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High Quality Content by WIKIPEDIA articles! In mathematics, Bertrand's postulate (actually a theorem) states that for each n 2 there is a prime p such that n p 2n. It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan. The gist of the following elementary but involved proof by contradiction is due to Paul Erd s, the basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough.

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High Quality Content by WIKIPEDIA articles! In mathematics, Bertrand's postulate states that for each n 2 there is a prime p such that n p 2n. It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan. The gist of the following elementary but involved proof by contradiction is due to Paul Erd s, the basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough. It is then shown by some extended computation that the second fact is inconsistent with the first one. Therefore Bertrand's postulate must hold. In order to present the main argument of the proof intelligibly, these lemmas and a few auxiliary claims are proved separately first.

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96,90 CHF *

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This textbook covers the mathematical foundations of the analysis of algorithms. The gist of the book is how to argue, without the burden of excessive formalism, that a given algorithm does what it is supposed to do. The two key ideas of the proof of correctness, induction and invariance, are employed in the framework of pre/post-conditions and loop invariants. The algorithms considered are the basic and traditional algorithms of computer science, such as Greedy, Dynamic and Divide & Conquer. In addition, two classes of algorithms that rarely make it into introductory textbooks are discussed. Randomized algorithms, which are now ubiquitous because of their applications to cryptography; and Online algorithms, which are essential in fields as diverse as operating systems (caching, in particular) and stock-market predictions. This self-contained book is intended for undergraduate students in computer science and mathematics.

Anbieter: Orell Fuessli CH

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Hillbilly Elegy: A Memoir of a Family and Culture in Crisis by J. D. Vance Book Summary Readtrepreneur (Disclaimer: This is NOT the original book, but an unofficial summary.) A tale of how hard it is to move up without going back down once again. Hillbilly Elegy portrays a family without money in their pockets and doing anything in their hands to escape from the clutches of poverty. Through a lot of struggle, they managed to have a grandchild who would graduate from Yale Law School. Everything appeared to be fine, but the ghosts of the past still haunts the protagonist who is trying to move up while supporting his family. (Note: This summary is wholly written and published by readtrepreneur.com It is not affiliated with the original author in any way) 'Psychologists call it 'learned helplessness' when a person believes, as I did during my youth, that the choices I made had no effect on the outcomes in my life.' - J.D. Vance A memoir of a man who suffered a lot to get to where he is. It serves as an analysis of a culture in crisis but also, as proof that hard work pays off and that it doesn't matter how bad your situation is, you can always move forward. A very touching story with a bit of humor and a lot of interesting anecdotes. Many people have lost the opportunity to touch the American dream, J.D Vance talks all about in this moving memoir. P.S. Hillbilly Elegy is an extremely touching book which serves as an eye-opener about the cultural decline of the United States. The Time for Thinking is Over! Time for Action! Scroll Up Now and Click on the 'Buy now with 1-Click' Button to Download your Copy Right Away! Why Choose Us, Readtrepreneur? &#9679; Highest Quality Summaries &#9679; Delivers Amazing Knowledge &#9679; Awesome Refresher &#9679; Clear And Concise Disclaimer Once Again: This book is meant for a great companionship of the original book or to simply get the gist of the original book.

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54,99 € *

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Anbieter: Thalia AT

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3,99 € *

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Anbieter: Thalia AT

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