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Mathematics Reading List For High School Students? 630

Posted by timothy
from the flatland-to-hawking dept.
Troy writes "I'm a high school math teacher who is trying to assemble an extra-credit reading list. I want to give my students (ages 16-18) the opportunity/motivation to learn about stimulating mathematical ideas that fall outside of the curriculum I'm bound to teach. I already do this somewhat with special lessons given throughout the year, but I would like my students to explore a particular concept in depth. I am looking for books that are well-written, engaging, and accessible to someone who doesn't have a lot of college-level mathematical training. I already have a handful of books on my list, but I want my students to be able to choose from a variety of topics. Many thanks for all suggestions!"
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Mathematics Reading List For High School Students?

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  • Flatland (Score:5, Funny)

    by Anonymous Coward on Sunday February 08, 2009 @06:34PM (#26776809)

    Sorry, my list is lacking some depth.

    • Re: (Score:3, Funny)

      What about "Life of Pi"? That sounds like it's got a lot of math in it.
    • by fm6 (162816)

      You can always fill it out with Sphereland.

    • by Gerzel (240421) *

      Try
      How to Lie with Statistics by Darrell Huff

  • by sando101x (1058590) on Sunday February 08, 2009 @06:34PM (#26776813)
    How to Lie with Statistics, Darren Huff, 1954
    • by fm6 (162816)

      That's a great book that everybody should read. But it's not about math. It's about how people misuse math. I know this because I have over a billion seconds of experience!

      • by Gerzel (240421) *

        Exactly. It is about how to use math and misuse it. Most courses today focus solely on how to do math and any use of math is so poorly linked into the discussion that it merely becomes another obstacle between the student and getting the drudge work done.

    • Re: (Score:3, Insightful)

      by mewshi_nya (1394329)

      I would go for things in other fields that are math-heavy - economics, science, business, stuff like that.

      Shows the usefulness of math!

    • by Gerzel (240421) * <<brollyferret> <at> <gmail.com>> on Sunday February 08, 2009 @08:24PM (#26777937) Journal

      Darrell not Darren, at least by my printing

  • by JaxWeb (715417) on Sunday February 08, 2009 @06:35PM (#26776829) Homepage Journal

    I wrote this:
    http://people.pwf.cam.ac.uk/jlnw3/maths/books/prime/ [cam.ac.uk]

    It was meant as an introduction to the idea of proof. Perhaps you might like it.

  • by Mikkeles (698461) on Sunday February 08, 2009 @06:38PM (#26776859)

    Principia Mathematica. It's all there ;^)

    • by fm6 (162816) on Sunday February 08, 2009 @07:09PM (#26777231) Homepage Journal

      No it's not. [everything2.com] Sorry.

    • Re: (Score:3, Interesting)

      by dprovine (140134)

      No, you want Fantasia Mathematica, by Clifton Fadiman, a bunch of stories with math themes. Like the guy who wants to paint a really long drive belt -- so, to keep him busy, somebody else unlaces it, flips one side over, and relaces it. Painting just the outside of a Möbius strip turns out to be tricky.

      After we read that story, my kids and I made some Möbius strips and drew on them, cut them lengthwise, and so on.

  • by davidwr (791652) on Sunday February 08, 2009 @06:40PM (#26776891) Homepage Journal

    It's normally taught as an upper-division college class but the only real prerequisite is 2nd-year high school algebra and a mind that can think abstractly.

    Students will find it different enough from trig and calculus to be fresh and knowing they can do "college math" can be a real ego-boost.

    By the way, if you know any elementary or middle school teachers, many of the concepts in abstract algebra can be taught to those age groups as well. Being able to do "adult math" can be a real point of pride and inspiration at those ages.

    First grade isn't too early. Anyone who can add or subtract time already has the basics for abstract algebra addition and subtraction.

    • by rpillala (583965) on Sunday February 08, 2009 @07:28PM (#26777451)

      I teach high school and try to put in the some of the abstract algebra topics when I teach Algebra 2. Some of the students enjoy it but most of them get really pained looks and only stop me to ask if the material will be on the test. That's not a big deal all it means is I'm not presenting it right yet. It also has something to do with how they've been taught in the past. But to support your recommendation I want to share that I was able to get a review copy of the current edition of my abstract algebra book from the publisher. I think at the college level this is more common than in secondary schools. Teachers should consider this method to build their resources.

