Ronald Graham – författare

Who first presented Pascal's triangle? (It was not Pascal.)Who first presented Hamiltonian graphs? (It was not Hamilton.)Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

This is a book about a gambling system that works. It tells the story of how the author used computer simulations and mathematical modeling techniques to predict the outcome of jai-alai matches and bet on them successfully - increasing his initial stake by over 500% in one year! His results can work for anyone: at the end of the book he tells the best way to watch jai-alai, and how to bet on it. With humour and enthusiasm, Skiena details a life-long fascination with computer predictions and sporting events. Along the way, he discusses other gambling systems, both successful and unsuccessful, for such games as lotto, roulette, blackjack, and the stock market. Indeed, he shows how his jai-alai system functions just like a miniature stock trading system. Do you want to learn about program trading systems, the future of Internet gambling, and the real reason brokerage houses don't offer mutual funds that invest at racetracks and frontons? How mathematical models are used in political polling? The difference between correlation and causation? If you are curious about gambling and mathematics, odds are this book is for you!

The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple, clear but rigorous definitions of mathematical concepts they handle intuitively in their work.

Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.

Jake came home from war. He just didn't come back whole. After years of service, Jake returns to a life that no longer fits — a house that feels foreign, relationships strained beyond recognition, and a silence inside him louder than anything he faced overseas. The weight he carries isn't visible. There are no wounds anyone can point to. But it's there, pressing down on every moment, every conversation, every attempt to simply be present. The Weight of Stillness is a raw and unflinching look at what homecoming actually costs. It's not a story about valor or glory — it's a story about a man trying to remember who he was before the war, and reckoning with the fact that person may be gone. Jake's journey is one of moral injury, fractured identity, and the terrifying work of learning to exist in stillness when everything in you is still braced for impact. For veterans who have felt unseen, for families who don't know what to say, and for anyone who has ever loved someone who came home changed — this book is for you.

She did everything right. The institution didn't.Amber Clark came home from the Army with an honorable discharge, a structured life, and a fracture so quiet she had nearly convinced herself it wasn't there. She had served with distinction. She had filed a report. She had watched it disappear into a system designed to protect itself. So she did what survivors do — she kept going, built a life, and became very good at being fine.The Quiet Fracture is the story of military sexual trauma told not in headlines or hearings, but in grocery store parking lots and two a.m. wakeups and the exhausting labor of seeming whole. It's about the specific grief of trusting an institution that failed you, and what it costs to carry that alone for years — and what becomes possible when you finally stop. Amber's story is not easy. It was never meant to be. It was meant to be true.For every woman who served. For the ones who reported and weren't believed. For the ones who never reported at all.

Jimmy and Kyle didn't serve. They didn't have to — the war came home to them. Raised in households shaped by deployment, trauma, and the particular silence of parents who couldn't talk about what they'd seen, these two young men are navigating adulthood with maps drawn from someone else's damage. They're angry in ways they can't name. They're loyal to people who hurt them. And they're trying to figure out who they are when the only models they had were men held together with suppression and willpower. Jaded Youth is a story about inheritance — not the kind in wills, but the kind passed down in patterns, in wounds, in the way a father's flinch becomes a son's worldview. It's about breaking cycles that were never yours to carry, and finding your own footing when the ground was always shifting.For the children of veterans, the next generation carrying weight they didn't ask for — and for anyone trying to become something different than what they came from.