Fundamentals of Advanced Mathematics 1

Categories, Algebraic Structures, Linear and Homological Algebra
Erscheinungsjahr 2017
ISBN: 978-1-78548-173-4
Verlag: Elsevier Science

Buch, Englisch, 268 Seiten, Format (B × H): 236 mm x 160 mm, Gewicht: 560 g

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.

Autoren/Hrsg.

Bourles, Henri

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

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

Über Autor(innen)

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