      I also want to recommend Men of Mathematics by E. T. Bell. The calc kids were very interested to know about Newton and Riemann's lives. Considering that most of what we do in middle and high school is actually math history, it seemed fitting to bring some of the personalities in.

      • Books, People, Ideas (Score:3, Interesting)

        by omb (759389)
        I agree, history and sociology of hard science, Mathematics, ideas and philosophy are __very__ important, as is understanding of intuitional, inductive and deductive reasoning in __everything__, NOT ONLY Mathematics. That is one of the reasons why Professional Teachers teach Math and Science so poorly. You have to like it and want to understand it yourself to teach it properly. I was fortunate to have two excellent teachers, an Oxford 2nd Wrangler and one of Fred Hoyles postdocs, and most of what they taugh
    • Re: (Score:2, Informative)

      by Nigel Stepp (446)

      I was thinking something similar, but wasn't sure if it would be outside of the scope of what the OP wanted.

      In particular, I really like this: Linear Algebra Done Right [amazon.com].

      It's an abstract linear algebra book that does a great job of motivating topics *without* resorting to determinants, which are weird to get your head around.

      Anyway, getting through it would give students some good insights into the mathematical process, I think.

    • by ClassMyAss (976281) on Sunday February 08, 2009 @08:10PM (#26777819) Homepage
      IMO, abstract algebra is a great way to turn off all but the best of the best to math in general. I know many math majors that switched to stats and econ after floundering in the intro to abstract algebra class.

      And I strongly object to trying to slip those things into early math classes; even concepts like commutativity, associativity and distributivity are simply counterproductive to students until they have some reason to need to use them in the abstract.

      And FWIW, I was not personally put off by this stuff, so that's not my reason for saying this (I almost bailed thanks to calculus, though, thanks to the unreasonable focus on limits and all that garbage which any competent person can pick up practically by osmosis once they know how to actually use the damn techniques). I got quite far along in abstract math (and had the pleasure to learn some of it from Serge Lang himself, and the displeasure of fighting through the sadistic exercises in his textbooks - the guy was far more comprehensible in person!), and I absolutely love it now; however, I think it's the type of thing that a person needs to realize they want to learn about before they will be receptive to it.

      On that note, I think number theory is a good soft intro to higher math, because the open problems are so easy to state and understand (3k+1, Goldbach, etc.), and you can at least see "evidence" for them using simple methods. It's hard to draw connections between number theory and the abstract stuff without a lot of machinery in place (I don't think high school students are quite ready for adeles!), but interest in those problems is what spurs a lot of work in abstract techniques, so I think it's worth nurturing.
    • Re: (Score:3, Insightful)

      I agree sort of. I actually did a major in math and I focused primarily on algebraic geometry. I have to admit that math didn't really get interesting in college until upper division math courses. The problem is these courses are extremely rigorous. I remember abstract algebra being very difficult to learn when I was used to my previous college level calculus courses which were basically memorization and solving equations. Abstract algebra on the other hand was taught by proof. Groups, rings, fields, homomo
    • Re: (Score:3, Interesting)

      By the way, if you know any elementary or middle school teachers, many of the concepts in abstract algebra can be taught to those age groups as well. Being able to do "adult math" can be a real point of pride and inspiration at those ages.

      I was rather surprised how much Finnish math teaching had evolved since I was in elementary school when I recently read a first grade math book.

      Those kids are solving equations in first grade.

      The genius behind it is that the symbol layer is taught after the concepts. The kids learn to do the basics all with pictures. A simple equation like 2+X = 4 can be presented like a set of scales with four apples on one side, and two on the other. The task is to make the scales balance out.

      Using this principle a lot of

  • If this book doesn't make them think that math is cool, nothing will.

