| Date | Class Topic | Readings/Assignments |
|---|---|---|
| 9/4 | Course Introduction -- why is algebra so hard for some people? | Read course syllabus and ask if anything is unclear in class on Friday, 9/6 |
| 9/6 | Background -- Positional number systems with bases 2, 8, 10, 16 | |
| 9/9 | Old Babylonian Mathematics -- an overview | [KP], Chapter 2, pp. 12-32. |
| 9/11 | The Babylonian base-60 number system | (materials on course homepage) |
| 9/13 | The role of tables in Babylonian arithmetic | (handouts in class) |
| 9/16 | Old Babylonian Problem Texts -- the tablet YBC 6967 | (materials on course homepage) |
| 9/18 | Different interpretations of YBC 6967 | (materials on course homepage) |
| 9/20 | Deciphering the tablet YBC 7289 -- small group discussion | (handouts in class) -- Problem Set 1 due by 5:00pm |
| 9/23 | Comparing Babylonian mathematics and Greek geometry | [KP], Chapter 3, pp. 33-57 |
| 9/25 | More on ``geometric algebra'' in Euclid, Book II, Propositions 1-5 | (materials on course homepage); you're not responsible for the Greek, of course(!) |
| 9/27 | Why did the Greeks do things this way? Euclid, Book X, Proposition 117 | (materials on course homepage) |
| 9/30 | Greek mathematics post Euclid | [KP], Chapter 4, pp. 58-80 |
| 10/2 | Diophantus and the Arithmetica | (materials on course homepage) |
| 10/4 | More on Diophantus | (materials on course homepage) |
| 10/7 | Diophantus and symbolic algebra | (materials on course homepage) -- Problem Set 2 due by 5:00pm |
| 10/9 | The influence of Diophantus on later mathematics | (materials on course homepage) |
| 10/11 | Spare day | (materials on course homepage) |
| 10/14,16,18 | October Break -- no class | Start reading [KP], Chapter 7, pp. 132-173. |
| 10/21 | Islamic Mathematics -- an overview | [KP], Chapter 7, pp. 132-173 |
| 10/23 | Review for Midterm | See review sheet and practice questions |
| 10/25 | Midterm Exam | Topics and format to be announced |
| 10/28 | al-Khwarizmi and the Hisab al-jabr wa'l muqabala | Read pages 67 - 83 in Robert of Chester's translation (odd-numbered pages only, unless you want to compare with the Latin version!) |
| 10/30 | al-Khwarizmi, continued. | Read pages 85 - 109 (see above) |
| 11/1 | Other Islamic mathematicians and their contributions | (materials on course homepage) |
| 11/4 | How these ideas were transmitted back to Europe | (materials on course homepage) |
| 11/6 | Leonardo Pisano (Fibonacci), other Italians, and the transmission of algebra | [KP], Chapter 8, pp. 179-184 -- Problem Set 3 due 5:00pm |
| 11/8 | The ``cossists'' and symbolic algebra | [KP], Chapter 8, pp. 204-213 |
| 11/11 | Renaissance algebra -- Cardano and the solution of the cubic | [KP], Chapter 9, pp. 214-227 |
| 11/13 | Algebra as a general problem-solving technique | [KP], pp. 227-236 |
| 11/15 | Viète's The Analytical Art | Read the Wikipedia page on François Viète and pages 315-328 of the Analytical Art (course homepage) -- Paper topic proposals due, Problem Set 4 due by 5:00pm |
| 11/18 | Viète, continued | Read pages 328 - 338 of the Analytical Art |
| 11/20 | Viète, continued | Read pages 339 - 353 of the Analytical Art |
| 11/22 | ``Analysis'' and ``synthesis'' in mathematics | (materials on course homepage) -- Problem Set 4 due 5:00pm |
| 11/25 | Is algebra difficult because it is analysis? | (materials on course homepage) |
| 11/27, 29 | Thanksgiving break -- no class | |
| 12/2 | Descartes, La Géometrie | (materials on course homepage) |
| 12/4 | Descartes and ``analytic'' geometry | (materials on course homepage) |
| 12/6 | The problem of the four lines from Pappus | (materials on course homepage) -- Problem Set 5 due by 5:00pm |
| 12/9 | Abel, Ruffini, Galois, and the insolvability of the quintic by radicals | [KP], Chapter 11. |
| 12/11 | What is ``algebra'' in 2019? | (materials on course homepage) |
| 12/13 | Course wrap-up -- Papers due |
Last modified: November 13, 2019