Download Free A Sheaf Of Leaves Book in PDF and EPUB Free Download. You can read online A Sheaf Of Leaves and write the review.

Bulletin

Montana Extension Service in Agriculture and Home Economics

Published: 1917

Total Pages: 394


Get eBook

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.
This project presents in three volumes the Mishnah’s and the Tosefta’s first division, Zera‘im (Agriculture), organized in eleven topical tractates, together with a systematic history of the law of Zeraim in the Mishnah. To the exposition of the Halakhah on the chosen topic, the Mishnah-tractates are primary but complemented by the Tosefta’s presentation of its collection of glosses of the Mishnah’s law and supplements to that law. The Mishnah’s and the Tosefta’s tractates are integrated, with the Tosefta’s complement given in the setting of the Mishnah’s rules, and the whole is given in English translation. The presentation in each case encompasses an introduction, a form-analytical translation and commentary, a systematic integration of the Tosefta’s compositions into the Mishnah’s laws, an explanation of the details of the law, and an inquiry into how the Halakhah of the Mishnah and that of the Tosefta intersect, item by item.
Sheila Cordner traces a tradition of literary resistance to dominant pedagogies in nineteenth-century Britain, recovering an overlooked chapter in the history of thought about education. This book considers an influential group of writers - all excluded from Oxford and Cambridge because of their class or gender - who argue extensively for the value of learning outside of schools altogether. From just beyond the walls of elite universities, Jane Austen, Elizabeth Barrett Browning, Thomas Hardy, and George Gissing used their position as outsiders as well as their intimate knowledge of British universities through brothers, fathers, and friends, to satirize rote learning in schools for the working classes as well as the education offered by elite colleges. Cordner analyzes how predominant educational rhetoric, intended to celebrate England's progress while simultaneously controlling the spread of knowledge to the masses, gets recast not only by the four primary authors in this book but also by insiders of universities, who fault schools for their emphasis on memorization. Drawing upon working-men's club reports, student guides, educational pamphlets, and materials from the National Home Reading Union, as well as recent work on nineteenth-century theories of reading, Cordner unveils a broader cultural movement that embraced the freedom of learning on one's own.
An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas.