I heart 60’s-era math books


doverpublications_1975_494728369.jpegI’m teaching differential equations next semester, and I’m changing the course in some fundamental ways since the last time I taught it — so much so that I needed a new book for the course. (I’ve ruled out the textbook-free option for this class for reasons I explained here.) After some searching, I ended up going with the Boyce/DiPrima text. But I gained a lot of respect, and found a lot of affection, for Tenenbaum and Pollard’s classic text on the subject from 1963.

First of all, the textbook is a giant brick of a book, loaded with great exposition, clear examples, and challenging problems. And being a Dover paperback, it’s only a measley $16.47 through Amazon. But the thing I love about it, which is something I love about all math and science books from this era, is its tone — clear, precise, tough-minded, and no-nonsense. And yet inviting and enjoyable at the same time. (Which precisely describes what I’d like the students in the course to be.)

A great example is the following quote that appears at the end of a solid review of functions and just before they start looking at differential equations proper. Note that there is no intervening review of calculus between these two sections. That’s because the authors expect students to actually know calculus upon entering the course. They say:

In the calculus course, you learned how to differentiate elementary functions and how to integrate the resulting derivatives. If you have forgotten how, it would be an excellent idea at this point to open your calculus book and review this material. [emph. added]

I actually cheered when I read that. Differential equations is an extension of calculus; calculus is a prerequisite; you had calculus once; so if you forgot how to do it, get off your duff and crack a freaking book. End of story.

It’s the exact opposite of most modern math textbooks that start by assuming that the reader is five years younger and 30 IQ points dumber than s/he really is, and scared witless of math and unable to read past a 5th-grade level on top of that, and which proceeds to hand-hold and touchy-feel its way through whatever subject it is supposedly about. But not so with this book, nor with any other post-Sputnik era math and science books I’ve seen. That softening up seems to have occurred sometime around 1980.

Ironically, this 1963 text is superbly written with great clarity, vivid illustrations to motivate the material, and plenty of useful examples. When books started softening up — supposedly in an attempt to help struggling students — the things that actually help those students such as clarity and completeness actually went away.

I ended up going with the more modern book because I needed more in the way of computer applications (not many of those were around in 1963). But I will be using this Tenenbaum and Pollard text quite a bit, for my own enjoyment if nothing else, and perhaps as a lesson in how to write mathematics clearly.

10 Comments

Filed under Education, Math, Teaching, Textbooks

10 responses to “I heart 60’s-era math books

  1. tannenbaum/pollard retails for $25; boyce/di prima for $150:
    is it *six times* better for having the computer applications?

    maybe. you’re obviously a pro and have given the matter some thought;
    it would be arrogant to second-guess you so i’m not going to beg you
    to reconsider (though i’ll admit i thought of it [arrogance be @#$%!!!]).
    many of our colleagues appear to be incabable even of asking
    themselves this kind of question at all. thanks for bringing it up.

  2. I was definitely aware of the price difference, and trust me, it wasn’t an easy decision to make. I actually spent about a week thinking about it, asking students and colleagues about it… I think what finally tipped the scales for me was that I actually took both books to some students in my upper-level classes (including one who will be in the course). I presented them both the prices and the pros and cons of each book, and asked them which they’d rather have, given all that information. Every one of them picked Boyce/DiPrima.

    So I figured unless I had a really compelling reason to choose otherwise, their opinion was good enough for me.

    Also, B/D may not be 6 times as good as T/P, but I do think it’s better for what I have in mind and will require less manual retrofitting to do what I need to do. I am teaching a 14-hour load in the spring and I’m just not going to have all the time in the world to run around figuring out which parts of T/P are really appropriate and how do I make a computer lab out of them!

  3. Love when the professor picks a Dover Classic (independent studied topology this way once. I think the two books together cost $25).

    Same idea, I teach my high school combinatorics elective from Ivan Niven’s “Mathematics of Choice – How to Count without Counting” Not that it saves kids money (public hs, they don’t buy books), but the 60s writing is really to the point, and with illustrations as needed, not to add bulk or color.

  4. I’m a big fan of Ivan Niven’s number theory text (definitely NOT a cheap reprint!) — he’s a great expository/instructional writer. So I might have to go snag that combinatorics book.

  5. a student

    As a student (in Italy) i have to say that the only Odes book me and some of my friends don’t find boring (even as a first course) is “Differential Equations, Dynamical Systems, and an Introduction to Chaos” by Hirsch and Smale (the new edition), If my teacher had suggested that book for the odes part of the “Analisi Matematica” course i would have thanked him with all my heart, unfortunately he didn’t… so i ended up hating odes, thinking of them as useless calculations with useless existence theorems etc…, until a math-physics teacher showed us the geometrical beauty behind the subject, suggesting that book and renewing my interest.

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  8. “When books started softening up — supposedly in an attempt to help struggling students — the things that actually help those students such as clarity and completeness actually went away.”

    i noticed this same phenomenon in teaching English at my current institution not that long ago. whether it was called “schema-building” or “scaffolding”, attempts to provide information deemed necessary/useful for the struggling student just ended up creating more confusion…for everybody. students didn’t know which language task to perform and teachers didn’t know what language task they were supposed to be evaluating.

  9. Yes grand father @amtog I agree with your opinion. Thx. I promise to learn more idiom of English Language.

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