Hard Proof
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| Author | : Martin Aigner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 194 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662223430 |
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
| Author | : Jan Krajíček |
| Publisher | : Cambridge University Press |
| Total Pages | : 533 |
| Release | : 2019-03-28 |
| Genre | : Computers |
| ISBN | : 1108416845 |
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
| Author | : Richard H. Hammack |
| Publisher | : |
| Total Pages | : 314 |
| Release | : 2016-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780989472111 |
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
| Author | : Steve Johnson |
| Publisher | : Pearson Education |
| Total Pages | : 625 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 0789751623 |
Need answers quickly? Adobe Photoshop CC on Demand provides those answers in a visual step-by-step format. We will show you exactly what to do through lots of full color illustrations and easy-to-follow instructions. Includes * Online Workshops that focus on real-world techniques * Online Adobe certification resources for both ACE and ACA * More than 500 essential Photoshop CC tasks Inside the Book * Improve productivity and efficiency with Adobe Creative Cloud * Use automatic saving options for better efficiency and protection * Use automatic layer alignment and blending to work with objects * Use Adobe Camera Raw to enhance or correct a photo * Use content-aware options for scaling and fill * Create eye-catching images with special effect filters * Select and modify one or more shapes at the same time * Create character and paragraph styles to manage and use text * Transform video in Photoshop just like an image * Create and manipulate 3D models using presets and custom options Numbered Steps guide you through each task See Also points you to related information in the book Did You Know alerts you to tips and techniques Illustrations with matching steps Tasks are presented on one or two pages Bonus Online Content Register your book at queondemand.com to gain access to: * Workshops and related files * Keyboard shortcutsVisit the author site: perspection.com
| Author | : Jan Krajíček |
| Publisher | : Cambridge University Press |
| Total Pages | : 265 |
| Release | : 2010-12-23 |
| Genre | : Mathematics |
| ISBN | : 1139493922 |
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
| Author | : Boting Yang |
| Publisher | : Springer |
| Total Pages | : 491 |
| Release | : 2008-08-20 |
| Genre | : Computers |
| ISBN | : 354085097X |
This book constitutes the refereed proceedings of the Second International Conference on Combinatorial Optimization and Applications, COCOA 2008, held in St. John's, Canada, in August 2008. The 44 revised full papers were carefully reviewed and selected from 84 submissions. The papers feature original research in the areas of combinatorial optimization -- both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.
| Author | : Ethan D. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461221307 |
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
| Author | : Hans Holzer |
| Publisher | : Open Road Media |
| Total Pages | : 74 |
| Release | : 2012-09-25 |
| Genre | : Body, Mind & Spirit |
| ISBN | : 1453279709 |
DIVProfessor Hans Holzer carefully examines historic photographic evidence of ghosts and paranormal activity, explaining which images contain convincing proof and which may be trickery/divDIV For more than a century, psychic researchers have amassed a body of photographic evidence of the afterlife. Indeed, according to professor Hans Holzer, photography gives us one of the greatest tools in documenting souls that continue to exist among us after death. Here Holzer looks at the evidence of ghosts revealing themselves to us on film, and shares examples of psychic photographs, many of which were taken during séances. /div
| Author | : Daniel J. Velleman |
| Publisher | : Cambridge University Press |
| Total Pages | : 401 |
| Release | : 2006-01-16 |
| Genre | : Mathematics |
| ISBN | : 0521861241 |
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
| Author | : Jirí Fiala |
| Publisher | : Springer |
| Total Pages | : 916 |
| Release | : 2004-08-06 |
| Genre | : Computers |
| ISBN | : 3540286292 |
This volume contains the papers presented at the 29th Symposium on Mat- matical Foundations of Computer Science, MFCS 2004, held in Prague, Czech Republic, August 22–27, 2004. The conference was organized by the Institute for Theoretical Computer Science (ITI) and the Department of Theoretical Com- terScienceandMathematicalLogic(KTIML)oftheFacultyofMathematicsand Physics of Charles University in Prague. It was supported in part by the Eu- pean Association for Theoretical Computer Science (EATCS) and the European Research Consortium for Informatics and Mathematics (ERCIM). Traditionally, the MFCS symposia encourage high-quality research in all branches of theoretical computer science. Ranging in scope from automata, f- mal languages, data structures, algorithms and computational geometry to c- plexitytheory,modelsofcomputation,andapplicationsincludingcomputational biology, cryptography, security and arti?cial intelligence, the conference o?ers a unique opportunity to researchers from diverse areas to meet and present their results to a general audience. The scienti?c program of this year’s MFCS took place in the lecture halls of the recently reconstructed building of the Faculty of Mathematics and P- sics in the historical center of Prague, with the famous Prague Castle and other celebratedhistoricalmonumentsinsight.Theviewfromthewindowswasach- lengingcompetitionforthespeakersinthe?ghtfortheattentionoftheaudience. But we did not fear the result: Due to the unusually tough competition for this year’s MFCS, the admitted presentations certainly attracted considerable in- rest. The conference program (and the proceedings) consisted of 60 contributed papers selected by the Program Committee from a total of 167 submissions.
