Requirements for the Book Report

You may earn up to 0.3 grade points for reading a book on some aspect of calculus and writing a report on the book and how it relates to our course. A short progress report is due by April 30, and the book report is due by May 21. (Those are Saturdays; both reports will be turned in on-line in the M422 Sp11 Journals and Papers dropbox.)

The goal of this assignment is for you to read a book presenting some aspect of the world of calculus for readers who are not professional mathematicians; and to reflect on how it relates to our course or what you learned from it that may be helpful to you as a future math teacher.

The progress report is due by April 30. By this time you should have selected which book you will read, and started to read it. You should tell me which book you have picked, and how you will have access to it: have you bought it, or borrowed it from an off-campus library, or you will be using the copy on reserve? Also tell me a few details about the book and your reaction to it.

The final report is due by May 21. It should be about 1.5 to 2 pages long (single-spaced, extra line between paragraphs, in reasonable sized type). You should give an overall impression of the book, and discuss some aspect of the book that relates to issues in Math 421 and 422. Here are some questions you might consider.

• What did you find interesting/learn/want to remember from this book?
• How did ideas in the book enhance, reinforce, or contradict ideas we've studied and discussed in the text and course (in 421 and/or 422)?
• What ideas from the book might be useful to remember when you are teaching high school math?
• Would you recommend this book to a high school student taking calculus, or to a high school math teacher? For each case, why or why not?

Suggested books. All of the books below are on reserve at the Math Library. Most are also available in other libraries or can be bought as paperbacks, but a couple (in particular, the Grabiner book) may not be. (One of the reasons I'm asking for the progress report is to find out if more than one person needs to use one of the books on reserve. If so, I'll put you in touch with each other so you can coordinate times to use the book.) If you know of a book you'd like to read which is not on this list, talk me (soon) about the possibility of using it for this assignment.

1. The calculus wars: Newton, Leibniz, and the greatest mathematical clash of all time, by Jason Socrates Bardi. The "wars" in question were between the allies of Newton and those of Leibniz, about who really invented the subject. Not exactly John Grisham, but a good read.


2. Newton's gift: how Sir Isaac Newton unlocked the system of the world, by David Berlinski. As the title suggests, this focuses on Newton and his life, as well as his mathematics and science. Newton was a rather strange character to say the least.


3. The calculus gallery: masterpieces from Newton to Lebesgue, by William Dunham. This book gives a little history and some idea of the mathematical interests of not only Newton and Leibniz but also the Bernoullis, Euler, and Cauchy, with mention of others such as Lagrange. It may require more mathematics background* than the other books. Read only through p. 95.


4. The origins of Cauchy's rigorous calculus, by Judith V. Grabiner. This book discusses how Cauchy's "ε-δ" version of calculus both grew out of earlier mathematical ideas and used them in new ways and from new viewpoints, so that they had completely new meanings. Though scholarly, much of it is quite readable. Read pp. 1-90 and pp. 167-175, skipping pp. 58-68 if you wish. (If you would like to read more, I recommend the middle of p. 96 through p. 101, and/or the introduction of chapter 5 or 6.)


5. e : the story of a number, by Eli Maor. The number e connects in multiple ways to calculus and limits, as well as to a surprisingly large number of applications. Read at least through Chapter 10 (including the "interlude" following it - don't worry, these are short chapters!), more (skipping to chapters that appeal to you) if you like.


6. Everything and more : a compact history of infinity, by David Foster Wallace. This book can be described as "zippy" and "mouthy." But, hey, try it, you might like it. Read only up to p. 145. It's full of rich allusions, images, and ideas. Many students have reported that they enjoyed this book.


7. A tour of the calculus, by David Foster Wallace. This book was a best seller; it's very readable. Students in this class are sometime put off by his "artsy" writing.

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Most recently updated on April 30, 2011.