From Classical to Modern Analysis

Rinaldo B. Schinazi

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English

Springer Nature Switzerland AG
03 January 2019

Real analysis, real variables; Functional analysis & transforms; Integral calculus & equations

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis. To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuityon metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

By: Rinaldo B. Schinazi
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: Softcover Reprint of the Original 1st 2018 ed.
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 454g
ISBN: 9783030068790
ISBN 10: 303006879X
Pages: 270
Publication Date: 03 January 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Rinaldo Schinazi is a Professor of Mathematics at the University of Colorado, USA.

Reviews for From Classical to Modern Analysis

This textbook is designed for a two-semester introductory course on real analysis, and its unique feature is that it focuses on both elementary and advanced topics. ... the book is written in an accessible and easy to follow style. (Antonin Slavik, zbMATH 1408.26001, 2019)