson (still very much worth reading!) but moving from biology (of which there's still lots) into other realms, this well-illustrated book is a fascinating read. The effects of size on antelope, saxophone, bridge, dragonfly, and clock are all discussed. Yes, a very few differential equations are shown, but the exposition does not depend on your understanding them. After all, this is a Scientific American book, and very few Americans, scientific or otherwise, get along with equations, differential or otherwise. So tell your students to skip the rare harder math, follow the easy math, understand the graphs, and look at the pretty pictures.

 Sagan, Carl. The demon-haunted world

I got a catalog in the mail that advertised a silver bracelet that can "eliminate harmful positive ions and guide helpful negative ions into your body" as well as "keeping you safe from dangerous electromagnetic fields (EMF)". A science fair project at a school for the gifted began, "Since homeopathy is a precise science..." Aside from daily injections of articles from the Skeptical Inquirer, few readings are as likely to be as helpful to weeding the mind of the sprouts of superstition as this one. Sagan takes a temperate tone and a moderate stance when it comes to religious issues, the book is not likely to offend any but the most extreme fundamentalists. "The demon-haunted world" is a long book, but most of the chapters can be read independently. The chapter "The fine art of baloney detection" is especially useful for its list of ways people argue illogically.

Gonick, L. and Huffman, A. The cartoon guide to physics

Physics presented with a sugar coating. Some subjects are treated more deeply (or, should I say, more shallowly) than others, but all are treated with care and accuracy. Not a text, but a fine supplement. Who knows, it might reach someone that more conventional approaches don't. And for the student who likes physics, or the adult who wants to brush up on basic terms and principles, it makes a fine, quick overview. And it's fun (which is what the authors were trying for).

 Guy, Richard and Woodrow, Robert, editors. The lighter side of mathematics

For the very advanced student or adult who knows how to work through a math book, this one looks into a few interesting topics in some depth. I found it was not as light as its title hinted. Nonetheless, some of the games presented can be profitably studied (or at least enjoyed) by fifth-graders and up, and the analyses of Escher's tessellations are accessible. And even where the proofs at the ends of articles may be difficult and the terminology esoteric, the problem statements are often elementary and can be happily explored by kids. If nothing else, a math teacher will be able to extract ideas useful for class and individual enrichment.

 Blatner, David. The Joy of Pi

Stories and lore of pi. There are better books on the subject, but this one is small, colorful, and informal. And it does tell a few tales (some from non-Western mathematics and some of which it accurately labels as apocryphal) that are not well known. The back of the book tells it like it is, "breezy narratives tell the history of pi and the quirky stories of those obsessed with it." [Available December 1997]

 Pullum, Geoffrey. The great Eskimo vocabulary hoax

Why do I not capitalize the important words in the book titles in this list? Read this book. This book is very, very funny. It is also quite educational about the nature of language, and very sane. It would probably be appreciated best by adults, since the humor is sophisticated (not ribald). I wish it had been three times as long. At least. The essay on the Eskimo vocabulary hoax is a good example of why you should go to primary sources, recommended for middle school and up. The chapters, originally published as columns in a linguistics journal, are quite independent, and the teacher can pick and choose.

 Dupre, Lyn. Bugs in writing

How often does a book come along that has you laughing out loud as it improves your writing, especially of technical and scientific material. How often does a book on writing come out aimed at scientists, mathematicians and computer specialists in the first place? How often does a book on grammar keep you turning the pages from pleasure? Never, you say? Then get this one. It is organized into small sections, very useful for the teacher, since the sections can be read as needed to help cure specific bad writing habits. Indeed, Dupre recommends you use the book this way. Splendid.

 Bruce, Colin. The strange case of Mrs. Hudson's cat

Surprisingly good as a pastiche of the Canon; Holmes, Watson, Mycroft and the usual gang explore some "science mysteries" in a readable account. It is not a bad way to tackle a bit of classical physics, and a pretty good way to examine a few of the paradoxes of quantum mechanics and special relativity. Totally devoid of mathematics, it is an easily read, thought-provoking book. The student should, however, be familiar with Holmes's modus operandi from having read Sir Arthur Conan Doyle's original. If the student is already a Holmes fan, this is a natural.

