The probabilistic method
by Noga Alon, Joel H. Spencer · first published 1992
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The leading reference on probabilistic methods in combinatorics-now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as m
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The Probabilistic Method by Noga Alon and Joel H. Spencer. I took a seminar on the probabilistic method and my advisor recommended me to read this book. This book is for scientists. It lays out the foundation of the probabilistic…
on “Ask HN: What are your favorite statistics and probability textbooks?” ↗…existence of objects with desired properties. Some of them rely on the "first moment" (expectation) which seems to be what you are saying. These tend to be the simpler ones. A good book on the topic is The Probabilistic Method by Alon and Spencer. To give you some hint of what randomness can get you, look at the most typical random graph model, which for a probability p selects an edge uniformly and independently with that…
on “Randomness Improves Algorithms” ↗…the most, so I'd probably go with that, though I haven't really read them in parallel yet. For the discrete math students out there, after learning the basics of probablistic method (Alon, Spencer's Probabilistic Method being the seminal textbook, I think), you could continue with both some probabilistic algorithm book to apply what you've learned in CS (I did take a course in that, though, so I can't vouch for the best…
on “Math ∩ Programming” ↗