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 #

Stepbystep directions for “squaring” the rectangle, a triangle, and the lune, that I wrote a million years ago (2015).

The first instance of π in Jones, W. (1706). Synopsis Palmariorum Matheseos: Or, a New Introduction to the Mathematics. J. Matthews at the Angel in St Paul’s ChurchYard.
Resources for “linear thinking” topics #
 False position
 Bunt, L. N. H., Jones, P. S., & Bedient, J. D. (1988). The Historical Roots of Elementary Mathematics. Dover.
 Āryabhaṭa: (I LOVE Āryabhaṭa)
 Keller, A. (2006). Expounding the Mathematical Seed. Vol. 1: The RTranslation: A Translation of Bhāskara I on the Mathematical Chapter of the Āryabhatīya. Birkhäuser Basel. https://doi.org/10.1007/3764375922
 Examples from Ahmes papyrus as presented in
 Joseph, G. G. (2010). The Crest of the Peacock: NonEuropean Roots of Mathematics (3rd ed., p. 592). Princeton University Press; 3rd edition edition.
 Scrollable version of the papyrus from the British Museum’s website
 Mesopotamian examples
 Katz, V. J. (2003). The history of mathematics: Brief version (Vol. 2003, p. 560). Pearson/AddisonWesley. http://books.google.com/books?id=pI8_AQAAIAAJ&pgis=1
 and the tablet/prism in the Louvre here.
Resources for Quadratics #

Link to the English translation (1831) of alKwharizmi’s Algebra. (on Archive.org). Note: it’s called “The Algebra of Mohammed Ben Musa” because that was a common Latinization of Muhammed ibn Musa (Muhammed, son of Musa)

The English translation of the $x^2 + 21 = 10x$ question is from:
 Lévy, T. (2002). A NewlyDiscovered Partial Hebrew Version of alKhwārizmī’s “Algebra.” Aleph, 2, 225–234.
 Here’s a link to the library’s catalog entry so you can get the fulltext.
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 twentythree 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, selfrestraint, 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 1223)

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

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


The “play” form of the letters of Cardano and Tartaglia
 Nordgaard, M. A. (1938). Sidelights on the CardanTartaglia Controversy. National Mathematics Magazine, 12(7), 327–346. Link to pdf

This book is excellent and should be read covertocover 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 alKhwarizmi to noether. SpringerVerlag. ( available at our library)

Bombelli’s crazy algebra:
 Arcavi, A., & Bruckheimer, M. (1991). Reading Bombelli’s xPurgated 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
 Dunham, W. (1991). Euler and the fundamental theorem of algebra. The College Mathematics Journal, 22(4), 282–293.
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 easytoread popular science author).

This article claims to be “accessible to nonexperts” 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), 443551. https://doi.org/10.2307/2118559
Sines and Logarithms #

Kepler’s relationship between science and religion: Kozhamthadam, J. (2002). The Religious Foundations of Kepler’s Science. Revista Portuguesa de Filosofia, 58(4), 887–901.

Bhaskara’s transation of Aryabhata Keller, A. (2006). Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhāskara I on the Mathematical Chapter of the Āryabhatīya. Birkhäuser Basel. https://doi.org/10.1007/3764375922

John Napier:
 Napier’s end of the world prediction: A Plaine Discovery of the Whole Revelation of Saint John
 Napier’s lattice multiplication via number rods:
Rabdologia: The Art of Numbering by Rods
 this edition is in English by Seth Patridge in 1648. Napier’s latin version was taken down 😟
 Logarithms! Here is Napier’s Mirifici logarithmorum canonis descriptio.
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/10.1016/03150860(87)900644
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 PascalFermat 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 #

Old Computers

Napier’s Bones simulator

Video demonstrating Pascal’s Pascaline (recommend at least 1.5x speed).

Illustrations and reconstruction of Leibniz’ Stepped Reckoner.

The Arithmometer mechanical calculator

Babbage’s difference engine with relaxing music https://www.youtube.com/watch?v=be1EM3gQkAY

This video demos the math behind the machine https://www.youtube.com/watch?v=PFMBU17eo_4

Really great photo collection from the Computer museum
 setting it up https://www.computerhistory.org/revolution/birthofthecomputer/4/78/316
 operating it https://www.computerhistory.org/revolution/birthofthecomputer/4/78/321
 implemented in a circuit chip in 1995: https://www.computerhistory.org/revolution/birthofthecomputer/4/78/327


Article on the History of Computing in ComputerWorld 1981 https://archive.org/details/TheHistoryOfComputing/mode/2up

Excellent book on the subject and a major source for my talk:
Ifrah, G. (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. Wiley.

Historical logical
 George Boole’s Laws of Thought https://www.gutenberg.org/files/15114/15114pdf.pdf
 And Augustus de Morgan’s Formal Logic: https://archive.org/details/formallogicorthe00demouoft
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.