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About this book
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
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Information
Table of contents
- Cover
- Half-Title Page
- Title Page
- Copyright Page
- Contents
- Preface
- 1. Algebraic Background for Numerical Methods, Control Theory and Renormalization
- 2. From Iterated Integrals and Chronological Calculus to Hopf and Rota–Baxter Algebras
- 3. Noncommutative Symmetric Functions, Lie Series and Descent Algebras
- 4. From Runge–Kutta Methods to Hopf Algebras of Rooted Trees
- 5. Combinatorial Algebra in Controllability and Optimal Control
- 6. Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application
- List of Authors
- Index
- EULA