  • Flatland (Score:5, Informative)

    by Ponderoid (311576) on Sunday February 08, 2009 @06:41PM (#26776899)
    Flatland [wikipedia.org] by Edwin Abbott Abbott. Higher-dimensional math packaged as a parody about Victorian culture. :)

    *** Ponder

  • by rolfwind (528248) on Sunday February 08, 2009 @06:41PM (#26776911)

    How to Think like a Mathematician:
    http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/0521895464 [amazon.com]
    Online here (for how much longer?):
    http://www.maths.leeds.ac.uk/~khouston/httlam.html [leeds.ac.uk]

    I bought this in the discount bin for $1 somewhere, I think it's (Playthinks) really good to develop logic and just try a little bit of every mathematical discipline:
    http://www.amazon.com/Big-Book-Brain-Games-Mathematics/dp/0761134662 [amazon.com]

    This isn't pure math, but lisp, but since Lisp is inspired by lambda calculus, perhaps it'll inspire more programming (shrugs):
    http://www.cs.cmu.edu/~dst/LispBook/index.html [cmu.edu]

  • by QuantumG (50515) * <qg@biodome.org> on Sunday February 08, 2009 @06:44PM (#26776943) Homepage Journal

    Even the dullest high school student has a memory that makes us adults seem slow. There is exactly one way to motivate teenagers: tell them they are not "ready", although telling them they are "not allowed" has a similar effect. With that in mind I recommend you give one or two of them a copy of All the Mathematics You Missed But Need to Know for Graduate School [amazon.com], and suggest they pass it onto someone else if they find it "too hard". It's a great book that gives a quick skim over all the different fields of mathematics that a graduate student in mathematics is expected to know. A typical college student will read this book, shake their head and decide that maybe graduate school isn't for them. A typical high school student, even one not interested in math, will read this book and decide that mathematics is awesome and maybe they should pay attention in class, because if they can't grasp differential linear equations then they're never going to understand Lebesgue integration and infinite Fourier series.

    • by rufusdufus (450462) on Sunday February 08, 2009 @07:37PM (#26777521)

      It seems likes kids only do what you tell them not to do, so this advice may seem wise. However, this is a form of confirmation bias; adults notice when kids don't listen because mainly because they usually do.
      If you tell someone a student some skill is difficult, they will believe you. You have set them up to expect failure. This expectation is easy to meet, and most students will give up early.
      If you tell a student something is easy, they are likely to believe you. Believing a subject is easy, they are more likely to follow through to mastery because they have been set up to expect success.
      Reverse psychology is a trick. Tricking students is a way to alienate them; it may work on the few, but the many will respond better to affirmative attitudes.

      • Re: (Score:3, Insightful)

        by QuantumG (50515) *

        Umm.. the material likely *is* too hard for them. You're not tricking them at all.. you're just giving them the opportunity to accept the challenge.

  • FIRST robotics, while not a 'reading list', would provide your math students hundreds or thousands of opportunities both in the field of mathematics but also engineering and science.

    Right now I can think of a few dozen 'practical' real world problems for this years competition that I could use some students seriously grounded in math to think about and solve (radius of turn for Ackermann steering, forces on a gyro during a turn, etc) not to mention coding up and implementing algorithms.

    Anyway- don't sell ma

  • Godel Escher Bach (Score:5, Interesting)

    by firmamentalfalcon (1187583) on Sunday February 08, 2009 @06:45PM (#26776955)

    Excellent explanations. It is completely understandable if the student puts in the time to understand it. It requires almost no outside knowledge.

    I would have loved it if someone showed me this book earlier.

    • by Dunx (23729)

      Exactly right - it worked for me. I read this when I was sixteen, and (with no irony intended) it changed my life.

      Pace Neal Stephenson, I call GEB "The Geek's Illustrated Primer".

  • by Lupulack (3988) on Sunday February 08, 2009 @06:45PM (#26776967)

    was full of the sort of stuff that's fascinating to inquiring minds. I read one of his collections many moons ago and was enthralled! Not common to find a math book that could be called a "page turner"

    Link is to a CD-ROM of all his books
    http://www.amazon.com/Martin-Gardners-Mathematical-Games-Gardner/dp/0883855453 [amazon.com]

  • by Anonymous Coward

    "The Higher Arithmetic" by Harold Davenport is a fantastic book on number theory. It explains the concept of proof in the first 10 pages without using any formal notation. All of the proofs are given in an intuitive, explanation style. Aside from being a fantastic book on Number Theory (and thus a great primer to understanding modern cryptography), it is a very good introduction to the style of thinking and argument involved in actually doing /mathematics/ (as opposed to arithmetic, which is what seems t

  • by artor3 (1344997) on Sunday February 08, 2009 @06:46PM (#26776975)

    I read Prisoner's Dilemma by William Poundstone when I was that age, and found it to be a very intriguing introduction to game theory. It is fairly light on math, providing only enough to show that there are calculable solutions to situations that are otherwise difficult to reason through. It also provides some real life examples which are easy to relate to, e.g. letting one child cut a piece of food in half and the other choose the half they want in order to ensure "fair" portions.

