| Week | Topics Covered | Assignments | Presentations |
|---|---|---|---|
| I-8/24 | Administrative details What is mathematics? The begining of counting Timeline of mathematics |
Register on for the interactive platform before the first lecture, use your SB email. Fill form: Homework 0 (due 8/27) Fill form: topics for presentation (due 8/27) |
Not yet |
| II - 8/30 |
The Ishango bone Number systems Primary and Secondary Sources |
Homework 1 is here Reading: Familarize yourself with the syllabus and review slides of Week I. |
Not yet |
| III - 9/6 |
Reliable sources: Using the Web Ancient Egypt Number system. Multiplication and Division Unit fractions and the 2/n table Method of False position. Areas and Volumes. |
Readings (due Tuesday 9/7): The World's First Mathematics Textbook On the Egyptian method of decomposing into unit fractions(first six pages) Form bibliography, outline and draft of slides (both lectures). Here you'll find examples of of abstract, outline, slides, paper and presentation. The posted example contains finished slides. You need to submit a draft, not the finished product. This form has to be submitted on Friday 9/10 regardless on the date of your presentation. It will be graded as "completed" or "not completed". If all entries except one are filled it will be marked as completed. However, it will be good if you put a bit of effort because will try to give you feedback on your entries. It is fine if by the time of your presentation you need to change some of the items.. Quizz 1.Sample Quiz Optional Reading: Egyptian Mathematics |
Thursday: On the Egyptian method of decomposing into unit fractions (L1: Ioannis, L2: Matt ) |
| IV - 9/13 |
Ancient Egypt Method of False position. Areas and Volumes. The Pythagorean Theorem Mesopotamia Number System and cuneiform notation Tables of reciprocals and multiplications |
Homework 2 and sample quizz 2 are here Readings (due Tuesday 9/14): Words and Pictures: New Light on Plimpton 322 (Sections 1, 2, and 6) |
Tuesday: A River-Crossing Problem in Cross-Cultural Perspective2 (L1: Jailing, L2: Owen) |
| V -9/20 |
Mesopotamia Number System and cuneiform notation Square roots and the Pythagorean theorem Plimpton 322 |
Quizz 2 Form topic, bibliography, abstract and math point of the paper is here . Reading: Mayan calendar and number system |
Tuesday Graph in cultures (L1: Keisuke, L2: Kenny ) (see also here) Thursday: Aztec Arithmetic: Positional Notation and Area Calculation (L1: Daniel, L2: Chun-chi )(see also here) |
| VI - 9/27 |
Around the world Mayan Mathematics Inca Mathematics Mathematics in Africa The beginnings of mathematics in Greece Three famous problems of the antiquity |
Homework 3 is here Reading |
Tuesday: Origin and Evolution of the Secant Method in One Dimension (L1: Martin, L2: NOT ASSIGNED ) Tuesday: Thales (L1: Zoya, L2: Mary ) Thursday: Euler and the Bridges of Konigsberg (L1: Jay , L2: Solomon) Thursday: History of graph theory after Euler (L1: Syed, L2: Richard ) |
| VII - 10/4 |
The beginnings of mathematics in Greece Plato, Aristotle Zeno The idea of proof Euclid's Elements Postulates and common notions. The Platonic Solids |
Quizz 3: (Topics: Number systems: Mayan, Mesopotamian. Mayan calendars -Haab and Tzolkin, see the slides-, Computation of areas in Mesopotamia Mathematics) Form: Paper outline can be found here. (The outline is the skeleton of the paper. Your paper should be divided into sections, the title of htose sections form the outline.) |
Tuesday: Rigor and Proof in Mathematics I (Sections 1 to 6) (L1: Wenrui (John), L2: Tianyu ) Thursday: Rigor and Proof in Mathematics II (Sections 7 to 14)(L1: Cody, L2: Patryk ) |
| VIII - 10/11 |
Escher, curvature and two dimensional geometries Discussion about Euclid's fifth postulate. |
Fall break: No class on Tuesday Oct 12. Nothing due this week. |
Thursday: Is Mathematical Truth Time-Dependent (L1: Mohammed, L2: He ) Thursday: How Hyperbolic Geometry Became Respectable(L1:Lauren , L2: Henry ) |
| IX - 10/18 |
Euclid's Elements Geometric Algebra Pythagorean Theorem Areas and volumes Incommensurables Infinitude of primes |
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Tuesday: Archimedes' Quadrature of the Parabola(L1: Jeremy, L2: Twentififty) Tuesday: The Geometry of Burning-Mirrors in Antiquity (L1: Nicole, L2: Helen) Thursday: The Birth of Literal Algebra (L1: Alex , L2: Zenhao ) |
| X - 10/25 |
More Helenic Mathematics Archimedes Apollonius Diophantus Ptolemy Trigonometry Mathematics in Ancient and Medieval China The rod number system Volume of the sphere The Nine Chapters of the Mathematical Art |
Homework 4 is here . Optional Reading ( related to Homework 4)On proof and progress in mathematics by William Thurston Proofs in Mathematics by Alexander Bogomolny When is a proof? by Keith Devlin Reading |
Tuesday: The "Piling up of squares" in Ancient China (L1: Zifeng, L2: Qinting) Tuesday: Liu Hui and Tsu Keng-chih on the Volume of a Sphere(L1: Xirui , L2: Yike) Thursday: The Chinese Hexagram (L1: Zhaoqi-Logan , L2: Lake )See also here and here. |
| XI - 11/1 |
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 |
Quizz 4 Form: Draft of paper . Submit the link to the approriate Google doc here Reading |
Tuesday: History of zero (see also here) (L1: Grace, L2: Aiden) Tuesday: Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics (L1: Nigel, L2: Joshua ) Thursday: Multiplication from Lilavati to the Summa (L1: Qiankun, L2: Yinan) |
| XII - 11/8 |
Mathematics in the Islamic World The Islamic Golden Age al-Khwirizmi Omar Khayyam |
Homework 5 is here Reading |
Tuesday: Kepler's disovery of elliptical orbits (L1: Hannah, L2: Eial) Tuesday: The Story of the Binomial Theorem (L1:Avary , L2: Adam) Thursday: The Algebra of Abu Kamil (L1: Pemla, L2: Natalia) |
| XIII - 11/15 |
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 Fermat |
Paper! Submit it in Blackboard. Since I received many requests for extensions, the deadline is postponed until Nov 26 (but you can submit anytime from now on) |
Tuesday: Fermat (L1: Briona, L2: Aaron) Tuesday: History of the Euclidean Steiner tree problem (L1: Sierra, L2: Qimeng ) Thursday: Descartes and Problem-Solving (L1: Elizabeth, L2: Divyan) |
| XIV - 11/22 |
Calculus ideas before the invention of Calculus Barrow Fermat The invention of Calculus Newton Leibniz |
Thanksgiving, no class Thursday |
Tuesday: On Gauss’s First Proof of the Fundamental Theorem of Algebra (L1: Hayley , L2: Eric) Tuesday: Sophie Germain (L1:Rebecca , L2: Weiling ) (see also here ) |
| XV - 11/29 |
Selected topics among the following Back to the Fifth Postulate The four color theorem Mathematical history of computers A chronology of π A brief history of Number theory Fermat Gauss |
Reading |
Tuesday: Mathematicians on Mathematical Patterns in nature, from Antiquity to Turing ( L2: Doyeon) Tuesday: Bernhard Riemann and his contributions to mathematics (L1 : Thomas) Thursday: Hilbert's problems ( L2: Pen) |