{"product_id":"real-analysis-a-visual-approach-from-field-axioms-to-metric-spaces-paperback","title":"Real Analysis: A Visual Approach from Field Axioms to Metric Spaces - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003ePaul L. Dayao\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWhile many real analysis texts prioritize brevity over clarity, this volume focuses on the student's conceptual journey. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThe text begins with a rigorous construction of the Real Number System from the Field and Order Axioms, moving through the topology of R, sequences, and series. It provides a thorough treatment of continuity and differentiation, including the topological characterization of continuity. A key feature is the rigorous development of the Riemann Integral via Darboux sums, leading to the Lebesgue Criterion. The final chapters transition into Pointwise vs. Uniform Convergence and an introduction to Metric Spaces. The book uses a modern layout with color-coded theorem environments and visual proofs to aid learning.  \u003cp\u003eIt is designed as a core text for a one-semester Real Analysis course, specifically for students who find standard texts too opaque.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003ePaul L. Dayao is a faculty member at the Ateneo de Manila University who brings over a decade of teaching experience to his writing. His research interests lie in Real Analysis and Functional Analysis. He has recently published works on integration theory in the Missouri Journal of Mathematical Sciences (MJMS) and Real Analysis Exchange.\u003c\/p\u003e\u003cp\u003eIn addition to his research, he is an active textbook author. He has a book forthcoming with De Gruyter, a book \u003cem\u003eIntroductory Course in Functional Analysis\u003c\/em\u003e with CRC Press\/Taylor \u0026amp; Francis, a college calculus textbook forthcoming with C\u0026amp;E Publishing, and a manuscript \u003cem\u003eLinear Algebra: A Coordinate-Free Approach\u003c\/em\u003e currently under review at Springer. He is also finalizing his PhD application in Measure Theory at the University of St Andrews. As a dedicated educator, he specializes in creating \"teaching-led\" mathematical materials that bridge the gap between intuition and rigor.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 308\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.65 x 9.61 x 6.69 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 03, 2026\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52804566581546,"sku":"9783112254974","price":100.12,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1016\/7910\/4298\/files\/nT1tb8COeY9783112254974.webp?v=1790790681","url":"https:\/\/corporatelinguaacademy.com\/products\/real-analysis-a-visual-approach-from-field-axioms-to-metric-spaces-paperback","provider":"Corporate Lingua Academy","version":"1.0","type":"link"}