Basic Real Analysis

ISBN-13: 9781461265030 / Angielski / Miękka / 2012 / 559 str.

Houshang H. Sohrab

Opis

Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.

Recenzje

"Students who find Goffman's 'Real Functions' (1953), Halmos's 'Measure Theory' (1950), Hewitt and Stromberg's 'Real and Abstract Analysis' (1965), Lang's (1969) or Royden's 'Real Analysis' (1963), or Rudin's (1973) or Yosida's 'Functional Analysis' (1965) to be too hard, or too easy, may find Sohrab's presentation just right. Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. . . . Recommended."

-CHOICE

"This book is intended as a text for a one-year course for senior undergraduates or beginning graduate students, though it seems to the reviewer that it contains more than enough material for one year's study. . . . The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest."

-MATHEMATICAL REVIEWS

"The book is a clear and well structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. . . . The author managed to confine within a reasonable size book, all the basic concepts in real analysis and also some developed topics . . . The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact this textbook can serve as a source of examples and exercises in real analysis. . . . This book can be highly recommended as a good reference on real analysis."

-ZENTRALBLATT MATH

Spis treści

Preface * Set Theory * Sequences and Series of Real Numbers * Limits of Functions * Topology of R and Continuity * Metric Spaces * The Derivative * The Riemann Integral * Sequences and Series of Functions * Normed and Function Spaces * The Lebesgue Integral * Lebesgue Measure * General Measure and Probability * Appendix A: Construction of Real Numbers * References * Index