From Classical to Modern Analysis

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book From Classical to Modern Analysis by Rinaldo B. Schinazi, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Rinaldo B. Schinazi ISBN: 9783319945835
Publisher: Springer International Publishing Publication: September 21, 2018
Imprint: Birkhäuser Language: English
Author: Rinaldo B. Schinazi
ISBN: 9783319945835
Publisher: Springer International Publishing
Publication: September 21, 2018
Imprint: Birkhäuser
Language: English

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 continuity on 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 continuity on 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.

More books from Springer International Publishing

Cover of the book Human-Computer Interaction. Theories, Methods, and Human Issues by Rinaldo B. Schinazi
Cover of the book Children and Young People Living with HIV/AIDS by Rinaldo B. Schinazi
Cover of the book Celebrating America’s Pastimes: Baseball, Hot Dogs, Apple Pie and Marketing? by Rinaldo B. Schinazi
Cover of the book Sport and Social Entrepreneurship in Sweden by Rinaldo B. Schinazi
Cover of the book Trends and Applications in Knowledge Discovery and Data Mining by Rinaldo B. Schinazi
Cover of the book On Stein's Method for Infinitely Divisible Laws with Finite First Moment by Rinaldo B. Schinazi
Cover of the book The European Roots of the Eurozone Crisis by Rinaldo B. Schinazi
Cover of the book Comprehensive Pain Management in the Rehabilitation Patient by Rinaldo B. Schinazi
Cover of the book Esophageal Cancer by Rinaldo B. Schinazi
Cover of the book Virtual Taste and Smell Technologies for Multisensory Internet and Virtual Reality by Rinaldo B. Schinazi
Cover of the book Herbert C. Kelman: A Pioneer in the Social Psychology of Conflict Analysis and Resolution by Rinaldo B. Schinazi
Cover of the book Smartphone-Based Human Activity Recognition by Rinaldo B. Schinazi
Cover of the book Endodontic Prognosis by Rinaldo B. Schinazi
Cover of the book Ultra Low Power Transceiver for Wireless Body Area Networks by Rinaldo B. Schinazi
Cover of the book Pseudo-Complex General Relativity by Rinaldo B. Schinazi
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy