The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Undergraduates, graduate students, and research mathematicians interested in mathematics.
The authors manage to breathe new life into topics that at first glance appear to be old hat.
This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. It is appropriate for either It could also be used as a starting point for undergraduate research topics or a place to find a short undergraduate seminar talk. This is a wonderful book that is not only fun to read, but gives the reader new ideas to think about.
-- Springer Science & Business
Dmitry Fuchs and Serge Tabachnikov display impeccable taste in their choice of the material, level of exposition, and the balance between concrete and more conceptual mathematical themes. Each of the thirty lectures tells a unique mathematical story, each with a display of mathematical narrative art, with great care for the details, revealing masters of their craft at work. Both novice and more experienced readers will find many pleasant surprises at all levels of exposition. ...[A] book suitable for such a noble and demanding goal to serve as an introduction to the world of 'serious mathematics' for new generations of mathematicians. ...[E]very page has one or more diagrams, graphs, and pictures illustrating the material. ...[T]he special artistic spirit and atmosphere the book owes to numerous, witty, humorous, and mysterious illustrations of the artist Sergey Ivanov. Without much exaggeration, one may say that these provocative, yet mathematically correct drawings can alone serve as a layman's guide to the beauty and mystery of mathematics. Summarizing, we can say that Mathematical Omnibus is a 'desert island book,' a 'coffee table book,' a book to share with friends, colleagues, and students, a gift for a beginner and an expert alike. In short, it is a wonderful addition to our personal, school, and university libraries.
-- Rade T. Zivaljevic, The American Mathematical Monthly
This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinite-dimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups. Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of Kac-Moody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields. The paper by Retakh and Shander contains a generalization of the Schwarz derivative to the noncommutative case.