Fundamentals of Advanced Mathematics 1: Categories, Algebraic Structures, Linear and Homological Algebra

ISBN-13: 9781785481734 / Angielski / Twarda / 2017 / 268 str.

Henri Bourles

Opis

This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients.

• Part of the New Mathematical Methods, Systems, and Applications series
• Presents the notions, results, and proofs necessary to understand and master the various topics
• Provides a unified notation, making the task easier for the reader.
• Includes several summaries of mathematics for engineers

Recenzje

"The volume is well organized and carefully written, and the reader gets useful knowledge about various topics, mainly from category theory and algebra. The volume will surely be a valuable tool for the targeted specialists, who may take advantage of the solid mathematical foundation set by the author. But it also produces an interesting selection of results, which may offer some perspectives to algebraists interested in applications to other fields of research." --MathSciNet

Spis treści

1. Categories and Functors 2. Elementary Algebraic Structures 3. Modules and Algebras

O autorze

Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.