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Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.
This book tells the story of Polish immigrants in Chicago's history. From their arrival in 1837 until 1937, you'll learn how the Polish community helped shape the city of Chicago. Fueled with determination, hard work, and a love for their homeland, this book chronicles the Poles' struggle for acceptance and the impact they had on their new home. If you're curious about the history of Chicago's Polish community, this modern classic is a must-read. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Civil Rights and the Idea of Freedom is a groundbreaking work, one of the first to show in detail how the civil rights movement crystallized our views of citizenship as a grassroots-level, collective endeavor and of self-respect as a formidable political tool. Drawing on both oral and written sources, Richard H. King shows how rank-and-file movement participants defined and discussed such concepts as rights, equality, justice, and, in particular, freedom, and how such key movement leaders as Martin Luther King Jr., Ella Baker, Stokely Carmichael, and James Forman were attuned to this "freedom talk." The book includes chapters on the concept of freedom in its many varieties, both individual a...
This book defines the dilemmas related to the interface between legal regulations and planning practice in the spatial management system. Based on specific case studies, it gives examples of possible problems and ways of solving them. It applies to Poland's standard and the determinants of spatial policy in other countries. It provides the basis for a developed international discussion and concretely suggests specific actions at local, regional and national levels.