Calculus problems solved by elementary geometrical methods --- P. 4 of cover.

This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.

Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

This classic text serves as a tool for self-study; it is also used as a basic text for undergraduate courses in differential geometry. The author's ability to extract the essential elements of the theory in a lucid and concise fashion allows the student easy access to the material and enables the instructor to add emphasis and cover special topics. The extraordinary wealth of examples within the exercises and the new material, ranging from isoperimetric problems to comments on Einstein's original paper on relativity theory, enhance this new edition.