You are here: Home / Shop / Product Detail Page |

## Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926 (Hardback)"Written by the recipient of the 1997 MAA Chauvenet Prize for mathematical exposition, this book tells how the theory of Lie groups emerged from a fascinating cross-fertilization of many strains of nineteenth and twentieth century geometry, analysis, mathematical physics, algebra, and topology. The reader will meet a host of mathematicians from the period and become acquainted with the major mathematical schools." — From the back cover ## $79.95 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**LIKE NEW:** This book is in excellent, like-new condition. It was printed on acid-free paper.

## Description

This book is in the Springer series *Sources and Studies in the History of Mathematics and Physical Sciences*.

Continued from the back cover: “The first part describes the geometrical and analytical considerations that initiated the theory at the hands of the Norwegian mathematician, Sophus Lie. The main figure in the second part is Weierstarss’s student Wilhelm Killing, whose interest in the foundations of non-Euclidean geometry led to his discover of almost all the central concepts and theorems on the structure and classification of semisimple Li algebras. The scene then shits to the Paris mathematical community and Élie Cartan’s work on the representation of Lie algebras. The final part describes the influential, unifying contributions of Hermann Weyl and their context: Hilbert’s Göttingen, general relativity, and the Forbenius-Schur theory of characters.

“The book is written with the conviction that mathematical understanding is deepened by familiarity with underlying motivations and the less formal, more intuitive manner of original conception. The human side of the story is evoked through extensive use of correspondence between mathematicians. The book should prove enlightening to a broad range of readers, including prospective students of Lie theory, mathematicians, physicists, and historians and philosophers of science.”

**BRIEF CONTENTS**

- Preface
- Part I: Sophus Lie
- The Geometrical Origins of Lie’s Theory
- Jacobi and the Analytical Origins of Lie’s Theory
- Lie’s Theory of Transformation Groups 1874-1893
- Part II: Wilhelm Killing
- The Background to Killing’s Work on Lie Algebras
- Killing and the Structures of Lie Algebras
- Part III: Élie Cartan
- The Doctoral Thesis of Élie Cartan
- Lie’s School & Linear Representations
- Cartan’s Trilogy: 1913-14
- Part IV: Hermann Weyl
- The Göttingen School of Hilbert
- The Berlin Algebraists: Frobenius & Schur
- From Relativity to Representations
- Weyl’s Great Papers of 1925 and 1926
- Afterword. Suggested Further Reading
- References. Published & Unpublished Sources
- Index

## Details

- SKU:
- 2423
- Author:
- Hawkins, Thomas
- Publisher:
- Springer
- Publish Date:
- 2000 (First)
- Format:
- Hardback
- Weight (pounds):
- 2.06
- Dimensions (W”xL”xH”):
- 6.4″x9.45″x1.25″
- ISBN-13:
- 9780387989631
- ISBN-10:
- 0387989633

## Related Products

### Products related to "Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926 (Hardback)"

- Views:

#### An Introduction to Random Matrices (Hardback)

$53.95

"The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic, and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even to the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences who have mastered probability theory at the graduate level, but who have not necessarily been exposed to advanced notions of functional analysis, algebra, or geometry." — From the back cover

#### Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians (Hardback)

$279.95

From the Preface: “This book is a classical and detailed introduction to advanced analytical mechanics (AM), with special emphasis on its basic principles and equations of motion, as they apply to the most general constrained mechanical systems with a finite number of degrees of freedom..."

#### The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Hardcover)

$169.95

"Provides an in-depth treatment of the Traveling Salesman problem—the archetypical problem in combinatorial optimization. Each chapter deals with a different aspect of the problem, and has been written by an acknowledged expert in the field. Focusses on the essential ideas in a self-contained manner. Includes exercises and an extensive bibliography."—from the publisher

#### History of Algebraic Geometry: An Outline of the History and Development of Algebraic Geometry (Hardback)

$136.99

"Algebraic geometry is undoubtedly the area of mathematics where the deviation is greatest between the intuitive ideas forming its starting point and the abstract and complex concepts at the foundation of modern research. The purpose of this work is to help the willing reader abridge the gap." — From the Foreword (page VII)

#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Hardback)

$123.50

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### Positive Harmonic Functions and Diffusion: An Integrated Analytic and Probabilistic Approach (Hardback)

$119.95

"In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach." — From the back cover

#### Introduction to Analysis of the Infinite, Book I (Hardback)

$89.95

"...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those things which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. ... [I]n the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..." — From the Preface by the Author, Leonhard Euler

#### Discrete Mathematics and Its Applications: Handbook of Computational Group Theory (Hardback)

$79.99

"The origins of computational group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics." — From the back cover

#### Studies in Advanced Mathematics: Harmonic Analysis and Applications (Hardback)

$79.95

"Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In

*Harmonic Analysis and Applications*, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject." — From the back cover#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Softcover)

$73.95

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### Discrete Mathematics and Its Applications: A Combinatorial Approach to Matrix Theory and Its Applications (Hardback)

$73.75

"Unlike most elementary books on matrices,

**A Combinatorial Approach to Matrix Theory and Its Applications**employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices." — From the back cover#### Numerical Solution of Stochastic Differential Equations (Hardback)

$71.49

"The book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations." — From the back cover

#### Iterative Methods for Sparse Linear Systems, Second Edition (Softcover)

AT AUCTION

Click Link for Details"This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science." — From the back cover

#### Graduate Texts in Mathematics: Introduction to Cyclotomic Fields, Second Edition (Hardback)

$57.95

"

*Introduction to Cyclotomic Fields*is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory." — From the back cover#### Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations (Hardback)

$54.95

"This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework." — From the back cover

#### Measure and Integral: An Introduction to Real Analysis (Hardback)

$53.29

"This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of

*n*-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given." — From the back cover#### Texts and Monographs in Computer Science: A Logical Approach to Discrete Math (Hardback)

AT AUCTION

Click Link for Details"Logic is the glue that binds together arguments and proofs in all domains. This text aims to teach the use of this fundamental and pervasive tool and exercise it thoroughly in applications that arise in computer science and mathematics." — From the back cover

#### Numerical Methods for Ordinary Differential Equations, Second Edition (Hardback)

$50.95

"In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments." — From the back cover

#### A Course in Convexity (Graduate Studies in Mathematics, Volume 54, Hardcover)

$49.95

"As a whole, [this book] is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research."— from the back cover

#### Universitext: The Calculus of Variations (Hardback)

AT AUCTION

Click Link for Details"This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations." — From the back cover