Note: Each student will be assigned one topic from the list below. Topics are presented on the dates shown.
| # | Date | Talk Topic (Left Column) | Talk Topic (Right Column) |
|---|---|---|---|
| 7 | Sep 15 | Area procedures in Egyptian papyri: exact results, approximations, and surviving evidence for plane figures (except the circle). | |
| 8 | Sep 17 | The seked and Egyptian methods for pyramid slope | |
| 9 | Sep 22 | Old Babylonian quadratic problems and the geometry of completing the square | |
| 10 | Sep 24 | The discovery of incommensurability and the irrationality of √2 | |
| 11 | Sep 29 | Hippocrates' lunes: exact quadrature before the quadrature of the circle | The doubling of the cube |
| 12 | Oct 1 | Geometric algebra in Euclid's Elements: Book II and the Unguru controversy | Saccheri and his quadrilateral |
| 13 | Oct 6 | The Euclidean algorithm: geometry, arithmetic, and the history of greatest common divisors | Eudoxus's theory of proportion: rigorous comparison without real numbers |
| 14 | Oct 8 | Regular solids in Plato's Timaeus and Euclid XIII: constructions and the possible attribution to Theaetetus. | |
| 15 | Oct 15 | Archimedes on the quadrature of the parabola | |
| 16 | Oct 20 | Archimedes' Method of "Mechanical" Theorems | |
| 17 | Oct 22 | Ptolemy's chord table: trigonometry before sines | Eratosthenes' measurement of Earth's circumference |
| 18 | Oct 27 | The Nine Chapters on the Mathematical Art on fangcheng methods for simultaneous linear equations. | The Chinese remainder problem from Sunzi to modern congruences |
| 19 | Oct 29 | Right triangles and the gou-gu theorem in ancient China | |
| 20 | Nov 3 | Brahmagupta's rules for zero and negative numbers | Indian methods for computing square roots |
| 21 | Nov 5 | The Kerala School and pre-Newtonian infinite series - Madhava's series for pi | |
| 22 | Nov 10 | Omar Khayyam's geometric solution of cubic equations | |
| 23 | Nov 12 | Ibn al-Haytham's work on optics | |
| 24 | Nov 17 | Bombelli and complex numbers in the casus irreducibilis (the irreducible case) | Pascal, Fermat, and the problem of points. |
| 25 | Nov 19 | False position in the Rhind Papyrus and Fibonacci's Liber Abaci: two procedures for solving linear problems | Fibonacci's Liber Abaci and the spread of Hindu-Arabic numerals in Europe |
| 26 | Nov 24 | Fermat's method for finding maxima and minima | Fermat's quadrature of higher parabolas: integrating x^n before calculus |
| 27 | Dec 1 | Newton and Leibniz through one problem: two calculi, two notations, two programs | Newton's discovery of the general binomial theorem |
| 28 | Dec 3 | Euler's Königsberg bridges |
Additional Topics
- Egyptian unit fractions. The Rhind Papyrus 2/n table.
- Zeno's paradoxes and early Greek ideas of infinity
- Hilbert's axioms and the modern reformulation of Euclid
- Apollonius and the theory of conic sections
- Diophantus and the origins of algebraic notation
- Ibn al-Haytham's work on the isoperimetric problem
- Descartes and the geometrization of algebra
- Napier's logarithms: turning multiplication into addition
- Cavalieri's method of indivisibles
- The brachistochrone challenge and the Bernoulli brothers
- Euler and the Basel problem: a brilliant argument before modern convergence theory
- The Turing Machine
- Gauss's Disquisitiones Arithmeticae: modular arithmetic and quadratic residues
- History of Map Coloring Problems
- Leibniz's notation and its lasting influence