Understanding Analysis - Stephen Abbott

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Résumé :
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises fromthe first edition, and three more project-style sections have been added. Investigations of Euler?s computation of ?(2), the Weierstrass Approximation ? Theorem, and the gamma function are now among the book?s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Biographie:
Nicholas H. Wasserman is Associate Professor of Mathematics Education at Teachers College, Columbia University. Previously, he taught mathematics for six years at the secondary level, in both a large public school in Austin and a private school in Manhattan. His scholarly interests focus on secondary teachers' mathematical knowledge and development, particularly how advanced mathematics can be relevant for teachers and influence their secondary classroom teaching and practice. Tim Fukawa-Connelly is Associate Professor of Teaching and Learning in the College of Education and Human Development at Temple University. His scholarly interests include teacher development, the relationship between what happens in mathematics classrooms and student learning, and hiking to as many waterfalls as possible. Keith Weber is Professor of Mathematics Education at Rutgers University. His scholarly interests include how students and mathematicians reason in advanced mathematics and the relationship between mathematical activity and mathematical learning. Juan Pablo Mej?a Ramos is Associate Professor of Mathematics and Mathematics Education at Rutgers University, jointly appointed in the Department of Mathematics (within the School of Arts and Sciences) and the Department of Learning and Teaching (within the Graduate School of Education). He is mainly interested in mathematical argumentation and proof, particularly the ways in which university students and research-active mathematicians construct, read and present arguments and proofs in mathematics. Stephen Abbott is Professor of Mathematics at Middlebury College. His research interests include classical and functional analysis as well as an ongoing fascination with the intersection of mathematics and the arts. He has held visiting positions at Saint Olaf College and the University of Virginia, was editor of Math Horizons (published by the MAA) from 2008-14, and is the author ofUnderstanding Analysis (Springer, 2015).