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

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

by Henri Bourles

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Overview

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

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

Product Details

ISBN-13: 9780081021125
Publisher: Elsevier Science
Publication date: 07/10/2017
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 268
File size: 11 MB
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About the Author

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

Table of Contents

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

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