How do you measure the size of a black hole? The motion of individual particles at the subatomic level? The possible shape of space-time itself? In short: How do you mathematically describe the world around you? The answer lies in the use of geometry and topology to study and understand the shape of nature, whether leaf formations, DNA entanglements, or quantum fields. Mysterious, complex, and undeniably captivating, the study of the shape of nature lies at the forefront of current research in both mathematics and science. What's more: It's provided us with previously unimaginable scientific and technological advances, including our ability to read genetic data to better determine the relationships between species; closely study how proteins are built through the intricate process of folding; model and predict wind currents around the globe; map the seemingly random terrain of vast mountain ranges; develop facial recognition software for cameras and high-level security systems; and design and improve the way that robots move and behave. While the mathematics involved in the study of shapes and nature is important to how we grasp and live in the world, it remains a mystery to many of us. But these concepts and ideas are not inaccessible. This visually stunning course is your authoritative guide to the mathematical shapes around us: how they're formed, how they're studied, and how they're applied to our everyday lives. In 36 lectures, you'll discover the relationship between mathematics and nature, get a pointed introduction to the language mathematicians use to study shapes and dimensions, and learn how to finally make sense of this abstract—yet undeniably intriguing—subject. Professor Satyan L. Devadoss of Williams College, is a dynamic instructor with a contagious passion for the worlds of geometry and topology. His clear and engaging presentation style, accompanied with animations and graphics, will make your journey into the world of shapes unforgettable.

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