{"product_id":"an-introduction-to-proof-through-real-analysis-hardcover","title":"An Introduction to Proof Through Real Analysis - Hardcover","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\u003eDaniel J. Madden\u003c\/b\u003e (Author), \u003cb\u003eJason A. Aubrey\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003e An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Proof through Real Analysis \u003c\/i\u003eis based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems.\u003c\/p\u003e \u003cp\u003e- Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects\u003c\/p\u003e \u003cp\u003e- Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation\u003c\/p\u003e \u003cp\u003e- Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction\u003c\/p\u003e \u003cp\u003e- Uses a particular mathematical idea as the focus of each type of proof presented\u003c\/p\u003e \u003cp\u003e- Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Proof through Real Analysis \u003c\/i\u003eis the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDaniel J. Madden, PhD, \u003c\/b\u003eis an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJason A. Aubrey, PhD, \u003c\/b\u003eis Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona. \u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e \u003cstrong\u003eAn engaging and accessible introduction to mathematical proof incorporating ideas from real analysis\u003c\/strong\u003e \u003c\/p\u003e\u003cp\u003eA mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. \u003c\/p\u003e\u003cp\u003e\u003cem\u003eAn Introduction to Proof through Real Analysis\u003c\/em\u003e is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. \u003c\/p\u003e\u003cul\u003e \u003cli\u003eConcentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects\u003c\/li\u003e \u003cli\u003eDeparts from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation\u003c\/li\u003e \u003cli\u003eWritten in an engaging narrative style to tell the story of proof and its meaning, function, and construction\u003c\/li\u003e \u003cli\u003eUses a particular mathematical idea as the focus of each type of proof presented\u003c\/li\u003e \u003cli\u003eDeveloped from material that has been class-tested and fine-tuned over thirty years in university introductory courses\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003e \u003cp\u003e\u003cem\u003eAn Introduction to Proof through Real Analysis\u003c\/em\u003e is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDaniel J. Madden, PhD, \u003c\/strong\u003e is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eJason A. Aubrey, PhD, \u003c\/strong\u003e is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 448\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.1 x 9.1 x 6.3 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 12, 2017\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52512743063859,"sku":"9781119314721","price":168.21,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/t0kmeY4VrI9781119314721.webp?v=1760352775","url":"https:\/\/www.vysn.com\/products\/an-introduction-to-proof-through-real-analysis-hardcover","provider":"VYSN","version":"1.0","type":"link"}