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Mathematics Reading List For High School Students?

Posted by timothy on 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!"

13 of 630 comments (clear)

  1. Flatland by Anonymous Coward · · Score: 5, Funny

    Sorry, my list is lacking some depth.

    1. Re:Flatland by theturtlemoves · · Score: 5, Interesting

      You laugh and mod parent funny, but I actually picked up the book on a whim because I wanted non-fiction. What I got was a kid in a rowboat with a tiger. Back on topic though, I really liked "The Code Book" by Simon Singh, and it has a significant amount of number theory and statistics that is light enough for someone without too much background to pick up.

      --
      Empires grow and crumble, and the Turtle Moves. Gods come and go, and still the Turtle Moves. The Turtle Moves.
  2. How to Lie with Statistics by sando101x · · Score: 5, Informative

    How to Lie with Statistics, Darren Huff, 1954

  3. Prime numbers online article thing by JaxWeb · · Score: 5, Interesting

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

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

    --
    - Jax
  4. Any abstract algebra text by davidwr · · Score: 5, Interesting

    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.

    --
    Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
    1. Re:Any abstract algebra text by rpillala · · Score: 5, Interesting

      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.

      --
      When the axe came to the forest, the trees said, "Look out - the handle was once one of us."
  5. Flatland by Ponderoid · · Score: 5, Informative
    Flatland by Edwin Abbott Abbott. Higher-dimensional math packaged as a parody about Victorian culture. :)

    *** Ponder

  6. Kids are ungreatful bastards by QuantumG · · Score: 5, Interesting

    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, 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.

    --
    How we know is more important than what we know.
  7. Godel Escher Bach by firmamentalfalcon · · Score: 5, Interesting

    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.

  8. Martin Gardner's column in Scientific American by Lupulack · · Score: 5, Informative

    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

    --
    The fact that no one understands you doesn't mean you're an artist.
  9. The Shape of Space by Pixie_From_Hell · · Score: 5, Interesting

    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.

  10. Re:Start with Basics... by fm6 · · Score: 5, Funny

    No it's not. Sorry.

  11. Re:High school is preparation for life by FiniteSum · · Score: 5, Insightful

    No. Simply no. There is no better way to turn a student off of math than to make them work SAT problems ad nauseum. It's so far removed from what an undergrad pursuing a degree in math will learn.