Aldersey-Williams, Hugh. The most beautiful molecule

An extremely well-written and engaging account of the discovery of C60, buckminsterfullerene, the soccer-ball-shaped molecule consisting of 60 carbon atoms. The book looks at the discovery, the personalities (without being sensational, a welcome change from the usual), the molecule, the science, the scientific milieu, and the ensuing technology. Occasionally, toward the end of the book, the author slips and expects more background than a school-age reader might usually have, but for most of the book everything is introduced and explained properly before it is used. Hard to put down once you've started. Not only good science, but a fine book per se. As a writer, I'm almost jealous.

 Wilson, Edward. Naturalist

Edward Wilson's autobiography. Wilson's fabulous work on ants is well-known and he has two Pulitzer prizes. Given that background, one would expect a great autobiography and here it is. Very non-technical and full of youthful adventure and the overcoming of adversity, it will attract the non-science-oriented student as well as the budding entomologist.

 Huxley, Thomas. On a piece of chalk (Scribners, 1967)

I give some information on the edition because it is a handsome book that is a pleasure in itself. Huxley, Darwin's contemporary and most prominent defender, draws his piece of chalk across the blackboard of geologic history to explain the origins of the chalk itself (as the skeletons of uncounted billions of Foraminifera) and to defend the then-nascent theory of natural selection. The defense is based on the physical evidence found in the chalk beds that form the famous white cliffs of Dover. The writing is clear and direct. This is a very accessible book, and a delight.

 Weaver, Jefferson. The world of physics

This three-volume set advertises itself accurately as "a small library of the literature of physics from antiquity to the present". From the pre-Socratic Greeks to Einstein and beyond, and not (for once) neglecting non-Western sources, this well-selected collection should be available to every science class, and is a worthy candidate for a school library. I found it fun to read: There were brief gems, many by famous scientists about their own work, I had never read--and should have.

 Ord-Hume, A.W.J.G. Perpetual motion, the history of an obsession

The fun part here is when students try to figure out why the many gadgets illustrated didn't work--or try to invent perpetual motion machines of their own. A nice segue into the conservation of energy, friction, entropy, and such. Mr. Ord-Hume is a bit shaky on his physics here and there even if he comes out on the right side of the perpetual motion issue.

 Harré, Rom. Great scientific experiments

From Aristotle's observation of the embryology of the chick, to Gibson on perception, to Thompson's discovery of the electron, 20 historically important experiments are described. This is a very good introduction to the importance of experiment in science. It reads well and is suitable for middle-school students and up. As with so many of these books, I found it enjoyable adult reading.

 Gardner, Martin.

All of his books on mathematics are winners. I need say no more, he is a classic. OK, some titles from my shelves: Gotcha!, The unexpected hanging, Mathematical magic show, The magic numbers of Dr. Matrix, Curious problems and puzzles, Time travel and other mathematical bewilderments, ...

 Barrow, John. Pi in the sky

I thought this would be a book about pi, but it is a rambling account of math, linguistics, and philosophy. Most of its contents have been done better elsewhere. Skip it.

 Maor, Eli. e, the story of a number

This is a book on the base of the natural logarithms, e. e permeates mathematics and pops up in all kinds of practical settings, nearly as often as does pi. More for teachers than their students, I found it useful as a source of answers when my eighth-grade son began to ask serious questions about e. Maor is always worth reading on the origins and history of mathematics. This book was hard to find because the computer systems in the stores couldn't deal with a one-letter key word!

 Thomas, Lewis. The lives of a cell

Lewis Thomas is one of our supreme stylists in science writing. And this book is among his finest. Read it as either science or literature, take your pick. "The lives of a cell" is a collection of independent essays, mostly related to biology and medicine: It can be parceled out to worthy students as if it were a box of bon-bons. If you haven't read this book yet yourself, today is as good a time as any to start it.

Bascom, Willard. Waves and beaches

Not intended for children, but not too difficult for the high school student, the treatment of the physics of water waves and beaches is surprisingly comprehensive and fascinating, with no advanced math. Any surfer will appreciate its description of where and how to get half-mile rides, and will gather on the way, a good understanding of wave motion. The title gives scant information on the breadth of the topics covered, including the stability of boats (kids will love the chapter "Why ships sink"), how to get more energy from salt domes than from the oil deposits that underlay them, and the amazing effects of seiches. Another very enjoyable book!

