Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Rie...(展开全部)

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a “holistic” introduction to representation theory, presenting it as a unifi...(展开全部)

Hua Loo Keng:Institute of Mathematics,Academica Sinica,Beijing,The People’s Republic of China

For undergraduate or graduate courses in Graph Theory in departments of mathematics or computer science. This text offers a comprehensive and coherent introduction to the fundamental topics of graph theory. It includes basic algorithms and emphasizes the understanding and writing of proofs about graphs. Thought-provoking examples and exercises develop a thorough understanding ...(展开全部)

Hailed by the "Bulletin of the American Mathematical Society" as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, it offers an accessible treatment that requires no previous knowledge of algebraic topology. 1963 edition.

This text covers the basic concepts and insights of game theory and offers classic examples and applications in a concise format. It provides a serious treatment of contract - an important, but often neglected topic in game theory - with minimal departure from the standard game coverage. Without skimping on mathematical precision, this text presents concepts and applications us...(展开全部)

How and why are languages constantly changing? Historical linguistics seeks to find out by going beyond the history of individual languages to discover the general principles which underlie language change. But our evidence is severely limited. Most of the world's languages are still unwritten, and even in areas with long written traditions, such as Europe and the Near East, do...(展开全部)