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The very idea of imaginary numbers appears at first glance preposterous, like something out of science fiction or the wildest philosophy. A real or ordinary number multiplied by an “imaginary unit” somehow mathematically produces a “complex” number that has both theoretical and practical applications. Rene Descartes, who coined the “imaginary” terminology, deemed them preposterous. And yet, imaginary numbers are indispensable—not only in geometry, number theory, and physics, but also for engineering and design in everything from aerospace to robotics to video games.
How did imaginary and complex numbers develop from their early roots in ancient classical algebra to their manifold applications today? And what are their implications not only for science and technology, but for our very philosophical conceptions of mathematics, and indeed mathematics’ relationship with physical reality?
In this course we will study the mathematics of imaginary numbers, their historical development, and questions they raise in the philosophy of mathematics. Students will trace their history and explore imaginary and complex numbers from an algebraic and geometric points of view. In particular, we will examine the elegant geometric interpretation of imaginary and complex numbers as forming a two-dimensional “complex plane,” which accelerated the acceptance of complex numbers as legitimate mathematical objects.
We will then investigate how applying calculus within this context gave rise to the field of complex analysis—which has proven to be remarkably useful in physics and engineering – and the field of complex dynamics which led to discovery of beautiful mathematical objects such as the Mandelbrot set—and the recognition of fractal geometry in natural phenomena like clouds, plants, geological formations, and more.
Finally, we’ll discuss not only our overarching questions but what are the further potential theoretical and practical implications of imaginary and complex numbers.
This course is available for "remote" learning and will be available to anyone with access to an internet device with a microphone (this includes most models of computers, tablets). Classes will take place with a "Live" instructor at the date/times listed below.
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This class isn't on the schedule at the moment, but save it to your Wish List to find out when it comes back!
The Brooklyn Institute for Social Research was established in 2011 in Boerum Hill, Brooklyn. Its mission is to extend liberal arts education and research far beyond the borders of the traditional university, supporting community education needs and opening up new possibilities for scholarship in the...
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What does it mean to be “avant-garde”? At the start of the 20th century, a heterogeneous assortment of artists undertook to explore and depict, in the words of Susan Buck-Morss, “a human sensorium fundamentally altered by the tempos and technologies of factory and urban life”—and, not least of all, world war and political revolution. The...
Monday Oct 17th, 6:30pm - 9:30pm Eastern Time(4 sessions)
When W.E.B. Du Bois declared that “the problem of the 20th century is the problem of the color line” in The Souls of Black Folk, it was not some miraculous prophecy or intuition. Having already authored the foundational text of American sociology, The Philadelphia Negro, Du Bois synthesized his social scientific training in Germany, including...
Tuesday Oct 18th, 6:30pm - 9:30pm Eastern Time(4 sessions)
Algeria was the crown jewel of the waning French empire. And so when the guerillas of the Algerian National Liberation Front launched the Algerian War of Independence, France, determined to retain its 120-year-old colony, responded with every available method of colonial oppression: torture, terror, rape, and massacre. The Algerian revolutionaries...
Sunday Oct 23rd, 2pm - 5pm Eastern Time(4 sessions)
Since its first formulation in the early 1960s, the concept of “participatory democracy” has come to take on multiple meanings—some of them complementary, others conflicting. Promoted by a wide variety of theorists, activists, social movements, and political parties, conceptions of participatory democracy range from deepened civic engagement...
Monday Nov 14th, 6:30pm - 9:30pm Eastern Time(4 sessions)
Critical Theory and the Now: a Contemporary Introduction to the Frankfurt School In 1930, Max Horkheimer became the director of the Institute for Social Research in Frankfurt, Germany. Along with his colleagues and a broader orbit of external scholars, he inaugurated the first wave of what came to be called “critical theory.” This course is...
Tuesday Nov 15th, 6:30pm - 9:30pm Eastern Time(4 sessions)
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