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.
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.
From concussion doctors pushing “science” that benefits their hidden business interests to lawyers clamoring for billion-dollar settlements in scam litigation, America’s game has become so big that everybody wants a cut. And those chasing the dollars show themselves more than willing to trash a great sport in hot pursuit of a buck. Everything they say about football is wrong. Football players don’t commit suicide at elevated levels, die younger than their peers, or suffer disproportionately from heart disease. In fact, professional players live longer, healthier lives than American men in general. More than that, football is America’s most popular sport. It brings us together. It is, and has been, a rite of passage for millions of American boys. But fear over concussions and other injuries could put football on ice. School districts are already considering doing away with football as too dangerous. Parents who used to see football as character-building now worry that it may be mind-destroying. Even the president has jumped on the pile by fretting that he might prevent a son from playing if he had one. But as author Daniel J. Flynn reports, football is actually safer than skateboarding, bicycling, or skiing. And in a nation facing an obesity crisis, a little extra running, jumping, and tackling could do us all good. Detailing incontrovertible fact after incontrovertible fact, The War on Football: Saving America’s Game rescues reality from the hype—and in doing so may just ensure that football remains America’s game.
After the events of the 2020 presidential election, a Cuban teacher in Miami identifies signs of the type of society he left behind. Concerned about the conversion of the United States into a totalitarian country, he begins sending email alerts to known people. The mails have become analyses of the evolving situation and a chronicle of the occupation of each field by the radical left. Education becomes indoctrination, news becomes harmful propaganda, and the health system is corrupt and used as a weapon to submit the population, purge people from their jobs, and control the individual. Workplaces, universities, and even the military create commissions that use race as a pretext to purge their ranks. CRT, the Marxist offspring, becomes the doctrine of people in power. The judicial system, including its head and their repressive corps, becomes servers of just one party. People are put in jail just for political reasons, and freedom of speech is canceled under the rules of a fascist document called NSCDT. This is a book with serious accusations but supported by the words and actions of those in power and their servers. It is also a call to react against the serious threat of losing freedom forever.
The third edition of Major Business Organisations of Eastern Europe and the Commonwealth of Independent Guide to the States provides comprehensive data on over 3,000 organisations including Manufacturers, Foreign Trading arrangement of this Organisations, Banks, Ministries, Chambers of Commerce and Services. book Due to the change in the import/export laws in Eastern Europe it is now possible to trade directly with many This book has been arranged in order to allow the reader organisations, and with over 7,000 named contacts and to find any entry rapidly and accurately. comprehensive details on each organisation, this directory enables the western business community to Company entries are listed alphabetically within each reach this new market. country section; in addition three indexes are provided on coloured paper at the back of the book. The information in this directory is the result of a careful research and extensive translation operation ensuring The alphabetical index of organisations throughout the entries are as accurate and up-to-date as possible. Eastern Europe and the C.I.S. lists all entries in The Editors would like to express thanks to the huge alphabetical order irrespective of their main country of number of organisations who provided information about operation. themselves for inclusion in this book. The alphabetical index of organisations within each Whilst the editors have taken every care to ensure the country of Eastern Europe and the C.I.S. lists information in this book is up-to-date, due to the fast organisations by their country of operation.
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