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I'm teaching a history of mathematics class for master students in an integrated teacher training program. They have calculus and linear algebra plus a "proof" course and a geometry course, but most of them don't have analysis. I want to cover topics that are "related" to school mathematics. It doesn't have to be things they will use when teaching, but things that will give them a better understanding to things they will be teaching. I've tried both Katz and Stilwell. Both are excellent books, but not quite right for my audience and my class. I liked Stillwell because it was more mathematical, but I would have liked to have seen more applied mathematics, too. I'm thinking about trying Mathematics in Civilization by Resnikoff and Wells or Journey through Genius by Dunham. Has anybody tried them? Or any other suggestions for similar books?

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  • $\begingroup$ Previously asked at Mathematics Stack Exchange (now on hold), where I suggested that it be posted here. $\endgroup$ – Joel Reyes Noche Mar 20 '17 at 8:31
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    $\begingroup$ Just so you know, there is also a History of Science and Mathematics Stack Exchange, but I think your question is more appropriate here. $\endgroup$ – Joel Reyes Noche Mar 20 '17 at 8:34
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    $\begingroup$ I have seen interesting posts about the teaching of history of math in all three groups. I will follow your suggestion and do a link next time. Thanks! $\endgroup$ – Helmer.Aslaksen Mar 20 '17 at 10:51
  • $\begingroup$ At our university we have a 1-credit hour class that math ed students take for a certification requirement. For that class I have used Journey through Genius successfully. It worked out nicely for a 1 lecture a week class, though I had to create my own homework problems. I don't think that it would be good as anything other than supplemental reading for a 3 credit hour class. $\endgroup$ – John Coleman Mar 20 '17 at 13:30
  • $\begingroup$ @JohnColeman Great comments, that is exactly the situation I could imagine it used as a solo text for. $\endgroup$ – kcrisman Mar 20 '17 at 13:31
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There are a number of good options for such a class, but it depends wildly on what your objectives are. I have only used Journey Through Genius in an actual class setting, so I have a few relevant comments.

Advantages:

  • Very readable
  • Many interesting personality anecdotes
  • Often connects to less well-known characters
  • Low prerequisites
  • Useful material not often covered in "normal" curriculum outside a math history course
  • Fun results
  • Could easily use other Dunham books to supplement without jarring stylistic changes
  • Very reasonable price and easy to obtain used copies

Disadvantages:

  • Couldn't possibly be a solo text, needs considerable supplement in terms of time periods and coverage even if you have a "short course"
  • Low prerequisites mean anything beyond infinite series (including calculus) can't be covered properly with just this
  • Definitely not a textbook, so some fairly noticeable gaps if you were to intend it used in this way (e.g. very heavy on Greek math and number theory)
  • You'll have to think of your own homework and/or quiz material

The way I've used it is as a cheap primary text with lots of stuff interesting to students who otherwise might see a math history class as a very tedious hoop to jump through, and then I supplement considerably with material from "missing" sections and more advanced results. I've found many MAA journals and the Notices of the AMS often have good material along those lines, and the MacTutor history site is great even if the interface is a bit dated.

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  • $\begingroup$ By the way, I really hope other people answer this, because I am not anywhere near as experienced teaching math history as many, many others! Just one person's experience. $\endgroup$ – kcrisman Mar 21 '17 at 1:50
  • $\begingroup$ Thanks! I am not worried about gaps. I'm not trying to do a complete overview of the history of mathematics, but just a highlights course. But I would like to have more calculus and more applications. That was why I was thinking about supplementing with Resnikoff and Wells. $\endgroup$ – Helmer.Aslaksen Mar 22 '17 at 8:33
  • $\begingroup$ Yeah, I'm not familiar with that one. Mathematical Masterpieces and Mathematical Expeditions by Laubenbacher and Pengelley (esp. the latter) might help you fill in on that. Sherman Stein has a great book on Archimedes. Etc., etc., if you have time to supplement. $\endgroup$ – kcrisman Mar 22 '17 at 18:45
  • $\begingroup$ Thanks! Yes, those books are great, but I have a feeling that they will cover a bit too much. I'm hoping for something between them and Dunham. $\endgroup$ – Helmer.Aslaksen Mar 23 '17 at 7:16
  • $\begingroup$ Oh, what I meant was to just pick a couple subsections from those as resources. Yes, you could teach two+ courses from those books if necessary. $\endgroup$ – kcrisman Mar 23 '17 at 14:21

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