Algebra: Rules and Symbols

Instructor: Suman Ganguli
This is an online course (Eastern Standard Time)

What is algebra? This question is not as simple as it seems. In this course, we will explore the meaning and extraordinary mathematical power of algebra through a study of its historical development. We’ll begin with so-called classical algebra—or the invented use of letter symbols (variables) to represent numbers and the rules for their manipulation. Using variables led to the key concepts such as polynomials and a focus on solving equations–a focus that drove the development of algebra for a millenia, from Babylonian cuneiform tablets to the influential 9th-century treatise “?is?b al-jabr wa’l-muq?bala(Calculation by Completion and Balancing) by al-Khwarizmi. Next, we’ll explore the development of symbolic algebra (initiated by the Latin translation of al-Khwarizmi), the utilization of cubic equations, which gave rise to complex numbers, and Descartes’s breakthrough invention of an X-Y coordinate system, which tied together for the first time algebra and geometry. Finally, we’ll explore the multiplicity of algebras that blossomed in the 19th century till today: linear (matrix) algebra, which arose from solving system of linear equations; “abstract” algebra, which defined algebraic structures such groups, fields, and rings; and Boolean algebra, which treated logic algebraically. Throughout, we’ll ask: how does algebra undergird the ways we interpret, organize and manipulate the world? 

Course Schedule

Tuesday, 6:30-9:30pm EST
October 20 — November 17, 2020
4 sessions over 5 weeks
Class will not meet Tuesday, November 3rd.


Registration Open

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