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Additional Resources

A list of supplemental readings and resources to explore topics further

History of mathematical notations #

This is a link to Florian Cajori’s History of Mathematical Notations, volume 2. Specifically, it points to the history of the dollar sign, $, because that might be an interesting entry point into the book. Hosted by the Internet Archive

Plimpton 322 Papers #

Here are some of the many papers discussing the Plimpton 322 tablet:

  • Buck, R. C. (1980). Sherlock holmes in babylon. The American Mathematical Monthly, 5, 335. Link to pdf
  • Robson, E. (2001). Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322. Historia Mathematica, 28(3), 167–206. https://doi.org/10.1006/hmat.2001.2317 Link to pdf
  • Robson, E. (2002). Words and Pictures: New Light on Plimpton 322. The American Mathematical Monthly, 109(2), 105–120. Link to pdf
  • Mansfield, D. F., & Wildberger, N. J. (2017). Plimpton 322 is Babylonian exact sexagesimal trigonometry. Historia Mathematica, 44(4), 395–419. https://doi.org/10.1016/j.hm.2017.08.001 Link to pdf

Works of Archimedes, translated by Heath in 1920 #

The Works of Archimedes, edited in modern notation by Thomas Heath, 1897  (available on the Internet Archive)

Page 91 begins the Measurement of a Circle

π resources #

Resources for “linear thinking” topics #

Resources for Quadratics #

Resources for Cubics (Cardano, Tartaglia, and more) #

  • Here’s a link to Cardano’s Ars Magna translated into English (requires free Archive.org account).

  • The Book of My Life by Cardano.  I’m linking to the table of contents. I forgot to mention that he is also an astrologer. The second paragraph of chapter two, “My Nativity” discusses his own horoscope (later in life he gets in trouble for casting the horoscope of Jesus).

    • Personal comment: it’s been awhile since I’ve just sat with Cardano. Reading this now I’m reminded that he’s a really repellant and truly toxic person. Fun story and big deal in history, but I am glad to not interact with him.
    • … but, between complaints, discussing twenty-three years of lawsuits, and all, he gives a very broad list of things that make him happy and can bring happiness to everyone:

Let us live, therefore, cheerfully… if there is any good thing by which you would adorn this stage of life, we have not of such been cheated - rest, serenity, modesty, self-restraint, orderliness, change, fun, entertainment, society, temperance, sleep, food, drink, riding, sailing, walking, keeping abreast of events, meditation, contemplation, education, piety, marriage, feasting, the satisfaction of recalling an orderly disposition of the past, cleanliness, water, fire, listening to music, looking at all about one, talks, stories history, liberty, continence, little birds, puppies, cats, consolation of death, and the common flux of time, fate, and fortune, over the afflicted and favored alike. There is good in the hope for things beyond all hope; good in the exercise of some art in which one is skilled; good in meditating upon the manifold transmutation of all nature and upon the magnitude of the Earth. (pages 122-3)

  • The poem, translated into English, preserving the rhyme structure.

    • Gutman, K. O. (2005). Quando Che’l Cubo. Mathematical Intelligencer, 27(1), 32–36. 

      Link to pdf

  • The “play” form of the letters of Cardano and Tartaglia

    • Nordgaard, M. A. (1938). Sidelights on the Cardan-Tartaglia Controversy. National Mathematics Magazine, 12(7), 327–346.  Link to pdf 

  • This book is excellent and should be read cover-to-cover for any topic. In particular there is a great chapter on Cardano and Tartaglia along with Cardano’s geometric proof of the cubic formula (remember that everything is backed up with geometry! A “cube” means a literal cube.

    • Dunham, W. (1991). Journey through genius: The great theorems of mathematics (p. 300). Penguin Books.  http://books.google.com/books?id=_IbWAAAAMAAJ&pgis=1
    • (you can find it at the library or just search with “pdf” added and you’ll find many copies of questionable sourcing online).

Fundamental Theorem of Algebra topics #

  • Good historical overview of algebra from the beginning through Noether in the 20th century

    • van der Waerden, B. L. (1985). A history of algebra: From al-Khwarizmi to noether. Springer-Verlag.  ( available at our library) 

  • Bombelli’s crazy algebra: 

    • Arcavi, A., & Bruckheimer, M. (1991). Reading Bombelli’s x-Purgated Algebra. The College Mathematics Journal, 22(3), 212–219. Link to the PDF

  • Talking about Euler and others trying to solve the question: 

    • Dunham, W. (1991). Euler and the fundamental theorem of algebra. The College Mathematics Journal, 22(4), 282–293.
      Link to the PDF

Fermat’s Last Theorem Resources #

  • Simon Singh has an excellent book on the story called Fermat’s Enigma. It’s available at the library. (Singh is a very easy-to-read popular science author).

  • This article claims to be “accessible to non-experts” overview of Wiles’ proof.

  • WIles’ correction for his proof of Fermat’s Last Theorem Wiles, A. (1995). Modular elliptic curves and fermat’s last theorem. Annals of Mathematics, 141(3), 443-551. https://doi.org/10.2307/2118559

Sines and Logarithms #

Calculus #

  • Main source for the series - thorough history of all the players (and more than can be covered in a week of classes): Boyer, C. B. (1988). The history of the calculus and its conceptual development: The concepts of the calculus (Repr). Dover Publ.
  • The article I recommended answering questions about rigor and symbols: Grabiner, J. V. (1983). Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus. The American Mathematical Monthly, 90(3), 185–194.
  • History of math book that provided me with computational details of Newton’s fluxional calculus Katz, V. J. (2009). A history of mathematics: An introduction (p. 976). ADDISON WESLEY Publishing Company Incorporated.
  • … and another Katz paper I haven’t yet read (it’s on my list) that goes into the history of the calculus of trig functions. Spoiler: It’s Euler again! Katz, V. J. (1987). The calculus of the trigonometric functions. Historia Mathematica, 14(4), 311–324. https://doi.org/10.1016/0315-0860(87)90064-4

Probability and Statistics #

  • Pascal and Fermat’s correspondance on probability (and sums, and Fermat primes, and health…), collected translated into English available here.

    • Devlin, K. (2010). The Pascal-Fermat correspondence: How mathematics is really done. The Mathematics Teacher, 103(8), 578.

  • Really enjoyable book explaining the development of statistics:

    Salsburg, D. (2002). The lady tasting tea: How statistics revolutionized science in the twentieth century (1. Holt Pp. Ed). Holt.

Computing Devices #

Cantor’s Infinity #

  • For more information about Cantor’s arguments on the sizes of infinity, check out chapters 11 and 12 of William Dunham’s Journey Through Genius (link to a pdf subtle cough).

    Dunham, W. (1991). Journey through genius: The great theorems of mathematics (p. 300). Penguin Books.

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