    It's a good choice for showing that there's more to math than finding the length of the hypotenuse.

  • My math is cool (Score:5, Insightful)

    by CMonk (20789) on Sunday February 08, 2009 @06:46PM (#26776979)
    http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1234132982&sr=8-1 [amazon.com] Godel, Escher, Bach: An Eternal Golden Braid Very interesting book and should get students of that age excited about math and science IF they are predisposed to that sort of thing.
  • which i don't really recommend for your purposes, but want to tell everyone about anyway, is Bourbaki. Available in French and English. Have a taste [google.com]. It's very dry and concise and I love it!

  • Prime Obsession (Score:2, Informative)

    by zackhugh (127338)

    Prime Obsession [amazon.com]: A well-written history of the still-unproven Riemann Hypothesis. Maybe one of your students will solve it over summer break!

  • You need to provide more information about your target audience. "16-18 year olds" is a pretty broad demographic. But let's say for the sake of discussion that you mean the average kid in the average high school math class. I can sum up your lesson ideas in a word: Practicality. For most people, mathematics is tiresome, and the majority of adults don't use it for anything more than figuring out if they got the right change at the drive-thru, not spending too much at the grocery store, and taxes (for those s

  • by thrope (830256)
    I really enjoyed this book when I was at that stage... http://books.google.co.uk/books?id=wUdtVHBr-OQC [google.co.uk] Really a book about operational research, but covers lots of maths in a really applied accessible way with examples from history (spread of cholera outbreaks, optimal fleet size to avoid submarines in WW2, enigma machine etc.) Lots of exercises, and each section is relatively self contained - so ideal for starting off the kind of short projects you are talking about. Highly recommended...
  • If you want to stretch their minds, Gödel, Escher, Bach by Douglas Hofstadter is excellent. It's much deeper than it may seems, so it needs some support from a teacher who knows what he or she is doing.

    If you want to make their first year in college much easier, have them work trough Schaum's Outline of Linear Algebra by Seymour Lipschutz. It's the best introduction to LA I've ever seen, accessible, but without dumbing things down.

  • by cellocgw (617879) <<moc.liamg> <ta> <wgcollec>> on Sunday February 08, 2009 @06:55PM (#26777067) Journal

    Let them loose on The Feynmann Lectures on Physics. Quite readable and bound to get them interested in one branch or another of physics.

    The Golden Ratio -- or some other book on the same constant -- which goes into things like sunflowers and nautilus shells IIRC.

    Mathenauts: a collection of sci fi short stories in which (in most cases) the hero is a mathematician.

    • Re: (Score:3, Informative)

      by gardyloo (512791)


      The Golden Ratio -- or some other book on the same constant -- which goes into things like sunflowers and nautilus shells IIRC.

      I do hope (I have not read The Golden Ratio) that this isn't one of those popular mathematics books which presents a lot of very intriguing factoids as though they're actually true. There are some very good pop maths books (The Story of I comes to mind), and this may be one of them. However, I'm pretty leery of the "fact" that the golden ratio describes a lot

  • by Ruie (30480)
    First take a look at Quantum magazine (http://www.nsta.org/quantum/) it had many interesting articles, it was an attempt to port over Russian magazine "Quant" famous for many high-quality mathematics and physics articles.
    Also AMS has some translated (or written anew) books from Russian mathematical tradition. The books that I read personally (and liked a lot):
    • Stories about Maxima and Minima, Vladimir Mikhailovich Tikhomirov
    • Knots : Mathematics with a Twist, A. B. Sossinsky
    • Intuitive Topology, Vol. 4,
  • by c_forq (924234) <forquerc+slash@gmail.com> on Sunday February 08, 2009 @06:56PM (#26777077)
    If you're trying to get kids interested in the possibilities of math I would suggest Bringing Down The House, about the MIT Blackjack team.
  • Simon Singh (Score:5, Informative)

