Numbers surround us. They mark our days, light our nights, foretell our weather, and keep us on course. They drive commerce and sustain civilization. But what are they? These 24 lectures explore this fascinating question and the equally fascinating history of numbers. Professor Burger’s historical, global, and conceptual approach to numbers gives you not only a revealing tour of mathematical history but shows how and why numbers evolved, as well as the transforming implications of each advance for both mathematics and society. Professor Burger structures this investigation into the concept of number with five main points of focus, each of which informs the other and allows our understanding to grow and evolve in step with the numbers themselves. You’ll examine early conceptual underpinnings of numbers that led to our current common notion of number; learn how numbers eventually took on a life of their own within the larger structure of mathematics; ponder the stories of ? and e - the two most important numbers in our universe; explore the algebraic and analytic evolutions of number; and delve into the idea of infinity, which holds many fascinating features. Among the types of numbers you explore throughout the course are: real numbers, or numbers that can be given by an infinite decimal representation; natural numbers, used primarily for counting and ordering; prime numbers, which are natural numbers greater than 1 that can be divided by only 1 and itself; irrational numbers, which are numbers that cannot be expressed as simple fractions; and transcendental numbers, or irrational numbers that are not algebraic.

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