Understanding Analysis (Undergraduate Texts in Mathematics)

Springer

$37.16 - $42.74
(No reviews yet) Write a Review
UPC:
9781493927111
Maximum Purchase:
2 units
Binding:
Hardcover
Publication Date:
5/20/2015
Release Date:
8/22/2016
Author:
Abbott, Stephen
Language:
English: Published; English: Original Language; English
Edition:
2nd ed. 2015, Corr. 2nd printing 2016
Pages:
324
Adding to cart… The item has been added

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 from the first edition, and three more project-style sections have been added. Investigations of Eulers computation of (2), the Weierstrass Approximation Theorem, and the gamma function are now among the books cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.