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From Numbers To Analysis
Inder K Rana
出版World Scientific Publishing Company, 1998-10-06
主題Mathematics / GeneralMathematics / Differential Equations / General
ISBN981310516X9789813105164
URLhttp://books.google.com.hk/books?id=3GJIDQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. The book provides the logical foundation of Analysis and gives a basis to Abstract Algebra. It complements those books on real analysis which begin with axiomatic definitions of real numbers.The book can be used in various ways: as a textbook for a one semester course on the foundations of analysis for post-calculus students; for a seminar course; or self-study by school and college teachers.