{"product_id":"a-circleline-study-of-mathematical-analysis-9783031197376","title":"A Circle-Line Study of Mathematical Analysis","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThe book covers the rigorous foundations of mathematical analysis, including naive set theory, real numbers, topology, sequences, series, limits, differentiation, and integration. It is suitable for graduate courses and self-study for students interested in mathematical analysis. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 469 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 16 March 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer International Publishing AG\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThe book delves into the intricate foundations of mathematical analysis, encompassing a comprehensive exploration of fundamental topics. In the first part, a thorough review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation, and integration according to Riemann is presented. This section serves as a foundational framework for the subsequent discussions.\u003cbr\u003e\u003cbr\u003eThe second part of the book takes a more mature approach to these subjects. It explores potential axiomatizations of set theory, introduces general topology with a focus on convergence in abstract spaces, constructs the abstract Lebesgue integral in the spirit of Daniell, and delves into the discussion of differentiation in normed linear spaces. This part offers a deeper understanding of the core concepts of mathematical analysis.\u003cbr\u003e\u003cbr\u003eThe book is designed for graduate courses in real and abstract analysis, providing a comprehensive and rigorous foundation for advanced study. It can also serve as a valuable resource for students embarking on a Ph.D. program in Analysis, offering a self-study guide for those seeking to deepen their understanding of the field. Additionally, the first part of the book can be recommended as a second reading for undergraduate students with a strong interest in mathematical analysis, providing a more advanced and comprehensive perspective.\u003cbr\u003e\u003cbr\u003eIn summary, the book offers a comprehensive and rigorous introduction to mathematical analysis, covering a wide range of topics and providing valuable insights for both graduate students and self-study enthusiasts. Its comprehensive nature and detailed explanations make it an essential resource for anyone seeking to advance their knowledge in this field.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 924g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 153 x 235 x 27 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783031197376\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2022\u003c\/p\u003e","brand":"Simone Secchi","offers":[{"title":"Paperback \/ softback","offer_id":44162059403514,"sku":"9783031197376","price":42.83,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/1680878249284_book.jpg?v=1681111177","url":"https:\/\/shulphink.com\/products\/a-circleline-study-of-mathematical-analysis-9783031197376","provider":"Shulph Ink","version":"1.0","type":"link"}