    by Ian Alexander (997430) on Sunday February 08, 2009 @06:56PM (#26777081)
    You might look at some of Simon Singh's stuff if you haven't already- there are some good chapters in The Code Book regarding the basics of public-key cryptography which don't require any more than a basic education in algebra.
    • Re: (Score:3, Interesting)

      by Ian Alexander (997430)
      Also, I was a bit of a math nerd in high school, and so I suggested to my math teacher that he try a class where you give the students a simple monoalphabetic substitution cipher, do a quick rundown on how to crack them, and then give them some time to crack it. The declaration of independence was long enough for most of the kids to have gotten most of the alphabet cracked by the end of the hour. Saved me a boring class and it was a big hit. You might think about setting some kind of similar challenge.
    • Re:Simon Singh (Score:4, Informative)

      by JuanCarlosII (1086993) on Sunday February 08, 2009 @07:45PM (#26777601)
      I opened this post expecting every second person to be recommending Simon Singh's 'Fermat's Last Theorem [amazon.co.uk]'. I never met an UG mathmetician at my college (at a moderately well-known collegiate university) that hadn't read it at some point before admissions interviews.

      I am shocked to see it not mentioned even once.
  • "Innumeracy" and others are very good general introductions to how math is used in the real world. The kids who are going to do an extra-credit reading list will likely be right at the target level you're going for. A lot of them are also structured so you can take in a couple small chapters at a time and move on.

  • The Shape of Space (Score:5, Interesting)

    by Pixie_From_Hell (768789) on Sunday February 08, 2009 @07:00PM (#26777125)

    I highly recommend The Shape of Space by Jeff Weeks. (He's a freelance geometer, something he can afford after winning a MacArthur Genius Grant.) I've used this book a couple of times -- once with bright high school kids and once with bright college freshman -- and even if they don't get everything, just a taste is enough.

    It builds on Flatland (which someone mentioned above), but has the advantage of being more modern and not sexist. But very quickly you're learning about Klein bottles, connected sums, and all sorts of topology you typically don't see until you're well into your undergraduate (or grad!) program in math. All aimed at high school kids. Very cool stuff.

    Oh, and the big punchline at the end: what is the shape of the universe? At least you'll get a good understanding of the possibilities...

    Here's a taste for you from a page related to the book [geometrygames.org].

  • by hcetSJ (672210) on Sunday February 08, 2009 @07:00PM (#26777131)
    by Eli Maor. ISBN: 0691141347 I read this book the summer before taking calculus, and I learned the core concepts of calculus from it (limit, derivative, integral, fundamental theorem). I still had to learn the specifics in class, but having that conceptual foundation made everything easier. The book is full of interesting historical tidbits. For instance, did you know that the inventor/discoverer of the logarithm was excommunicated from the Catholic Church? I don't remember the circumstances now--I suppose Google could help, but I know it's in this book.
  • Applied Geometry for Computer Graphics and CAD
    (Springer Undergraduate Mathematics Series)

    Pages: 352 Seiten
    Publisher: Springer
    Language: Englisch
    ISBN-10: 1852338016
    ISBN-13: 978-1852338015

    I've read it by myself and even if it says "undergraduate" it will perfectly fit,
    give it a try applied mathematics is fun either.
  • by XxtraLarGe (551297) on Sunday February 08, 2009 @07:02PM (#26777163) Journal
    Not strictly mathematics, but Richard Feynman's "autobiography" [amazon.com] might be a good one for inspiring your kids to show what they can do with their math knowledge.
  • Courant-Robbins (Score:3, Informative)

    by fph il quozientatore (971015) on Sunday February 08, 2009 @07:03PM (#26777171) Homepage
    Courant and Robbins, "What is mathematics?"
  • "The Pattern On The Stone: The Simple Ideas That Make Computers Work" by Danny Hillis.

    It is a masterful piece on computation, and how computers work, and uses mathematics and logic in a very down-to-reality way that I think is certainly readable by a motivated high school student.

    I'd write more but my laptop battery is about to die. It's a great book!

  • Fermat's Enigma (Score:3, Interesting)

    by brechmos (679454) on Sunday February 08, 2009 @07:09PM (#26777213)
    I really like Fermat's Enigma by Simon Singh. Relatively easy read and I found it inspiring.
  • But particularly his book on Phi... ("The Golden Ratio")

    dave

    p.s. has anyone read anything by John Allen Paulos, e.g. "A Mathematician Reads the Newspapers"?

