## The First 498 Bernoulli Numbers By: Simon Plouffe (1956-) |
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In "The First 498 Bernoulli Numbers," mathematician Simon Plouffe takes readers on an informative journey through the intricate world of Bernoulli numbers. Plouffe's meticulous exploration of this mathematical concept is both comprehensive and accessible, offering an insightful perspective for both experts and those new to the subject. Plouffe begins by introducing readers to the fascinating history of the Bernoulli numbers, shedding light on the significant contributions made by the Bernoulli family over several generations. This historical context helps readers appreciate the profound impact these numbers have had on various areas of mathematics, including number theory, algebra, calculus, and beyond. One of the standout features of this book is Plouffe's exceptional ability to explain complex mathematical concepts in a way that is understandable to a wide range of readers. Through clear explanations and engaging examples, he unravels the mysteries behind the Bernoulli numbers, making them accessible to both advanced learners and those with less mathematical background. Furthermore, the author delves into the many applications of Bernoulli numbers, demonstrating how they find relevance in diverse fields such as physics, computer science, and cryptography. Plouffe skillfully intertwines theory and practicality, showcasing the versatility and significance of these numbers in real-world contexts. "The First 498 Bernoulli Numbers" is also commendable for the inclusion of mathematical proofs, which allow readers to fully grasp the underlying principles and logic. Plouffe presents these proofs in a step-by-step manner, guiding readers through each logical deduction with clarity and precision. However, one potential drawback of the book is its limited discussion on recent developments and applications of Bernoulli numbers. While Plouffe adequately covers the historical and foundational aspects, a more comprehensive exploration of contemporary advancements would have added value to the overall reading experience. In conclusion, Simon Plouffe's "The First 498 Bernoulli Numbers" is a captivating and enlightening exploration of an important mathematical concept. Through his clear and concise explanations, historical narratives, and engaging examples, Plouffe makes Bernoulli numbers accessible to all curious minds. Despite the slight absence of contemporary developments, this book is an invaluable resource for anyone seeking a deeper understanding of the Bernoulli numbers and their significance in the mathematical realm. ## First Page:Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.caThe first 498 Bernoulli numbers are the coefficients of the series expansion of texp(xt)/(exp(t) 1) = sum( B(n,x)/n!t^n, n=0..infinity ). Bernoulli(2) 1/6 Bernoulli(4) 1/30 Bernoulli(6) 1/42 Bernoulli(8) 1/30 Bernoulli(10) 5/66 Bernoulli(12) 691/2730 Bernoulli(14) 7/6 Bernoulli(16) 3617/510 Bernoulli(18) 43867/798 Bernoulli(20) 174611/330 Bernoulli(22) 854513/138 Bernoulli(24) 236364091/2730 Bernoulli(26) 8553103/6 Bernoulli(28) 23749461029/870 Bernoulli(30) 8615841276005/14322 Bernoulli(32) 7709321041217/510 Bernoulli(34) 2577687858367/6 Bernoulli(36) 26315271553053477373/1919190 Bernoulli(38) 2929993913841559/6 Bernoulli(40) 261082718496449122051/13530 Bernoulli(42) 1520097643918070802691/1806 Bernoulli(44) 27833269579301024235023/690 Bernoulli(46) 596451111593912163277961/282 Bernoulli(48) 5609403368997817686249127547/46410 Bernoulli(50) 495057205241079648212477525/66 Bernoulli(52) 801165718135489957347924991853/1590 Bernoulli(54) 29149963634884862421418123812691/798 Bernoull... Continue reading book >> |

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