Varieties of Integration (Dolciani Mathematical Expositions)

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9780883853597: Varieties of Integration (Dolciani Mathematical Expositions)
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Varieties of Integration explores the critical contributions by Riemann, Darboux, Lebesgue, Henstock, Kurzweil, and Stieltjes to the theory of integration and provides a glimpse of more recent variations of the integral such as those involving operator-valued measures. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation with little attention paid to the relationships between them or to the historical issues that motivated their definitions. This book redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals in a single volume using a common set of examples. This approach allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the Fundamental Theorems of Calculus.

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Young mathematicians typically encounter three definitions of integration which are often treated as disparate. This book, perfect as both a reference and as a textbook for a second undergraduate analysis course, redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals using a common set of examples.

About the Author:

C. Ray Rosentrater is a Professor of Mathematics at Westmont College where he has also served as department chair and Associate Dean for Curriculum. He has been recognized as Westmont s Teacher of the Year in the Natural and Behavioral Sciences and has received the Faculty Research Award. He earned a PhD in mathematics from Indiana University and an MSc in computer science from the University of Toronto. Awarded a Fulbright Fellowship in 1995, he now serves as Westmont s Fulbright Program Advisor. He served multiple terms on the ACMS board including terms as Vice President and President. His other publications include papers in operator theory and articles connecting analysis to computer science and linear algebra to statistics. He co-wrote two chapters in Mathematics through the Eyes of Faith.

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C. Ray Rosentrater
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Book Description Mathematical Association of America, United States, 2016. Hardback. Condition: New. Language: English . Brand New Book. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation, with little attention paid to the relationships between them or to the historical issues that motivated their definitions. This book redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals using a common set of examples. This allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the Fundamental Theorems of Calculus. With a thorough set of appendices and exercises, and interesting historical context, this book is equally useful as a reference for mathematicians or as a text for a second undergraduate course in real analysis. Seller Inventory # AAA9780883853597

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Book Description Mathematical Association of America, United States, 2016. Hardback. Condition: New. Language: English . Brand New Book. By the first year of graduate school, a young mathematician will have encountered at least three separate definitions of the integral. The associated integrals are typically studied in isolation, with little attention paid to the relationships between them or to the historical issues that motivated their definitions. This book redresses this situation by introducing the Riemann, Darboux, Lebesgue, and gauge integrals using a common set of examples. This allows the reader to see how the definitions influence proof techniques and computational strategies. Then the properties of the integrals are compared in three major areas: the class of integrable functions, the convergence properties of the integral, and the best form of the Fundamental Theorems of Calculus. With a thorough set of appendices and exercises, and interesting historical context, this book is equally useful as a reference for mathematicians or as a text for a second undergraduate course in real analysis. Seller Inventory # AAA9780883853597

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Book Description Mathematical Association of America, 2015. Condition: New. A textbook that studies and compares the various different types of integration that young mathematicians encounter. Series: Dolciani Mathematical Expositions. Num Pages: 330 pages, illustrations. BIC Classification: PBKL. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 238 x 159 x 25. Weight in Grams: 578. . 2015. Hardcover. . . . . . Seller Inventory # V9780883853597

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Book Description Mathematical Association of America. Condition: New. A textbook that studies and compares the various different types of integration that young mathematicians encounter. Series: Dolciani Mathematical Expositions. Num Pages: 330 pages, illustrations. BIC Classification: PBKL. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 238 x 159 x 25. Weight in Grams: 578. . 2015. Hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9780883853597

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