  • by JoshuaZ (1134087) on Sunday February 08, 2009 @07:10PM (#26777245) Homepage

    Do you want them interested in math or do you want them to know more math? Since many people have already listed more applied books I'm going to try to focus on the less applied end of things.

    Books with much mathematical content I'd recommend for that age group are:

    Oyestein Ore's "Number Theory and its History" which is an excellent, highly concrete introduction to number theory with a lot of interesting historical material thrown in. I read this first in 9th or 10th grade.

    Sawyer's "Concrete Introduction to Abstract Algebra" is an excellent introduction to many ideas that will be necessary in higher level math classes. The material is of a level that can be understood by most high school students.

    A more difficult but still good book is Adams' "The Knot Book" which is an introduction to knot theory.

    All of the above do not include any understanding of calculus or any other advanced topics.

    If one wants a less mathematically advanced book that is more about the stories and people I'd recommend Simon Singh's "Fermat's Enigma" which tells the story of Fermat's Last theorem and along the way sketches out the great stories of mathematicians including the tragic life of Galois, the fate of Hypatia at the hands of a mob and many other great stories, all woven into the overarching narrative the quest to prove Fermat's Last Theorem. (I'm also going to take this an opportunity to strongly disrecommend vos Savant's book on Fermat's Last Theorem which contains serious errors and other problems).

  • William Dunham's books are excellent reads. They're a mix of biography and math, usually focused on the more playful, clever parts of math. (As opposed to the tedious, but necessary bits.) He covers a lot and anyone who reads them with any attention at all would come away with a pretty good conversant knowledge of mathematics.

  • by fm6 (162816)

    Oops, somebody screwed up. This is an Ask Slashdot that asks an interesting question that some of us are actually qualified to answer, and that can't be answered by trivial means such as googling. I don't think that's allowed!

  • Master of Space and Time by Rudy Rucker. It has some math in it, and it's funny to boot.

  • by DrJimbo (594231) on Sunday February 08, 2009 @07:18PM (#26777325)
    I love this book. It contains a wide variety of topics and although some of it is elementary, there is plenty of depth to challenge and enchant your students.

    Albert Einstein praised it as:

    A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easy to understand introduction for the layman and helps give the mathematical sudent a general view of the basic principles and methods.

    If you want to teach your students to love math, try this book. Courant was a leading mathematician of his day. He co-authored the formidable Methods of Mathematical Physics with David Hilbert. Courant's love of mathematics shines throughout What is Mathematics.

  • Gamow's book covers some of the most interesting areas of mathematics without excessive simplification or condescension.

    Another good book is

    The "Language of Mathematics: Making the invisible visible" by Keith Devlin. This is an expansion of his earlier book for Scientific American Library.

    Finally, consider mathematics which involves interactive projects with a computer. Turtle Geometry is a great starting place. Advanced students can tackle a professional book on computer graphics and will learn a massiv

  • Freakanomics... (Score:4, Informative)

    by lordsid (629982) on Sunday February 08, 2009 @07:21PM (#26777369)

    I suggest Freakanomics.

    Although not really a pure math book I think you can see the relevance. I found it very enlightening to read and it provided a very interesting insight into odd things like Why Sumo Wrestlers Cheat and How much Crack Dealers really make an hour.

  • A History of PI (Score:2, Insightful)

    A History of PI [amazon.com] by Petr Beckmann is a great book for that age group. It has lots of historical information about PI and its calculation by various historical figures and cultures. The writing style is engaging and even moving. Another plus for that age group - it's less than 200 pages long.

    I second a previous poster's suggestion of Simon Singh's The Code Book.
  • Unlike a lot of the posters here, I think at that age, it's more important to show students why math is important than the concepts used by upper year college students. When I started my Math/CS undergrad, the department pretty much dismissed everything I was taught in high school and started from first principles. Even things I taught myself at that time outside of school like computer graphics turned out to be irrelevant.

    In relation to statistics, I think they're vastly under taught and under appreciate

  • The book that made me understand multi-variable calc... well, kind of:

    Div, Grad, Curl and All That

    Of course, that would only be suitable for students with at least some calc.

    Also, how about A Beautiful Mind (the book, not the movie.)

