Fundamentals of Advanced Mathematics 1 - 1st Edition - ISBN: 9781785481734, 9780081021125

Fundamentals of Advanced Mathematics 1

1st Edition

Categories, Algebraic Structures, Linear and Homological Algebra

Authors: Henri Bourles
eBook ISBN: 9780081021125
Hardcover ISBN: 9781785481734
Imprint: ISTE Press - Elsevier
Published Date: 1st July 2017
Page Count: 268
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Description

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.

 

Key Features

  • 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

Readership

Undergraduate and graduate students in Mathematics. Graduate students in Systems Theory. Researchers and teachers in Mathematics / Systems Theory, students in Engineering

Table of Contents

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

Details

No. of pages:
268
Language:
English
Copyright:
© ISTE Press - Elsevier 2017
Published:
Imprint:
ISTE Press - Elsevier
eBook ISBN:
9780081021125
Hardcover ISBN:
9781785481734

About the Author

Henri Bourles

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

Affiliations and Expertise

Conservatoire National des Arts et Metiers, France