This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology. The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.

The Concept of a Riemann Surface (Dover Books on Mathematics)

Science & Math

Hermann Weyl

Mathematics

Dover Publications

This original anthology assembles eleven accessible essays by a giant of modern mathematics. Hermann Weyl (1885–1955) made lasting contributions to number theory as well as theoretical physics, and he was associated with Princeton's Institute for Advanced Study, the University of Göttingen, and ETH Zurich. Spanning the 1930s–50s, these articles offer insights into logic and relativity theory in addition to reflections on the work of Weyl's mentor, David Hilbert, and his friend Emmy Noether. Subjects include "Topology and Abstract Algebra as Two Roads of Mathematical Comprehension," "The Mathematical Way of Thinking," "Relativity Theory as a Stimulus in Mathematical Research," and "Why is the World Four-Dimensional?" Historians of mathematics, advanced undergraduates, and graduate students will appreciate these writings, many of which have been long unavailable to English-language readers.

Levels of Infinity: Selected Writings on Mathematics and Philosophy (Dover Books on Mathematics)

Peter Pesic

"The standard treatise on the general theory of relativity." — Nature "Whatever the future may bring, Professor Weyl's book will remain a classic of physics." — British Journal for Philosophy and Science Reflecting the revolution in scientific and philosophic thought which accompanied the Einstein relativity theories, Dr. Weyl has probed deeply into the notions of space, time, and matter. A rigorous examination of the state of our knowledge of the world following these developments is undertaken with this guiding principle: that although further scientific thought may take us far beyond our present conception of the world, we may never again return to the previous narrow and restricted scheme. Although a degree of mathematical sophistication is presupposed, Dr. Weyl develops all the tensor calculus necessary to his exposition. He then proceeds to an analysis of the concept of Euclidean space and the spatial conceptions of Riemann. From this the nature of the amalgamation of space and time is derived. This leads to an exposition and examination of Einstein's general theory of relativity and the concomitant theory of gravitation. A detailed investigation follows devoted to gravitational waves, a rigorous solution of the problem of one body, laws of conservation, and the energy of gravitation. Dr. Weyl's introduction of the concept of tensor-density as a magnitude of quantity (contrasted with tensors which are considered to be magnitudes of intensity) is a major step toward a clearer understanding of the relationships among space, time, and matter.

Space, Time, Matter

Physics

This book is devoted to the consistent and systematic application of group theory to quantum mechanics. Beginning with a detailed introduction to the classical theory of groups, Dr. Weyl continues with an account of the fundamental results of quantum physics. There follows a rigorous investigation of the relations holding between the mathematical and physical theories. Topics covered include: unitary geometry, quantum theory (Schrödinger's wave equation, transition probabilities, directional quantization, collision phenomena, Zeeman and Stark effects); groups and their representations (sub-groups and conjugate classes, linear transformations, rotation and Lorentz groups, closed continuous groups, invariants and covariants, Lie's theory); applications of group theory to quantum mechanics (simple state and term analysis, the spinning electron, multiplet structure, energy and momentum, Pauli exclusion principle, problem of several bodies, Maxwell-Dirac field equations, etc.); the symmetric permutation group; and algebra of symmetric transformation (invariant sub-spaces in group and tensor space, sub-groups, Young's symmetry operators, spin and valence, group theoretic classification of atomic spectra, branching laws, etc). Throughout, Dr. Weyl emphasizes the "reciprocity" between representations of the symmetric permutation group and those of the complete linear group. His simplified treatment of "reciprocity," the Clebsch-Gordan series, and the Jordan-Hölder theorem and its analogues, has helped to clarity these and other complex topics.

