| Week | Topics Covered | Assignments and presentations | |
|---|---|---|---|
| I - 8/22 |
Introduction and organizational details About mathematics and its the history What is mathematics? What do we mean by mathematics? How do we study the history of mathematicsSources: Primary and secondary. Reliable sources. The very beginning of mathematics What is counting Counting in different societies What is a natural (or counting) number |
Optional reading about the beginnings of counting. Homework 0 form (Google form)On Thursday of this week, we are going to decide the groups for the presentations. It would be good if you look at the topics of the presentations and think which ones you would like to work on. |
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| II - 8/29 |
Number systems Characteristics of number systems Number systems of different societies. About mathematics and its the history Rough timeline of mathematics Why trust statements in mathematics? The very beginning of mathematics History of mathematics hidden in language. |
Reading for this week. HW1 (covering topics of week I) |
Not yet |
| III - 9/5 | 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: Read 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 |
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| IV - 9/12 | 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: This text from the Open University from the beginning to Section 1.5 Plimpton 322 (as usual, you are encouraged to read it all.) Google Form (to be filled individually): outline, abstract, math point, bibliography and draft of slides of the presentation (Note: The slides should be done in Google slides. Make sure you share the slides with Nicole -our grader- and me, using the stonybrook.edu email addresses.) |
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| V -9/19 | 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 Presentation: History of Mathematics in the Sub-Saharan Africa (pre-independence) |
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| VI - 9/26 | 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. Q2: Egypt Optional (and recommended) assignment: There is an assignment in Blackboard to fill the topic of your paper so I can give you feedback. Presentation: History of Mathematical Games and Recreations |
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| VII - 3/10 | Mathematics in Ancient Greece: Euclid's Elements Axiomatic systems now and then Geometric Algebra Pythagorean Theorem Areas and volumes |
Reading: This paper. Quiz 3: Mesopotamia Form: Paper outline, bibliography and abstract. Presentation: History of Perfect Numbers |
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| VIII - 10/10 |
Fall break. No class on Tu Oct 11th Mathematics in Ancient Greece: Euclid's Elements Incommensurables Infinitude of primes Geometry Number theory |
Presentation: History of the Method of Exhaustion |
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| IX - 10/17 | Mathematics in Ancient Greece: Euclid's Elements, Archimedes Archimedes on the law the lever Computation of the volume of the sphere |
HW4 Euclid's Elements. Presentation: Archimedes on the Quadrature of the Parabola |
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| X - 10/24 | Mathematics in Ancient Greece: After Euclid's Elements Erathostenes Apollonius on conic sections Ptolemy Diophantus Astronomy |
Quiz 4: Euclid's Elements Presentation: Diophantus: his work and impact |
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| XI - 10/31 |
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 |
Presentation: History of Japanese Mathematics The link for Baby Draft Paper has to be submitted here. This is the same paper form with one more question. You can edit it, if needed. But remember that I have to give you the OK for the topic.In this link you can find a Google Doc with a list of the items that you have to include in the first page of your draft and your paper. You can copy the text and paste it in your own document and fill it up. Remember, you only need to submit a text with at least 200 words. I suggest that you write the introduction at the very end (and of course you did not need to submit the introduction with the draft). The assignment will be graded by "Complete" or "Incomplete." (Recall that here is sample page like the one you are asked to fill.) |
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| XII - 11/7 |
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 |
The link draft Paper has to be submitted here. (same as the baby draft) In this link you can find a Google Doc with a list of the items that you have to include in the first page of your draft and your paper. You can copy and paste it in your own document and fill it up. You need to submit 500 words in the body of the paper. The assignment will be graded by "Complete" or "Incomplete." Presentation: Ideas of Calculus in India |
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| XIII - 11/14 |
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 |
Here you can find the rubric for the paper. Please read it!.
Presentation: Thabit Ibn Qurra and the Pythagorean Theorem HW5 |
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| XIV - 11/21 | Thanksgiving. No class on Th Nov 24 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 |
Presentation (on Tuesday ): The length of curves and their history |
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| XV - 11/28 | Miscellanea Mathematical history of "the fourth dimension" Area of the circle through the times Map coloring problems History of number theory and The Prime Number Theorem History of the parallel postulate - Curvature Mathematics, computers and calculators. |
The paper is due on Monday Nov 28th. Please submit it in Blackboard and make sure that the paper starts with the information (abstract, outline, etc) requested in the draft. |
