This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.
'Analysis situs' is the name used by Poincaré when he was creating, at the end of the 19th century, the area of mathematics known today as topology. These lectures contain what is probably the first text where Poincaré's results and ideas were summarized, and an attempt to systematically present this difficult new area of mathematics was made. Of the two streams of topology existing at that time, point set topology and combinatorial topology, it is the latter to which this book is almost totally devoted. The first four chapters present, in detail, the notion and properties (introduced by Poincaré) of the incidence matrix of a cell decomposition of a manifold. The author's main goal is to show how to reproduce main topological invariants of a manifold and their relations in terms of the incidence matrix.
This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Final Thoughts (Illustrated) by Henri Poincaré invites readers on a captivating journey through the mind of one of history's greatest intellectuals. Henri Poincaré, renowned for his contributions to mathematics, physics, and philosophy, offers profound insights into the nature of existence and the universe itself. In this illustrated edition, Poincaré's timeless reflections are accompanied by stunning visuals that illuminate his complex ideas. Through elegant prose and captivating imagery, he delves into the mysteries of time, space, and the human condition, inviting readers to contemplate the profound questions that have puzzled humanity for centuries. From the nature of reality to the limits of human knowledge, each chapter of Final Thoughts offers a thought-provoking exploration of the fundamental principles that govern the cosmos. Poincaré's profound wisdom and keen intellect shine through on every page, offering readers a deeper understanding of the universe and their place within it. Whether you're a scholar, a philosopher, or simply a curious seeker of truth, Final Thoughts is sure to inspire and enlighten. Let its illustrated pages be your guide as you embark on a journey of intellectual discovery and contemplation. Embark on a journey of intellectual exploration with Final Thoughts by Henri Poincaré. Let its illustrated pages ignite your curiosity and expand your understanding of the universe and the mysteries that lie within.
