| Week | Topics | Presentations, deadlines, quizzes and homework |
|---|---|---|
| I - 2/1 | About the course What is mathematics? |
Register here
for the interactive platform for class questions and polls (In the
linked site, go to "Sign in with Google" and sign in with your SB
email) (due
2/2) Homework 0 (due 2/5) Form: topics for presentation (due 2/5) |
| II - 2/8 | Timeline of mathematics The Ishango bone Primitive counting Number systems |
Quiz 0 -
Open book (or "open website") about the syllabus (on Thursday
2/11) Homework 1 (due Friday 2/12. Posted in course website) |
| III - 2/15 | Ancient Egypt Number system. Multiplication and Division Parts (fractions) Areas and Volumes. Method of False position. The Pythagorean Theorem |
Homework 2 (due Friday of the week III, that is 2/19) |
| IV - 2/22 | Mesopotamia Number System Tables of reciprocal and multiplications Solutions of linear and quadratic equations Square roots and the Pythagorean theorem Plimpton 322 |
Quiz
1 (On Thursday) Outline and draft of slides of presentation due on Monday (note: the link is active) |
| V - 3/1 | Around the world Mayan Mathematics (special lecture!) Inca Mathematics Mathematics in Africa |
Presentation:
Quipus,
see also
here. Alexis,
Thursday Presentation: Mathematics in the History of the Sub-Saharan Africa (excluding Yoruba people) Infiniti, Thursday Presentation: Mathematics of the Yoruba People Cory, Thursday Homework 3 (due Friday) |
| VI - 3/8 | Helenic mathematics from
Pythagoras to Euclid Plato: Meno Plato on learning geometry Pythagoras: Figurate numbers Thales |
Presentation:
The
role of paradoxes in the evolution of mathematics Danny,
Tuesday Presentation: Impossible problems of the Antiquity Faye, Thursday Presentation:The number e (see also here) Renyu, Tuesday Homework 4 (due Friday) |
| VII - 3/15 | Euclid 1 Geometric Algebra Pythagorean Theorem The Fifth postulate |
Presentation: The Story of Tangents Weiheng, Tuesday Presentation: Lagrange and the Parallel Postulate Timothy, Thursday. Presentation: Historical stages of the definition of curves Jhecy, Tuesday Presentation: Euclid and the axiomatic method Enze, Thursday. Bonus: A story about the Pythagorean Theorem (in youtube) Quiz 2 on Thursday Cancelled Paper topic and abstract due Friday |
| VIII - 3/22 | Euclid 2 Areas and volumes Incommensurables The Platonic Solids |
Presentation: The tangency problem of Apollonius Joshu, Tuesday. Presentation: The evolution of mathematical certainty You Jun, Tuesday Presentation: Definitions and Nondefinability in Geometry Sharon, Thursday Presentation: Sophie Germain and a revaluation of her work on Fermat's Last Theorem (also here and here) William, Thursday. Homework 5 (due 3/25) |
| IX-3/29 | Helenic Mathematics After Euclid Archimedes Apollonius Diophantus |
Presentation:
Archimedes
and the quadrature of the Parabola (also
here)
Lingyue,
Tuesday Presentation: Diophantus and The birth of literal algebra Jose, Tuesday Presentation: The Geometry of Burning-Mirrors in Antiquity Joe Lo., Thursday Presentation: How Galileo dropped the ball and Fermat picked it up Yeong Lee, Thursday Homework 6 (due Friday) Homework cancelled (staycation!) Outline and bibliography paper due on Friday |
| X - 4/5 | Mathematics in Ancient and
Medieval China The rod number system Volume of the sphere |
Presentation:
Liu
Hui and Tsu Keng-chih on the Volume of a Sphere Yifan
Thursday Presentation: The "Piling Up Of Squares" in Ancient China (see also here) Hongbo, Tuesday Presentation: On the area of the semi-circle Kenneth, Thursday Quiz 3 on Thursday (Questions are here) Visit the Writing Center regarding with the draft of your paper before Friday (you have to make an appointment) |
| XI - 4/12 | Mathematics in Ancient and
Medieval India The Indus or Harappan civilisation Geometry and the sulba sutras Mathematics and Sanskrit grammar Development of Indian numerals Jaina Mathematics (Reading) Aryabhata |
Presentation:
Hermann
Grassman and the Creation of Linear Algebra Kim,
Tuesday Presentation: Ramanujan Daniel,, Tuesday Presentation: The use of series in Hindu mathematics Stachys, Thursday Presentation: The Discovery of the Series Formula for ? by Leibniz, Gregory, and Nilakantha Kristen, Thursday Homework 7 due Friday (same problems, with a few more, will be due on Friday, April 23rd) Draft of Paper due Friday submit it here . |
| XII - 4/19 | Mathematics in the Islamic World The Islamic Golden Age al-Khwirizmi, Omar Khayyam |
Presentation
Ideas
of Calculus in Islam and India BreAnna,
Tuesday
Presentation: Paul Erdos Eliana, Tuesday Presentation:Thabit Ibn Qurra and the Pythagorean Theorem Joey La., Thursday Presentation: Alicia Boole Stott on the four dimensional polytopes Joseph R., Thursday Homework 8 due Friday |
| XIII - 4/26 | A brief history of the solution
of polynomial equations Quadratic equations Cardan and Tartaglia (Reading) The equation of degree 5. A brief history of Analytic Geometry Descartes |
Presentation: Gauss and the Discovery of Ceres Omar, Tuesday Presentation: Euler and the Zeta Function Yanqiu, Tuesday Presentation: A Study of Newton's Presentation of the Calculus Julian, Thursday Homework 9 due Friday |
| XIV - 5/3 | Calculus ideas before the invention of Calculus Barrow Fermat The invention of Calculus Newton Leibniz |
Reading:
The history of
Calculus. and The
Development of Integral Calculus
For extra-interested: The History of the Calculus Presentation: Descartes Representation of Curves Charles, Tuesday Presentation: Fermat's Method of Finding Areas under Graphs Andy, Tuesday Presentation:Infinities, Infinitesimals, and Indivisibles: The Leibnizian Labyrinth Dayu He, Thursday Presentation: The Evolution of the Normal Distribution Vincent, Tuesday Presentation The history of the Fundamental Theorem of Integral Calculus Erika, Thursday. Presentation: Who gave you epsilon? Cauchy and the origins of rigorous calculus Rentai, Thursday Quiz 4 (On our last meeting Thursday. Submit in Blackboard) Paper due on (4/26) |
Selected topics among the following Back to the Fifth Postulate The four color theorem Mathematical history of computers A chronology of ? A brief history of Number theory Fermat Gauss |
if we get an extra day... |
|