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Science & Mathematics - Understanding Analysis (Undergraduate Texts in Mathematics)

Description

Book Synopsis: 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 Euler’s computation of ζ(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.

Details

Are you looking to dive into the fascinating world of mathematics analysis? Look no further than Understanding Analysis, an undergraduate text that will introduce you to the rewards of studying functions of a real variable. This lively and engaging book takes you on a journey through the intricate techniques and concepts needed to make sense of analysis. With an emphasis on approximation and resolving paradoxes, Understanding Analysis transforms complex definitions and theorems into a coherent progression of ideas. Whether you're a beginner or have some prior knowledge, this book will equip you with the skills to understand mathematical proofs and master the methods of analysis. Get started on your mathematical journey today!

With over fifteen years of classroom experience, the second edition of Understanding Analysis has been refined and enhanced to provide you with an even better learning experience. The book now includes roughly 150 new exercises that will help you solidify your understanding of the concepts. The best exercises from the first edition have also been included to provide a comprehensive practice. Additionally, three new project-style sections have been added, which explore Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function. These real-world applications serve as motivation and reward, allowing you to see the practical use of the methods you're learning. Are you ready to embark on this mathematical journey?

Get your copy of Understanding Analysis today and start unraveling the intricate world of mathematics. Don't miss out on this opportunity to enhance your mathematical knowledge and gain a deeper appreciation for the subject. Click here to order your copy now and take the first step towards becoming an analysis expert!

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