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Cargando... Elements of Mathematics: From Euclid to Gödel (2016 original; edición 2016)por John Stillwell (Autor)
Información de la obraElements of Mathematics: From Euclid to Gödel por John Stillwell (2016)
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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics-but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits.From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries. No se han encontrado descripciones de biblioteca. |
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Google Books — Cargando... GénerosSistema Decimal Melvil (DDC)510.71Natural sciences and mathematics Mathematics General Mathematics Education And Research EducationClasificación de la Biblioteca del CongresoValoraciónPromedio:
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How many professional mathematicians are, for example, going to patiently read Chapter 6 on Calculus? If, as seems to still be the case, Georgia Tech basketball players are required to take 2 semesters of Calculus, shouldn't it now be considered something understood by the educated layman?
I still view Stillwell as one of mathematics' most talented expositors, but trying to make a book like this be a worthwhile purchase for both high school students and professional mathematicians may be an impossible task for even him. ( )