Math Girls 3: Godel's Incompleteness Theorems

ISBN-13: 9781939326294 / Angielski / Twarda / 2016 / 394 str.

Hiroshi Yuki

Opis

In the early twentieth century, a massive undertaking to rid mathematics of all paradoxes and inconsistencies was underway. Known as Hilberts program, it sought to provide an unshakable foundation for all of mathematics. Things seemed to be proceeding well until young Kurt Gödel stunned the world by proving that Hilberts goals were unobtainable, that contradiction was part of the warp and weave of any mathematical system. Yet what at the time seemed to be a fatal blow to mathematical consistency now forms the basis of modern logic. Gödels incompleteness theorems are often misunderstood to be a statement of the limits of mathematical reasoning, but in truth they strengthen mathematics, building it up to be more powerful than what had come before. In this third book in the Math Girls series, join Miruka and friends as they tackle the basics of modern logic, learning such topics as the Peano axioms, set theory, and diagonalization, leading up to an in-depth exploration of Gödels famous theorems. Along the way, visit other interesting and important topics such as trigonometry and the epsilon-delta definition of limits, and of course take on challenges from the enigmatic Mr. Muraki. Math Girls 3: Gödels Incompleteness Theorems has something for anyone interested in mathematics, from advanced high school students to college math majors and educators.