The Theory of Groups and Quantum Mechanics (Dover Books on Mathematics)

"The hard won power ... to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part." — John Archibald Wheeler Hermann Weyl (1885–1955) ranks among the most important mathematicians and physicists of this century. Though Weyl was not primarily a philosopher, his wide-ranging philosophical reflections on the formal and empirical sciences remain extremely valuable. Besides indicating clearly which results of classical analysis are invalidated by an important family of "non-circular" (predicative) theories, The Continuum wrestles with the problem of applying constructive mathematical models to cases of concrete physical and perceptual continuity. This new English edition features a personal reminiscence of Weyl written by John Archibald Wheeler. Originally published in German in 1918, the book consists of two chapters. Chapter One, entitled Set and Function, deals with property, relation and existence, the principles of the combination of judgments, logical inference, natural numbers, iteration of the mathematical process, and other topics. The main ideas are developed in this chapter in such a way that it forms a self-contained whole. In Chapter Two, The Concept of Numbers &amp; The Continuum, Weyl systematically begins the construction of analysis and carries through its initial stages, taking up such matters as natural numbers and cardinalities, fractions and rational numbers, real numbers, continuous functions, curves and surfaces, and more. Written with Weyl's characteristic passion, lucidity, and wisdom, this advanced-level volume is a mathematical and philosophical landmark that will be welcomed by mathematicians, physicists, philosophers, and anyone interested in foundational analysis.

The Continuum: A Critical Examination of the Foundation of Analysis (Dover Books on Mathematics)

History & Philosophy

Defines symmetry through a discussion of its many uses in a wide variety of fields both academic and natural.

Symmetry

Arts & Photography

Princeton University Press

Four volumes in one: Das Kontinuum (Kritische Untersuchungen  ueber die Grundlagen der Analysis, by H. Weyl (reprint of 2nd  edition); Mathematische Analyse des Raumproblems, by H. Weyl;  Darstellung und Begruendung einiger neurer Ergebnisse der  Funktionentheorie, by E. Landau; Ueber die Hypothesen, Welche  der Geometrie zu Grunde Liegen, by B. Riemann (3rd edition,  edited and with comments by H. Weyl).

Das Kontinuum and Anders Monographien/4 Volumes in 1 (German Edition)

E. Landau

B. Riemann

Chelsea Pub. Co

"The hard won power ... to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part." — John Archibald WheelerHermann Weyl (1885–1955) ranks among the most important mathematicians and physicists of this century. Though Weyl was not primarily a philosopher, his wide-ranging philosophical reflections on the formal and empirical sciences remain extremely valuable. Besides indicating clearly which results of classical analysis are invalidated by an important family of "non-circular" (predicative) theories, The Continuum wrestles with the problem of applying constructive mathematical models to cases of concrete physical and perceptual continuity. This new English edition features a personal reminiscence of Weyl written by John Archibald Wheeler.Originally published in German in 1918, the book consists of two chapters. Chapter One, entitled Set and Function, deals with property, relation and existence, the principles of the combination of judgments, logical inference, natural numbers, iteration of the mathematical process, and other topics. The main ideas are developed in this chapter in such a way that it forms a self-contained whole.In Chapter Two, The Concept of Numbers & The Continuum, Weyl systematically begins the construction of analysis and carries through its initial stages, taking up such matters as natural numbers and cardinalities, fractions and rational numbers, real numbers, continuous functions, curves and surfaces, and more.Written with Weyl's characteristic passion, lucidity, and wisdom, this advanced-level volume is a mathematical and philosophical landmark that will be welcomed by mathematicians, physicists, philosophers, and anyone interested in foundational analysis.

The continuum: A critical examination of the foundation of analysis

Politics & Social Sciences

Philosophy

Thomas Jefferson University Press

Excerpt from Space-Time-MatterEinstein's Theory of Relativity has advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us from Truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a presentiment. It has brought us much nearer to grasping the plan that underlies all physical happening.(Although very recently a whole series of more or less popular introductions into the general theory of relativity has appeared, nevertheless a systematic presentation was lacking. I therefore considered it appropriate to publish the following lectures which I gave in the Summer Term of 1917 at the Eidgen. Technische Hochschule in Zürich. At the same time it was my wish to present this great subject as an illustration of the intermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher.)The theoretical equipment demanded of the reader at the outset is a minimum. Not only is the special theory of relativity dealt with exhaustively, but even Maxwell's theory and analytical geometry are developed in their main essentials. This was a part of the whole scheme.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

Space-Time-Matter (Classic Reprint)

Forgotten Books

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Books by Hermann Weyl