  • by dtmos (447842) * on Sunday February 08, 2009 @07:26PM (#26777423)

    A Pathway Into Number Theory [amazon.com], by R. P. Burn.

    It's the most unique math book I've ever read. There is no prose in the book per se; rather, the book is a series of small tasks and questions (usually starting by identifying patterns in tables of numbers) that, as the title suggests, gently lead the reader into Number Theory. All the major topics of a first course (the fundamental theorem of arithmetic, quadratic residues and forms, etc.) are there; the beauty of the book is that each task is such a small step from the previous one that the reader is led painlessly to a mastery of each concept. (Just don't skip steps!) This feature makes is suitable for advanced high school students looking for "stimulating mathematical ideas."

    It's a wonderful book, on a wonderful subject. I have often wished for books written in this format on other mathematics subjects.

  • It's an old book, but I like it.

    Lady Luck: The Theory of Probability [amazon.com]

    The author does a great job making the subject easy to understand for non-math people like myself.

  • Encourage kids to read math and consider the subject worth studying. I sure wish someone had clued me into that in high school! How I went on to become a high school math teacher is still a bit of a mystery to me, as my high school math teachers were pretty uninspiring. They never encouraged us to read the textbook, let alone any outside texts. Perhaps that was because high school texts tend to be pretty uninspired -- I'm a fan of Key Curriculum Press texts, and I encourage math teachers to check them ou

  • Here are several (Score:3, Insightful)

    by swillden (191260) <shawn-ds@willden.org> on Sunday February 08, 2009 @07:41PM (#26777555) Homepage Journal

    First, let me add my recommendation for GEB. It's an amazing book.

    Here are some others that I think are good:

    • "The Codebreakers: The Comprehensive Story of Secret Communication from Ancient Times to the Internet", by David Kahn. This is a frighteningly large book, but if you get the right sort of kid to pick it up (s)he will devour it. Most everyone is intrigued by secret writing, and this book covers it all, from ancient techniques like tattooing a message on the shaved scalp of a slave and letting his hair grow back before sending him, to the crypto-drama of WWII, and up to modern times. Not mathematical, per se, but it will quickly lead the interested student into some interesting mathematical territory.
    • "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography", by Simon Singh. Similar to the last. IMO, not as good, but also not as large, so perhaps more approachable.
    • "Against the Gods: The Remarkable Story of Risk", by Peter Bernstein. Very interesting book that traces the history of risk analysis. Relatively little mathematics, but probability is a crucial concept in modern applied mathematics and this book is a great way to build interest.
    • "Fermat's Enigma: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem", by Simon Singh. Singh does a good job of exposing the low-key but very real drama behind the centuries of attempts to prove Fermat's Last Theorem.
    • "Zero: The Biography of a Dangerous Idea", by Charles Seife. Seife traces the history of the development of zero, an idea which revolutionized counting and mathematics.
    • "The Divine Proportion", by H.E. Huntley. I read this one when I was a teenager, and it really impressed me just how prevalent phi is in the world, and I liked the tie between mathematics and art. Re-reading it recently I was less impressed -- a lot of the tie-ins really seemed to be reaching, but if the idea is to stimulate thinking and interest this is a good choice.
    • "A Brief History of Time", by Stephen Hawking. It's about physics not math, but it's definitely mind-expanding and fascinating.
    • "Surely You're Joking, Mr. Feynman", by Richard Feynman. This is a book about Feynman, not math or physics, but it's all about the curious and inquisitive nature of great mathematicians and physicists, and I know lots of kids who've found it inspiring.
  • If they are also interested in programming you could let them try Knuth's Fundamental Algorithms or its sequel. Just have them ignore the hard problems.

    The books I'm aware of are all either too easy or too hard for that audience, although I'm sure there are some in the middle. There are some easy but interesting topics that you might look for chapters on:

    1) Prove Fermat's little theorem, and show how it can be show a number is composite (but not prime).

    2) Derive the closed form for the nth Fibonacci numbe

  • by kurtis25 (909650)
    Perhaps my favorite is The Nothing that Is: A Natural History of Zero (http://www.librarything.com/work/147631). I read it in high school in a week at church camp. It mixes history with math and isn't a hard ready but it's no Harry Potter either. You could also go with Biographies since they are less number heavy and often more interesting. I may also suggest The Drunkard's Walk: How Randomness Rules Our Lives (http://www.librarything.com/work/4850753). I have not read it yet (darn you public library) but
  • Find topics in numerical analysis, so they know that after all that misery, plus calculus if they carry it into college, most of these problems can be solved with a scientific calculator and some reasonable assumptions.

