This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.

Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004.Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.Inspired by Chern and his work, former colleagues, students and friends — themselves highly regarded mathematicians in their own right — come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai), Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others.

The book is a collection of research and review articles in several areas of modern mathematics and mathematical physics published in the span of three decades. The ICM Kyoto talk “Mathematics as Metaphor” summarises the author's view on mathematics as an outgrowth of natural language.

This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."

This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to ShiingOCoshen Chern and Andr(r) Weil, as well as a proof of the GaussOCoBonnetOCoChern theorem based on the MathaiOCoQuillen construction of Thom forms; the second part presents analytic proofs of the Poincar(r)OCoHopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. Contents: ChernOCoWeil Theory for Characteristic Classes; Bott and DuistermaatOCoHeckman Formulas; GaussOCoBonnetOCoChern Theorem; Poincar(r)OCoHopf Index Formula: An Analytic Proof; Morse Inequalities: An Analytic Proof; ThomOCoSmale and Witten Complexes; Atiyah Theorem on Kervaire Semi-characteristic. Readership: Graduate students and researchers in differential geometry, topology and mathematical physics."

In recognition of professor Shiing-Shen Chern’s long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Symposium was published in a series of three separate volumes, comprising approximately a third of Professor Chern’s total publications up to 1979. Later, a fourth volume was published, focusing on papers written during the Eighties. This first volume comprises selected papers written between 1932 and 1975. In making the selections, Professor Chern gave preference to shorter and lesser-known papers.

"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

Although today's mathematical research community takes its international character very much for granted, this ``global nature'' is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom thegoal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians andmathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues. The resulting volume is essential reading for anyone interestedin the history of modern mathematics. It will be of interest to mathematicians, historians of mathematics, and historians of science in general.

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; and (3) topology and differential geometry. The features of this work include: an exposition style which is a fusion of those common in the standard physics and mathematics literatures; a level of exposition that varies from quite elementary to moderately advanced, so that the text should be of interest to a wide audience; a strong degree of thematic unity, despite the diversity of the topics covered; and cross references, so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.