| Week | Topics | Assignment due dates and presentations | Paper due dates | Presentations |
|---|---|---|---|---|
| I - 1/23 | Introduction About mathematics and its the history What is mathematics? What do we mean by mathematics? How do we study the history of mathematics Sources: Primary and secondary. Reliable and not so much. Why do we trust statements about mathematics? Why do we trust statements about the history of mathematics? |
HW0: Getting to know you. | ||
| II - 1/30 | The very beginning of mathematics What is counting Counting in different societies What is a natural (or counting) number History of mathematics hidden in language. Number systems Characteristics of number systems Number systems of different societies. Rough timeline of the history mathematics |
Reading for this week. HW1 (covering topics of week I, to submit in Brightspace) |
Here you can find guidelines for the presentation as well as which topic you were assigned, scroll down. (Make sure you check the correct lecture, 1 or 2) | |
| III- 2/6 | Ancient Egypt Primary sources Number systems Methods of multiplication and division. Fractions as a sum of parts False position and other algebraic problems Geometry: Areas and volumes, approximation of π |
Reading : These notes from the Open University from the beginning until Question 2 in Section 1.1.2. (Of course you are welcome to read them all...) HW2 Number systems (to submit in Brightspace) |
Summary of assigned paper (It should be between 200 and 400 words.) | |
| IV - 2/13 | Ancient Mesopotamia Primary sources Number systems Mathematical tablets: multiplication tables, reciprocals, square roots. Areas of plane shapes Solutions of linear and quadratic equations Plimpton 322 Mathematics and the beginning of writing |
Q1: Number systems Reading: text from the Open University from the beginning to Section 1.5 Plimpton 322 (as usual, you are encouraged to read it all.) |
Abstract of your paper (submit in Brightspace, between 200 and 400 words. It is OK if you need to change the abstract when you submit the paper.) Draft of the slides of your presentation (in Google Slides.You have to create the slides, with title, your name and the bibliography and share with your instructor and the grader. Of course you can do more... ) |
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| V - 2/20 | Mayan Mathematics Primary sources Number systems Calendars Inca Mathematics Primary sources Number systems Mathematics in Africa- Ethnomathematics |
Reading for this week. HW3: Egypt and Mesopotamia (to submit in Brightspace) |
Outline |
The Beginnings of Probability Theory Pascal and the Invention of Probability Theory (or Pascal and the Problem of Points) |
| VI - 2/27 | The beginning of Mathematics in Ancient Greece The Pythagoreans, Zeno, Plato, Aristotle The three impossible Problems of Antiquity Numbers and magnitudes |
Reading : The first two pages of this paper. |
Annotated bibliography |
Euler and the proof of the Fundamental Theorem of Algebra A Sampler of Euler's Number Theory book chapter The Extraordinary Sums of Leonhard Euler book chapter |
| VII - 3/5 | Mathematics in Ancient Greece: Euclid's Elements Axiomatic systems now and then Geometric Algebra Pythagorean Theorem Areas and volumes |
Q2: Egypt Reading |
Math point |
Gauss and the Regular Polygon of Seventeen Sides Gauss-Jordan Reduction: A Brief History On Gauss's First Proof of the Fundamental Theorem of Algebra |
| Spring Break! | ||||
| VIII - 3/19 | Mathematics in Ancient Greece: Euclid's Elements Incommensurables Infinitude of primes Geometry Number theory |
Q3: Mesopotamia This article, pages 412, 413, and 414 (and more if you wish!) |
Baby draft (500 words) |
How Ptolemy constructed trigonometry tables |
| IX - 3/26 | Mathematics in Ancient Greece: Archimedes
Archimedes on the law the lever Computation of the volume of the sphere |
Draft (1000 words) | ||
| X - 4/3 | Mathematics in Ancient Greece: After Euclid's Elements Erathostenes Apollonius on conic sections Ptolemy Diophantus Astronomy |
HW4: Greece (to submit in Brightspace) |
Heron's Formula for Triangular Area book chapter Hippocrates' Quadrature of the Lune book chapter |
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| XI - 4/10 | Ancient and Medieval China Number systems Counting boards and rod numerals Algorithms for multiplication, division, computation of square and cubic roots Solutions of linear, quadratic and higher degree polynomial equations. Chinese reminder theorem. The Nine Chapters of the Mathematical Arts and the Book of Numbers and Computations Liu Hui, Zu Chongzhi and Zu Geng The volume of the sphere Approximation of π The Pythagorean Theorem |
HW5: Iconic Wall - Review (to submit in Brightspace) Reading: Brief summary of Ancient Chinese Mathematics |
Paper |
The "piling up squares"in Ancient China The Non-Denumerabilty of the Continuum book chapter Cantor and the Transfinite Realm book chapter |
| XII - 4/17 | Ancient and Medieval India The Indus or Harappan civilisation Geometry and the sulba sutras Jain mathematics Mathematics and Sanskrit grammar Development of Indian numerals Aryabhatta, Brahmagupta, Bhaskara II Approximation of π The Pythagorean Theorem |
Q4: Greece. Reading: The hindu-arabic numerals.Reading: History of zero. Activity 1 link (lecture 1) Activity 2 link Activity 3 link Aryabhatta Table of Sines |
The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha | |
| XIII - 4/24 | Mathematics in the Islamic World Amalgamation and progress of knowledge Systematization of the positional number system Relation between algebra and geometry Advances in plane and 3D geometry, spherical geometry, number theory. al-Khwarizmi, Abu Kamil, Omar Khayyam Renaissance Perspective, geography and navigation, astronomy and trigonometry, logarithms, kinematics Cardano, Tartaglia and the saga of the solution of the cubic equation. The beginning of symbolic algebra: Stevin and Viete |
Q5: Review. The quiz will consist in two of the four questions of HW6. Reading: Brief summary of Mathematics in the Islamic World |
Ramanujan's Notebooks (also The Indian Mathematician Ramanujan) |
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| XIV- 5/1 | Calculus ideas before the invention of Calculus Tangents and extrema, areas and volumes, power series, rectification of curves and the fundamental theorem of calculus Barrow Fermat Descartes The discovery of Calculus Newton Leibniz |
HW6: Review (to submit in Brightspace) |
Ideas of Calculus in Islam and India The Lost Calculus (1637-1670): Tangency and Optimization without Limits |