Much of the content that students study in a high school geometry course is totally new to them. The middle school mathematics curriculum does not contain preparatory work for many of these topics as ...it does in preparing students for the study of Algebra. The proposed text would be a landmark book giving students the ability to gain some understanding of the content before it is formally addressed in the lesson in the course.While many teachers use initial classroom activities called 'DoNows,' there are no structured materials available to teachers of Geometry for this purpose. When teachers do use them, these activities are constructed by the teachers. The text provides the teachers with such materials and is structured to address what the teachers are about to present to the students.The Labs can also be used for exploration of topics at the middle school level enhancing the program there and giving students a better preparation for their high school Geometry program.
Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most ...recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. The book concludes with a comprehensive bibliography. It is destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigor and elegance to the field.
Abstract
This paper is a self-independent continuation of my article on Comparative geometry between the plane and the sphere that was presented at the previous edition of ICon-MaSTEd Conference ...2020. Below I discuss the possibility of adding a third geometry to the plane and the sphere, namely, the hyperbolic geometry on the hemisphere. I describe my own path to the subject, then the content of the syllabus which contains basic concepts of hyperbolic geometry for future preschool, elementary school, and secondary school teachers. Finally, I give reasons to introduce the subject into primary and secondary schools, not just for the “talented” but also for the “average” students.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a ...major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
In this paper, we classified the paracontact metric κ,μ-manifold satisfying the Miao-Tam critical equation with κ>−1. We proved that it is locally isometric to the product of a flat n+1-dimensional ...manifold and an n-dimensional manifold of negative constant curvature −4.
We revisit the famous Buffon’s needle problem, one of the first problems in geometric probability. Only now, the plane upon which we toss our needles is not Euclidean, as it was for Buffon, but ...instead has the simple but fascinating taxicab geometry. We find that we get the exact same solution as Buffon did, except that now π = 4! As a bonus, we get nice introductions to basic probability theory and geometry.
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ...important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
The ambient metric Fefferman, Charles; Graham, C. Robin
2012., 20111114, 2011, 2012-01-01, Volume:
178
eBook
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ...metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.
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