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 group. Arising as characters of these representations, the classical Schur polynomials are one of the keys to unification. Prerequisites for the book are minimized by self-contained introductions in the early chapters. Throughout the text, some of the easier proofs are left to the exercises, and some of the more difficult ones to the references.
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 style Timely and appropriate examples Numerous well-chosen exercises Flexible modular format Optional sections and appendices Highlights of Second Edition enhancements: Smoothed and polished exposition, with a sharpened focus on key ideas Expanded discussion of linear codes New optional section on algorithms Greatly expanded hints and answers section Many new exercises and examples
Soldiers of Shepshed includes a section on the various memorials erected in the town to honour the dead, and the reader will also hear something of life on the home front, from the tragedies incurred by the influenza pandemic of 1918-19, to the euphoria that greeted the signing of the Armistice and the Great Victory Parade held in Shepshed in July 1919.
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introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references.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 reference, this focused treatment goes deeply enough into a sufficiently wide variety of topics to illustrate the flavor, elegance, and power of graph theory. Another unique feature of the book is its user-friendly modular format. Following a basic foundation in Chapters 1-3, the remainder of the book is organized into four strands that can be explored independently of each other. These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya's enumeration of nonisomorphic graphs. In the edge coloring strand, the reader is presumed to be familiar with the disjoint cycle factorization of a permutation. Otherwise, all prerequisites for the book can be found in a standard sophomore course in linear algebra. The independence of strands also makes Graph Theory an excellent resource for mathematicians who require access to specific topics without wanting to read an entire book on the subject.
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 style Timely and appropriate examples Numerous well-chosen exercises Flexible modular format Optional sections and appendices Highlights of Second Edition enhancements: Smoothed and polished exposition, with a sharpened focus on key ideas Expanded discussion of linear codes New optional section on algorithms Greatly expanded hints and answers section Many new exercises and examples
As a young man Winston Churchill set out to become a hero, to make a name for himself in the public eye as a soldier and so make possible a life of politics and statesmanship. There were many chances to fail and many close calls in the face of sword, spear and bullet along the way. Yet Churchill survived and succeeded – an early measure of his courage and stubborn will that the world would come to know so well in the Second World War. This is the first full-length, fully-researched biography of Churchill's colourful military career. Using an unrivalled range of sources, and with previously unpublished photographs, and detailed maps by Sir Martin Gilbert, it brings to life Churchill's motives, abilities, experiences, successes and failures, and his unswerving sense of destiny as an officer in the British Army. The result is a story to echo the man himself – rich in action, courage, charismatic self-belief, patriotism and humour. Making extensive use of the contemporary accounts of Churchill and his fellow soldiers and archival documents from three continents, illustrated with many maps and previously unpublished photographs, Douglas S. Russell vividly brings to life the military career of the vigorous young officer of hussars who later became the greatest Briton of the twentieth century. From Sandhurst to the mountainous North-West Frontier of India, to the charge of the 21st Lancers at Omdurman, from the South African veldt to the deadly trench warfare of the Great War, the author – whom Sir Martin Gilbert calls 'a keen portraitist' – tells the gripping story of Churchill's army life with careful attention to historical detail and all the drama that the real life adventures of his subject deserve.
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 group. Arising as characters of these representations, the classical Schur polynomials are one of the keys to unification. Prerequisites for the book are minimized by self-contained introductions in the early chapters. Throughout the text, some of the easier proofs are left to the exercises, and some of the more difficult ones to the references.
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This bibliography lists the books, paintings, and portraits of the mystic Irish poet George William Russell, best known by his pseudonym, "AE." Russell was a late nineteenth-and early twentieth century Irish poet and essayist whose first book of poems, Homeward: Songs by the Way (1894), established him in what was known as the Irish Literary Revival.
In the accompanying commentary, Brian Dippie places each of Russell's letters within the broader context of the artist's life and career. Dippie identifies the recipient of each letter and the circumstances that prompted the correspondence, clarifies Russell's references to other friends and acquaintances and, where appropriate, relates events in the letter to Russell's artistic development. Photographs, including many that belonged to the Russells, further illustrate the world that the artist and his friends inhabited.
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