{"product_id":"real-analysis-paperback-9780521497565","title":"Real Analysis (Paperback) 9780521497565","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eReal Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eN. L. Carothers (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521497565, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 15 August 2000\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e416 pages, 45 b\/w illus.\u003cbr\u003e25.4 x 17.8 x 2.2 cm, 0.73 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The author writes lucidly in a friendly, readable style and he is strong at motivating, anticipating and reviewing the various themes that permeate the text … The overwhelming impression is that Real analysis was a labour of love for the author, written with a genuine reverence for both its beautiful subject matter and its creators, refiners and teachers down the ages. As such - and high praise indeed - it will sit very happily alongside classics such as Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and complex analysis and Hewitt and Stromberg's Real and abstract analysis.' The Mathematical Gazette\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Metric Spaces: 1. Calculus review\u003cbr\u003e 2. Countable and uncountable sets\u003cbr\u003e 3. Metrics and norms\u003cbr\u003e 4. Open sets and closed sets\u003cbr\u003e 5. Continuity\u003cbr\u003e 6. Connected sets\u003cbr\u003e 7. Completeness\u003cbr\u003e 8. Compactness\u003cbr\u003e 9. Category\u003cbr\u003e Part II. Function Spaces: 10. Sequences of functions\u003cbr\u003e 11. The space of continuous functions\u003cbr\u003e 12. The Stone-Weierstrass theorem\u003cbr\u003e 13. Functions of bounded variation\u003cbr\u003e 14. The Riemann-Stieltjes integral\u003cbr\u003e 15. Fourier series\u003cbr\u003e Part III. Lebesgue Measure and Integration: 16. Lebesgue measure\u003cbr\u003e 17. Measurable functions\u003cbr\u003e 18. The Lebesgue integral\u003cbr\u003e 19. Additional topics\u003cbr\u003e 20. Differentiation\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46001490264344,"sku":"9780521497565","price":50.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521497565i_87f71988-cb9c-43e3-aa46-c9f7032f5f4e.jpg?v=1691383139","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/real-analysis-paperback-9780521497565","provider":"Freshly Printed Books","version":"1.0","type":"link"}