Geosciences particularly numerical weather predication, are demanding the highest levels of computer power available. The European Centre for Medium-Range Weather Forecasts, with its experience in using supercomputers in this field, organizes a workshop every other year bringing together manufacturers, computer scientists, researchers and operational users to share their experiences and to learn about the latest developments. This volume provides an excellent overview of the latest achievements and plans for the use of new parallel techniques in the fields of meteorology, climatology and oceanography.
Professor Zhang presents a new toolkit for solving geometry problems. He neatly presents these tools with 9 theorems and their elegant proofs. The cornerstone of his techniques is the "Area Method," based on the directed area of triangles and their relationship to proportional sides. Professor Zhang instructs his students to do the algebraic deduction and calculation while making reference to the figures and their geometric relationships. The advantages of this approach are not only that it looks straightforward but his proofs frequently rely on an almost fixed recipe. For this reason the methods are important in Automated Geometric Reasoning. The Area Method and Full Angle Method theorem provers are based on the techniques introduced in this book. These methods have been used successfully by Chinese students training for the International Mathematical Olympiads. Throughout the book and all examples in the last two chapters present problems from various math competitions around the world, many from past International Mathematical Olympiads. This book will be of great interest to students and coaches of mathematics competitions, and to researchers in Automated Geometric Reasoning.
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
Geosciences particularly numerical weather predication, are demanding the highest levels of computer power available. The European Centre for Medium-Range Weather Forecasts, with its experience in using supercomputers in this field, organizes a workshop every other year bringing together manufacturers, computer scientists, researchers and operational users to share their experiences and to learn about the latest developments. This volume provides an excellent overview of the latest achievements and plans for the use of new parallel techniques in the fields of meteorology, climatology and oceanography.
This ground breaking work is the result of research by Plan International China and the China Agricultural University on children who have been left behind in their rural villages when their parents migrate to cities in search of work.
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