Foundations Of Advanced Mathematics Pdf

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

Hardcover ISBN: 9781785481734

eBook ISBN: 9780081021125

Imprint: ISTE Press - Elsevier

Published Date: 1st July 2017

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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

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

Details

No. of pages:: 268

Language:: English

Published:: 1st July 2017

Imprint:: ISTE Press - Elsevier

Hardcover ISBN:: 9781785481734

eBook ISBN:: 9780081021125

Henri Bourlès

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

"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

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