| #12 - Nov 9 | Mathematics
in the Islamic Word. Algebra: al-Khwarizmi Geometry: parallel postulate, trigonometry. Solution of cubic equations: Omar Khayyam
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| #13- Nov 16 |
Medieval
Europe: Selected TopicsLeonardo of Pisa Liber
abbaci (Fibonacci) Mathematics in the Renaissance: Selected topics The Italian Abacists. The solution of the cubic equation (Fibonacci, Cardano, Tartaglia, Ferrari) Galileo's arithmetic Descartes Discourse on Method. Geometry vs Algebra. An excerpt from Mathematics in the 20th century by Sir Michael Atiyah https://people.math.umass.edu/~hacking/461F19/handouts/atiyah.pdf
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| Nov 23rd |
Thanksgiving week |
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| #14- Nov 30 |
Seventeenth
century: Selected Topics Analytic geometry: Fermat and Descartes Pascal and Probability Fermat on Number Theory Cavalieri Calculus before calculus (methods to find tangents, extrema, lengths, areas, volumes. Infinitesimals and indivisibles. Cavalieri.) The fundamental theorem of calculus: Barrow and Gregory Newton Leibniz History of calculus Desargues Theorem (see demo here and here) Newton (see here) Draft
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| #15-Dec
7 |
Eighteen
Century-topics selected among the following) The parallel postulate Euler on the beginning of topology (seehere) Cramer, Euler and the solution of equations Euler on number theory Nineteenth Century The method of Least Squares (Gauss and Legendre) Gauss and Congruences, Quadratic Reciprocity The unsolvability of the Quintic Equation Non-euclidean Geometry. Cantor and the theory of sets Babbage, Lovelace and computers Matrices and Systems of Linear Equations Twentieth Century Computers and Mathematics The proof of the four color theorem
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The past |
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| 1- Aug 24 | Administrative
stuff What is mathematics? The Ishango bone Primitive Counting Number Systems>(click on the appropriate links on the left tab to see the content). See also here for a description of most of the number systems we discussed this week. A short description of hieroglyphic Egyptian number system can be found here. Math timeline from Mathigon Timeline for the History of Mathematics by Prof William H. Richardson from Wichita State University. Monday Lecture Slides Wednesday Lecture Slides
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| 2- Aug 31 | Ancient
Egypt Number system. Multiplication and division. Fractions (parts) Geometry: Areas and volumes. Here is a translation of the Rhind papyrus. The Rhind papyrus is in the British Museum, whose website, contains imageshereandhereof this document. Here is a podcast about the Rhind papyrus, also from the British Museum. A nice article about the first 6 problems of the Rhind Papyrus: Problems 1 to 6 of the Rhind Mathematical Papyrus. Three pyramides that make a cube
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3 -Sep 7 |
Ancient
Egypt Method of false position. Geometry: Areas and volumes. Wednesday Lecture Slides
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| 4-Sep 14 | Ancient
Mesopotamia Number system. Tables of reciprocals and multiplication Solutions of linear and quadratic equations. Square roots and the Pythagorean Theorem. Reading: Babylonian Mathematics Monday slides Wednesday slides Schedule your presentation rehearsal here. Email me if you cannot make any of the available times.
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| 5- Sep 21 | Mathematics around the world Mayan mathematics: (here is a good resource about the Mayan calendars) Incan kipus The Pacific Africa (see here)' Thanks to all of you who answered the questions about the class. Those of you who did not, can still answer here. Some of you mentioned that it would be useful to have the slides in advance. From now on, I will post then in this folder (it is now empty) on the day before the lecture, at 7pm the latest (I may do minor modifications of the slides after that). The folder is empty now. I will also post in the same folder the after class version of the slides, the day after the lecture (and will not put the links in this schedule) Link to class summary for Wednesday September 23rd.
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| 6-Sep 28 | Hellenic
mathematics up to Euclid Socrates,Plato, Aristotle Thales, Pythagoras and the Pythagoreans Figurate numbers Reading: Plato Meno Greek number systems
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| #7- Oct 5 | Euclid
and the Elements, part 1 Construction of the equilateral triangle Proof of the Pythagorean theorem Euclid's Elements (Website) Different versions of Euclid's Elements in pfd (here, here and here) The first six books of the elements of Euclid , by Oliver Byrne (interactive, with wonderful illustrations) pdf and website
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| #8- Oct 12 | Euclid
and the Elements, part 2 Proof of the Pythagorean theorem cont. Infinitude of primes. What is an axiom system? Time permits: Euclidean Algorithm and Number Theory Optional Read: Proclus and the history of geometry as far as Euclid
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| #9 - Oct 19 | Hellenic
mathematics after Euclid to fourth century AD Archimedes. Determination of π, Law of the lever, Method of Discovery, Volume of the Sphere. Eratosthenes: dimension of the Earth. Apollonius' Conics. Ptolemy: Table of chords, Solving Plane Triangles Three famous unsolved problems Diophantus and the Arithmetica History of Trigonometry by David E. Joyce. Interesting read related to proofs.
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| #10- Oct 26 | Ancient
and Medieval Chinese Mathematics Geometry: The Pythagorean theorem Calculating with numbers: Number System Calculating with numbers: Extractions of square roots. Magic squares An Outline on Ancient and Medieval Chinese Mathematics by David E . Joyce). Another survey can be found here
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| Week | Topics, Presentations, Reading and Deadlines | ||||||
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| #11-Nov 2 | Ancient
and Medieval Indian Mathematics Number system Sulba-sutras The so called Fibonacci numbers. Indian Mathematics: an Outline by David E. Joyce) About the zero.
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