 Bascom, Willard. The crest of the wave

Tales from the sea, me mateys. As exciting as anything experienced by Long John Silver or Captains Bligh and Queeg, a master oceanographer writes, and writes well, of his adventures seeking the exotic phenomena of the sea. Bascom tangles with torpedoes, undersea mining, pollution of the seas, monster waves, and--of course--sunken treasure. Completely non-technical, yet full of enticing facts and observations. I was tempted to stop writing these capsule reviews and just curl up with this book, again.

 Epstein, Lewis Carroll. Relativity visualized

The best book I've seen to explain relativity to the young scientist. Careful, accurate, and clear, with an occasional problem to help the reader see if her thinking is on the right track. The math is limited to elementary algebra (with a smidgen of calculus in a note to teachers). Even if you don't have to do much math, you do have to think, and think carefully. I found that I had mislearned a commonly misunderstood point about relativity (I'll bet it's not the only one) and the books explanation made it clear why I was wrong. It is one of my son's favorite books, and has been since his clever mother got it for him when he was in sixth grade.

 Lightman, Alan. Time travel & papa Joe's pipe

The opening essay on time travel is thin and soppy. And he goes on in this vein. Nice title.

 Fadiman, Clifton. Fantasia mathematica

The only work of fiction in this list, it is a nearly-forgotten compilation of some fine short stories with mathematical themes. When I read this as a youngster it triggered my mathematical imagination, and it did the same for kids I have shown it to since. The math concepts underlying the stories are often solid, but always entertaining. Start with the story "A subway named Moebius". There's Heinlein's classic "--And he built a crooked house", some poetical fripperies at the end, and much more. Highly recommended.

 Bell, E.T. Men of mathematics

The title alone tells you it's dated, and better scholarship (see Stein, Strength in Numbers, for some corrections) has undermined a few of the more glamorous incidents. But all in all it is one of the most readable set of short biographies of mathematicians and their work. And if it makes the lives and exploits of mathematicians sound a bit more exciting than they were, well...

 Greenstein, George. Portraits of Discovery

A few selected biographies of an unusual choice of subjects, which is what makes the book work. Included are Annie Jump Cannon and Cecilia Payne-Gaposchkin, astronomers at the last turn-of-the-century; Margaret Geller and John Huchra, astronomers currently; Ludwig Boltzmann; Homi Bhabha and the science of India; and so forth. Too often Greenstein injects his own comments explicitly into the book, and he too often states that some theory or fact is fascinating instead of making it fascinating for the reader; I found the book's style to be annoying at times. Your mileage may vary. On the other hand, having 3 female subjects out of 10 is a great batting average, and might commend this book to the young girl on her way to a love of science.

 Paulos, John Allen. A mathematician reads the newspaper

The author of "Innumeracy" takes on its effects in the daily press and the other mass media, to good effect. Books like this (and another on this list, Dewdney's "200% of nothing") are true must-reads if we are to inoculate our students against the diarrhea of bad statistics and incomplete numerical facts that contaminate the information fed to us each day.

 Steinhaus, H. Mathematical snapshots

Another book that inspired the pre-college me, it has been reprinted since I was a lad. "Mathematical snapshots" is a collection of interesting illustrations that illuminate mathematical topics. And what a range of topics! The way mud cracks, how to balance a broom without looking, polyhedra, bubbles, music, chess, tilings, growth of trees (the wooden kind), and on and on. Plenty of ideas for hands-on projects, things to build and touch, and lots of connections between unlikely mathematical partners. It's better than I remembered it. A gem.

 Gribbin, John. In search of Schrodinger's cat

When I read this book years ago, it left a strange, shadowed impression. So I reread all of it for this brief review. What a pleasant surprise: It contains the clearest account of the rise and nature of quantum theory (up to but not including quantum electrodynamics (QED)) that I have seen. For the student or adult who wants to get a feel for the beast (without the math), this book would be hard to better. I was wondering why I had put the book into the "dubious" category... until I got to chapter 11. My remembered distaste was clearly a result of the last few chapters in which Everett's parallel universe interpretation of quantum mechanics is enthusiastically discussed. After 234 pages of correctly emphasizing that one thing we have learned from quantum theory is to not make scientific claims about what cannot be observed, we have an explosion of philosophizing about parallel universes that, even in principle, cannot be observed. This finally leads him to the benighted anthropic principle. An epilog weakly discusses the development of QED and a bit beyond. This sad end does not diminish the value of the first 10 chapters.