Analysis Rn Volume 01: Foundations of Metric and Vector Spaces: Master's Degree in Mathematics Series (Graduate Mathematics Book 10)
English | May 8, 2026 | ASIN: B0GZZKW1FH | 416 pages | PDF | 14.86 MB
Analysis Rn Volume 01: Foundations of Metric and Vector Spaces is the first volume of the Master's Degree in Mathematics Series, a graduate-level collection designed for readers who want to build a rigorous foundation in advanced mathematics.This volume develops the fundamental structures of analysis in finite-dimensional spaces, with special emphasis on vector spaces, norms, metric spaces, convergence, completeness, and linear transformations.The book combines formal mathematical exposition with a didactic structure, including definitions, propositions, theorems, proofs, solved exercises, and proposed exercises. Its purpose is to help the reader understand not only how to apply mathematical results, but also why they are true.Inside this book, you will study:Vector spaces and norms in RnFundamentals of metric spacesConvergence and Cauchy sequencesComplete metric spacesConvergence in function spacesLinear transformations and continuityIntroductory connections with Banach spaces, Hilbert spaces, and operator theorySolved exercises and proposed exercises for independent practiceWho is this book for?This book is intended for mathematics students, graduate students, university instructors, independent learners, and readers preparing for advanced topics such as functional analysis, topology, measure theory, and operator theory.With a structured and progressive approach, Analysis Rn Volume 01 provides a solid conceptual bridge between linear algebra, metric spaces, and modern mathematical analysis.