Elements of Mathematics: From Euclid to Gödel by John Stillwell PDF

By John Stillwell

ISBN-10: 0691171688

ISBN-13: 9780691171685

ISBN-10: 0691178542

ISBN-13: 9780691178547

Elements of Mathematics takes readers on a desirable travel that starts off in uncomplicated mathematics—but, as John Stillwell exhibits, this topic isn't really as straightforward or effortless as one may possibly imagine. no longer all subject matters which are a part of state-of-the-art user-friendly arithmetic have been continually regarded as such, and nice mathematical advances and discoveries needed to ensue to ensure that definite matters to develop into "elementary." Stillwell examines uncomplicated arithmetic from a particular twenty-first-century standpoint and describes not just the wonder and scope of the self-discipline, but in addition its limits.

From Gaussian integers to propositional good judgment, Stillwell delves into mathematics, computation, algebra, geometry, calculus, combinatorics, likelihood, and good judgment. He discusses how each one sector ties into extra complex issues to construct arithmetic as an entire. via a wealthy choice of simple ideas, bright examples, and fascinating difficulties, Stillwell demonstrates that simple arithmetic turns into complex with the intervention of infinity. Infinity has been saw all through mathematical historical past, however the contemporary improvement of "reverse arithmetic" confirms that infinity is vital for proving recognized theorems, and is helping to figure out the character, contours, and borders of hassle-free mathematics.

Elements of Mathematics provides readers, from highschool scholars to specialist mathematicians, the highlights of effortless arithmetic and glimpses of the components of math past its boundaries.

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Elements of Mathematics: From Euclid to Gödel by John Stillwell

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