    My brother engineers can probably testify to how infuriating it was to spend those first couple miserable years mastering multi dimensional calculus, only to be shown how there were really damn good approximation algorithms in place for most of these problems. In my case it was twice infuriat

  • You might have a devil of a time finding it (out of print) but Ascent to Orbit by Arthur C Clarke was very inspiring to me when I was in high school.

    It's a collections of the scientific papers by ACC, explaining the mathematics of space flight (orbital velocities, geosynchronous orbit, space elevators, etc). Many of the papers were published before space flight was a reality, so it is historically interesting as well as mathematically approachable.

  • The best introductory book for "real mathematics" (theorem-proof style) that I've seen is Calculus by Michael Spivak. It is a large book, lucidly explained in great detail. It teaches insight and intuition, and has a very "chatty" style, as one of my professors once put it. Stay away from his other books, though. They are very advanced and leave much to the reader to prove.

    That being said, I think you ask the wrong question. Don't just give a reading list. As a teacher, you should be doing the reading

    • Re: (Score:3, Interesting)

      by jefu (53450)

      Spivak's Calculus is probably the best calculus text for someone interested in mathematics. But it may be one of the worse for someone who finds mathematics difficult. But I'm biased, I learned some of the basics from Spivak himself and he left me with a lifelong love of mathematics.

  • Any of Smullyan's books, particularly "What Is The Name Of This Book?", "The Lady Or The Tiger", "Alice In Puzzleland". Lots of fun, and not what high school students would consider math. "Disguised" as mere logic puzzles, they are great for learning formal logic and ultimately introduces Godel's Incompleteness Theorems. Much easier and more fun than Godel, Escher, Bach (which is truly a wonderfully fantastic book, if you have the students who are ready for it).
  • Feynman's Lectures on Physics are a little far afield from pure math but they do make math interesting by connecting it to the real world.

    1. Hofstadter's "Godel Escher Bach"
    2. Feynman's "The Character of Physical Law" (more accessible and much shorter than "Lectures on Physics")
    3. Polya's "How To Solve It"
  • Conceptual Mathematics by Lawvere and Schanuel is the one maths book that I wish I'd been exposed to in high school.
  • Jan Gullberg's book Mathematics: From the Birth of Numbers is a great read! It covers, well, a hell of a lot: number theory, trig, fractals, matrices, calc, probability, diff eq, combinatorics, symbolic logic, etc. It includes anecdotes and historical notes, and does a very good job of explaining many different things.

    Amazon has a couple of reviews [amazon.com].

  • by jefu (53450)

    "Winning Ways for your Mathematical Plays" (Berlekamp, Conway and Guy) is both fun and serious mathematics. It is probably too much for most students, but even doing some of the stuff in the first few chapters is likely to open their imagination to what mathematicians can do. The first volume (of the first, two volume, edition) covers basic combinatorial game theory with the second volume covering such things as the "dots and boxes" game, the Rubik's cube and the Game of Life.

    It has been reprinted

  • While in high school I read "Mazes for the Mind: Computers and the Unexpected [amazon.com]" by Clifford A. Pickover [wikipedia.org]. It ties math to a wide variety of topics, and should be entertaining and mostly accessible even if a little of the math goes over their heads. And it's full of pretty pictures!

    Apparently he has written a number of books since then. I haven't read any of them, so I wouldn't know which to recommend.

    (As mentioned a number of times already, I'd recommend Godel, Escher, Bach as well.)

  • Two great books (Score:4, Interesting)

    by swm (171547) * <swmcd@world.std.com> on Sunday February 08, 2009 @08:47PM (#26778113) Homepage

    1. A Long Way From Euclid
    Constance Reid

    A survey of math from the ancient Greeks on.
    Very accessible.
    I spent months reading it in 6th grade.

    2. Innumeracy: Mathematical Illiteracy and Its Consequences
    John Allen Paulos

    Lots of cool stuff on probability, estimation, and application of math to current events.

Somebody ought to cross ball point pens with coat hangers so that the pens will multiply instead of disappear.

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