An Invitation to Real Analysis (Maa Textbooks)

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9781939512055: An Invitation to Real Analysis (Maa Textbooks)

An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from The College Mathematics Journal and The American Mathematical Monthly. These articles are inviting in their level of exposition and their wide-ranging content.

Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology.

Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers.

Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.

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Book Description:

This book is written as both a stepping stone to higher calculus and analysis courses, and as a foundation for deeper reasoning in applied mathematics. As well as a rigorous account of sequences, series, functions and sets, the reader will also find fascinating historical material and over 600 exercises.

About the Author:

Luis Moreno received his BA in mathematics at Rensselaer Polytechnic Institute in 1973, an MS in mathematics education at State University of New York, Albany in 1976, and an MA in mathematics at State University of New York, Albany in 1982. He belongs to the Mathematical Association of America (Seaway Section 2nd vice-chair in 2000) and New York State Mathematics Association of Two-Year Colleges, being campus liaison for both organizations. He teaches at Broome Community College where, besides the standard undergraduate courses through linear algebra and real analysis, he has taught courses in statistics, statistical quality control, and logic.

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Book Description Mathematical Association of America, United States, 2015. Hardback. Book Condition: New. UK ed.. Language: English . Brand New Book. Both 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. Bookseller Inventory # AAA9781939512055

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Book Description Mathematical Association of America, United States, 2015. Hardback. Book Condition: New. UK ed.. Language: English . Brand New Book. Both 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. Bookseller Inventory # AAA9781939512055

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Book Description Mathematical Association of America. Book Condition: New. A broad and rigorous treatment of real analysis and a platform to higher mathematics, with historical material and 600 exercises. Series: Mathematical Association of America Textbooks. Num Pages: 678 pages. BIC Classification: PBCH; PBKB; PBW. Category: (U) Tertiary Education (US: College). Dimension: 264 x 184 x 41. Weight in Grams: 1316. . 2015. Hardcover. . . . . Books ship from the US and Ireland. Bookseller Inventory # V9781939512055

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