Algebra: Rules and Symbols (Live Online)

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. The use of variables led to key concepts such as polynomials and a focus on solving equations—a focus that drove the development of algebra for millennia, from Babylonian cuneiform tablets to the influential 9th-century treatise “al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabalah” (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’ 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 have blossomed from the 19th century to 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?