{"product_id":"invitation-to-real-analysis-hardback-9781939512055","title":"Invitation to Real Analysis (Hardback) 9781939512055","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInvitation to Real Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA broad and rigorous treatment of real analysis and a platform to higher mathematics, with historical material and 600 exercises.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eLuis F. Moreno (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781939512055, The Mathematical Association of America\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 July 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e678 pages\u003cbr\u003e26.1 x 18.2 x 4 cm, 1.32 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eBoth a stepping stone to higher analysis courses and a foundation for deeper reasoning in applied mathematics, this book provides a broad foundation in real analysis. In connection with this, within the chapters, readers are pointed to numerous accessible articles from The College Mathematics Journal and The American Mathematical Monthly. Axioms are presented with an emphasis on their distinguishing characteristic, culminating with the axioms that define the reals. Set theory is another theme found in this book, running underneath the rigorous development of functions, sequences and series, and ending with chapters on transfinite cardinal numbers and basic point-set topology. Differentiation and integration are developed rigorously with the goal of forming a firm foundation for deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises, dozens of figures, an annotated bibliography, and several appendices help the learning process.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eTo the student\u003cbr\u003e To the instructor\u003cbr\u003e 0. Paradoxes!\u003cbr\u003e 1. Logical foundations\u003cbr\u003e 2. Proof, and the natural numbers\u003cbr\u003e 3. The integers, and the ordered field of rational numbers\u003cbr\u003e 4. Induction, and well-ordering\u003cbr\u003e 5. Sets\u003cbr\u003e 6. Functions\u003cbr\u003e 7. Inverse functions\u003cbr\u003e 8. Some subsets of the real numbers\u003cbr\u003e 9. The rational numbers are denumerable\u003cbr\u003e 10. The uncountability of the real numbers\u003cbr\u003e 11. The infinite\u003cbr\u003e 12. The complete, ordered field of real numbers\u003cbr\u003e 13. Further properties of real numbers\u003cbr\u003e 14. Cluster points and related concepts\u003cbr\u003e 15. The triangle inequality\u003cbr\u003e 16. Infinite sequences\u003cbr\u003e 17. Limits of sequences\u003cbr\u003e 18. Divergence: the non-existence of a limit\u003cbr\u003e 19. Four great theorems in real analysis\u003cbr\u003e 20. Limit theorems for sequences\u003cbr\u003e 21. Cauchy sequences and the Cauchy convergence criterion\u003cbr\u003e 22. The limit superior and limit inferior of a sequence\u003cbr\u003e 23. Limits of functions\u003cbr\u003e 24. Continuity and discontinuity\u003cbr\u003e 25. The sequential criterion for continuity\u003cbr\u003e 26. Theorems about continuous functions\u003cbr\u003e 27. Uniform continuity\u003cbr\u003e 28. Infinite series of constants\u003cbr\u003e 29. Series with positive terms\u003cbr\u003e 30. Further tests for series with positive terms\u003cbr\u003e 31. Series with negative terms\u003cbr\u003e 32. Rearrangements of series\u003cbr\u003e 33. Products of series\u003cbr\u003e 34. The numbers e and γ\u003cbr\u003e 35. The functions exp x and ln x\u003cbr\u003e 36. The derivative\u003cbr\u003e 37. Theorems for derivatives\u003cbr\u003e 38. Other derivatives\u003cbr\u003e 39. The mean value theorem\u003cbr\u003e 40. Taylor's theorem\u003cbr\u003e 41. Infinite sequences of functions\u003cbr\u003e 42. Infinite series of functions\u003cbr\u003e 43. Power series\u003cbr\u003e 44. Operations with power series\u003cbr\u003e 45. Taylor series\u003cbr\u003e 46. Taylor series, part II\u003cbr\u003e 47. The Riemann integral\u003cbr\u003e 48. The Riemann integral, part II\u003cbr\u003e 49. The fundamental theorem of integral calculus\u003cbr\u003e 50. Improper integrals\u003cbr\u003e 51. The Cauchy–Schwartz and Minkowski inequalities\u003cbr\u003e 52. Metric spaces\u003cbr\u003e 53. Functions and limits in metric spaces\u003cbr\u003e 54. Some topology of the real number line\u003cbr\u003e 55. The Cantor ternary set\u003cbr\u003e Appendix A. Farey sequences\u003cbr\u003e Appendix B. Proving that\u003cbr\u003e Appendix C. The ruler function is Riemann integrable\u003cbr\u003e Appendix D. Continued fractions\u003cbr\u003e Appendix E. L'Hospital's Rule\u003cbr\u003e Appendix F. Symbols, and the Greek alphabet\u003cbr\u003e Bibliography\u003cbr\u003e Solutions\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], Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e], Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"The Mathematical Association of America","offers":[{"title":"Brand New","offer_id":52449446002968,"sku":"9781939512055","price":51.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781939512055i.jpg?v=1785199622","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/invitation-to-real-analysis-hardback-9781939512055","provider":"Freshly Printed Books","version":"1.0","type":"link"}