Valerie's Reviews > The World of Mathematics

The World of Mathematics by James Roy Newman
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Jul 29, 09

bookshelves: currently-reading, math

7/29-Today I read 2 essays about Newton and one about Gauss, as well as some of The Geometry by Descartes and and an analysis of infintesmals by Bishop Berkeley. Although the beauty of getting drawn into trying to understand the notations and drawings has its allure, it is really the biographical information that I am looking for in order to hook my students. The most singular fact about Newton and Gauss seems to be their ability to hold problems in their head for long periods of time. Most of the information about Newton I already had from the fabulous book, The Calculus Wars--I think more stuff about his work for the Mint would interest my students though. I learned more about Gauss this morning, and Bell's excellent essay made me want to learn more about him.

Nature of Mathematics by Jourdain

The following ideas for class discussions. Why did Descartes invent the notation of analytic Geometry? Why do we say -6 but not +6? (This is one that my students struggle with all the time. A definition of the tangent as given by the Greeks "a straight line through the point such that between it and the curve no other straight line can be drawn." And a great lesson activity for between.

The Great Mathematicians by Robert Turnbull

Napier spending 25 years on his log tables, I can't even get my students to spend 25 minutes on log problems. Must look at Napier's spherical trigonometry. Newton considered Euclid's elements a trifling work. And perhaps my favorite thought of the day describing light as either undulatory or copuscular.

The Rhind Papyrus by James R. Newman--didn't really grab me.

Observations on Archimedes by Plutarch and others.

The 3 different stories about his death and by remembrance of the Dutch puzzle and Descartes reminds me that I must share the nerdswiped xkcd comic with my students. Maybe on the syllabus.

Read a bit on The Greek Mathematics, which was incredibly dull, than a good essay on Kepler by Locke. No crazy new teaching ideas.
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Reading Progress

07/22 page 10 "I can't decide where to begin with the geeky goodness. I probably won't read this in order." 1 comment
07/23 page 79 "Finished Jourdain's Nature of Numbers this morning. A lot of great stuff about why we teach math the way we do, and why we shouldn't."
07/24 page 90 "Reading The Great Mathematicians, just got to good part about Thales when I had to drive to the airport."
07/24 page 112 "Have found a great quote from Plato, "Let no one destitute of Geometry enter my doors.""
07/27 page 188 "finished the The Great Mathematicians by Turnbull"
07/28 page 234 "Read a great essay about Kepler this morning."
07/30 page 365 "Read Bell's essay on Cayley and Sylvester, I may have been guilty of a Sylvester style lecture from time to time."
08/03 page 416 "Today essays by Bertrand Russell and Alfred Whitehead made me want to read more by both of these men. Reread in Russell's case."
08/04 page 429 "Archimedes proof that the grains of sand are finite made me think that from now on all student proofs must include ample teacher flattery."
08/05 page 442 "A fascinating cultural anthropological look at finger counting methods by Conant."
08/06 page 488 "This afternoon, read about human calculators."
08/08 page 518 "Cole's proof that Mersenne 67 is not a prime was a riot. LOL"
08/21 page 572 "Today I read 3 essays about non-Euclidean Geometry."
08/22 page 600 "Euler's essay on the Konigsburg bridges, which I think I'd read before, and a discussion of the 4 color problem.Which I will use in Geo."
08/24 page 621 "Very inspired by an essay on Durer's descriptive geometry and its use in art. I think I can use this in the classroom."
08/30 page 671 "Today's reading was by Heinholz about spherical geometry, learned why a Hertz is called a Hertz."
09/07 page 726 "This essay on symmetry made me think of symmetry in music and in dancing."
09/13 page 770 "Read some of Galilio's work."
11/14 page 840 "Using math to discover Neptune...good stuff."
06/20 page 850
33.0% "Spectra from x-rays, least squares, and atomic numbers."
06/22 page 881
34.0% "Two essays on using geometry to predict the shape of crystals. Mathematics and physics informing each others experiments and theorems. On page 869 a very good chart showing the relative lengths of rays, compared to comprehendable, visible objects. I'll have to use it in my classroom."
06/24 page 900
35.0% "Two essays today on the importance of minimization. The second one by Boys had a great problem on pg. 900 that I shall have to come back to."
06/27 page 936
38.0% "A fascinating essay on the topology of soap bubbles, and one by Mendeleev on his work, and one about him (this one did a good job of explaining his process of developing the periodic table and portraying him as a person."
06/28 page 952
39.0% "Read an essay by Mendel on the mathematics of heredity. I especially like reading about his exhaustive efforts to control his experiments."
06/29 page 958
39.0% "J.B.S. Haldane on Relative Size, I want to use this essay in my PreCalc class."
07/11 page 1036
42.0% "On Growth and Form...with a great description of bird flight, and many observations on the importance of scale."
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