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Shortly after defeating his last imperial rival in the Battle of Chrysopolis, Constantine set out to consolidate his supremacy by co-opting a tenacious religious movement that Diocletian had tried and failed to stamp out 30 years earlier. Summoning its leaders to the relatively remote setting of Nicaea, he offered them a seat at the imperial table in exchange for subscribing to a common framework of fundamental principles, i.e., a share of temporal power in return for embracing spiritual conformity. Seventeen centuries later, humankind is still living with the consequences of that bargain for...

A mathematical gem-freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition: Lively and engaging writing styleTimely and appropriate examplesNumerous well-chosen exercisesFlexible modular...

A lively invitation to the flavor, elegance, and power of graph theory

This mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic...

The prototypical multilinear operation is multiplication. Indeed, every multilinear mapping can be factored through a tensor product. Apart from its intrinsic interest, the tensor product is of fundamental importance in a variety of disciplines, ranging from matrix inequalities and group representation theory, to the combinatorics of symmetric functions, and all these subjects appear in this book. Another attraction of multilinear algebra lies in its power to unify such seemingly diverse topics. This is done in the final chapter by means of the rational representations of the full linear...