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Author: John W. Morgan Publisher: American Mathematical Soc. ISBN: 9780821843284 Category : Mathematics Languages : en Pages : 586
Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: John W. Morgan Publisher: American Mathematical Soc. ISBN: 9780821843284 Category : Mathematics Languages : en Pages : 586
Book Description
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Ruth W. Chabay Publisher: John Wiley & Sons ISBN: 0470503475 Category : Science Languages : en Pages : 1128
Book Description
Matter and Interactions offers a modern curriculum for introductory physics (calculus-based). It presents physics the way practicing physicists view their discipline and integrates 20th Century physics and computational physics. The text emphasizes the small number of fundamental principles that underlie the behavior of matter, and models that can explain and predict a wide variety of physical phenomena. Matter and Interactions will be available as a single volume hardcover text and also two paperback volumes.
Author: F. Albert Cotton Publisher: John Wiley & Sons ISBN: 0471505323 Category : Science Languages : en Pages : 858
Book Description
Explains the basics of inorganic chemistry with a primary emphasis on facts; then uses the student's growing factual knowledge as a foundation for discussing the important principles of periodicity in structure, bonding and reactivity. New to this updated edition: improved treatment of atomic orbitals and properties such as electronegativity, novel approaches to the depiction of ionic structures, nomenclature for transition metal compounds, quantitative approaches to acid-base chemistry, Wade's rules for boranes and carboranes, the chemistry of major new classes of substances including fullerenes and silenes plus a chapter on the inorganic solid state.
Author: Scott Barry Kaufman Publisher: Oxford University Press ISBN: 0190671947 Category : Education Languages : en Pages : 385
Book Description
In an educational system founded on rigid standards and categories, students who demonstrate a very specific manifestation of intelligence flourish, while those who deviate tend to fall between the cracks. Too often, talents and interests that do not align with classroom conventions are left unrecognized and unexplored in children with extraordinary potential but little opportunity. For twice-exceptional (2e) children, who have extraordinary strengths coupled with learning difficulties, the problem is compounded by the paradoxical nature of their intellect and an unbending system, ill-equipped to cater to their unique learning needs. Twice Exceptional: Supporting and Educating Bright and Creative Students with Learning Difficulties provides cutting-edge, evidence-based approaches to creating an environment where twice-exceptional students can thrive. Viewing the 2e student as neither exclusively disabled nor exclusively gifted, but, rather, as a dynamic interaction of both, leading experts offer holistic insight into identification, social-emotional development, advocacy, and support for 2e students. With chapters focusing on special populations (including autism, dyslexia, and ADHD) as well as the intersection of race and 2e, this book highlights practical recommendations for school and social contexts. In expounding the unique challenges faced by the 2e population, Twice Exceptional makes a case for greater flexibility in our approach to education and a wider notion of what it means to be academically successful.
Author: Dr. Kamlodvab Jha Publisher: Booksclinic Publishing ISBN: 9358238631 Category : Education Languages : en Pages : 280
Book Description
The book has been written for those students who wish to pursue B.Sc.chemistry Honours or general courses by covering the syllabuses of all the Indian Universities. The book is also suitable for the students who is preparing the JAM entrance examinations for M.Sc. courses. The book has been written in very simple language with clear three dimensional diagrams and appropriate reaction mechanism. It contains many problems which will useful for the readers.
Author: Peter Schuster Publisher: Springer ISBN: 3319395025 Category : Science Languages : en Pages : 728
Book Description
This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility. The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.
Author: László Fejes Tóth Publisher: Springer Nature ISBN: 3031218000 Category : Mathematics Languages : en Pages : 454
Book Description
The publication of the first edition of Lagerungen in der Ebene, auf der Kugel und im Raum in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen, the revised and updated Notes on the original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come.
Author: John W. Morgan
Author: 
Author: John W. Morgan
Author: 
Author: Ruth W. Chabay
Author: F. Albert Cotton
Author: Scott Barry Kaufman
Author: Dr. Kamlodvab Jha
Author: Peter Schuster
Author: László Fejes Tóth
Author: National Institute on Alcohol Abuse and Alcoholism (U.S.)