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he area of study known as the **history of mathematics** is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.

Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are *Plimpton 322* (Babylonian c. 1900 BC),^{[2]} the *Rhind Mathematical Papyrus* (Egyptian c. 2000–1800 BC)^{[3]} and the *Moscow Mathematical Papyrus* (Egyptian c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.

The study of mathematics as a demonstrative discipline begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek *μάθημα* (*mathema*), meaning "subject of instruction".^{[4]} Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics.^{[5]} Chinese mathematics made early contributions, including a place value system.^{[6]}^{[7]} The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in Indiaand were transmitted to the west via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī.^{[8]}^{[9]} Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations.^{[10]} Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.

From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day

#### Chapter 1: History of Mathematics

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Lecture 9: A.C. King, J. Billingham

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Lecture 10: S. Axler F.W. Gehring K.A. Ribet

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Lecture 12: D. W. Jordan and P. Smith

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Lecture 14: D. W. Jordan and P. Sm

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Lecture 15: Endre Suli and David F. Mayers

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Lecture 18: Shmuel Kantorovitz

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Lecture 20: Kenneth S. Williams

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