Theory of Transformation Groups I

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"Theory of Transformation Groups I" by Sophus Lie is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

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Best For: Students and researchers interested in the foundational aspects of continuous transformation groups and their applications in mathematics.

Focus: General properties and systematic organization of continuous transformation groups based on Sophus Lie's original work.

Covers: Introduction to the theory of transformation groups with emphasis on generalization from studied examples, reflecting the original German text's clarity and structure.

Why It Matters: Provides access to a foundational mathematical text with a contemporary approach, facilitating understanding of core concepts in group theory, geometry, and topology.

"Theory of Transformation Groups I" by Sophus Lie is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

Topic: Core Mathematics

Author: Sophus Lie

Who this is for:

Teachers and classroom instructors
Students building subject mastery
Readers looking for practical learning support

Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.

This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.