Fundamentals of Advanced Mathematics 1
：Categories, Algebraic Structures, Linear and Homological Algebra
Publication subTitle ：Categories, Algebraic Structures, Linear and Homological Algebra
Publisher： Elsevier Science
Publication year： 2017
E-ISBN: 9780081021125
P-ISBN(Paperback): 9781785481734
Subject： O1 Mathematics
Keyword： 数学
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
- 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
Chapter