In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful."
Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
With this revised edition, students can gain a more comprehensive understanding of differential equations. The book exploits students' access to computers by including many new problems and examples that incorporate computer technology.
"The solution to quasilinear first order hyperbolic systems of equations may be interpretated in terms of waves, which belong to a certain function class and propagate in some suitable space,...
University of Strathclyde Seminars in Applied Mathematical Analysis: Multiparameter Problems
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed...
This text is designed for engineers, scientists, and mathematicians with a background in elementary ordinary differential equations and calculus.
Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working...
This book strikes a balance between the traditional and the modern—combining the traditional material with a modern systems emphasis. Chapter topics cover an introduction to differential equations, first-order equations, modeling...
Differential Equations and Boundary Value Problems: Computing and Modeling
Elementary Differential Equations and Boundary Value Problems
本书主要内容包括:糖水的秘密——糖水不等式、木桶盛水有学问——木桶不等式、绝对值函数与绝对值不等式、耐克函数与耐克不等式、万丈高楼平地起——基本不等式、各种平均数,究竟谁最大——均值不等式等十三章。