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Science & Mathematics - Analysis I: Third Edition (Texts and Readings in Mathematics)

Description

Book Synopsis: This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Details

Looking to deepen your understanding of mathematics and real analysis? Look no further than Analysis I: Third Edition. This comprehensive two-volume book is tailored for senior undergraduate students with a background in calculus, focusing on building a strong foundation in analysis. From constructing number systems to exploring power series and Fourier analysis, this book covers all the essential topics in a structured and rigorous manner.

Written with a student-centered approach, Analysis I integrates theory with practical exercises to enhance learning and promote critical thinking skills. With a focus on real line and Euclidean spaces, as well as abstract metric and topological spaces, this book offers a well-rounded and in-depth exploration of the subject matter. Whether you're studying for exams or looking to expand your mathematical knowledge, Analysis I is the perfect companion for your academic journey.

If you're ready to elevate your understanding of analysis and delve into the foundations of mathematics, don't miss out on this invaluable resource. With clear explanations, comprehensive coverage of key topics, and engaging exercises, Analysis I: Third Edition is a must-have for any aspiring mathematician or student of higher mathematics.

Take the first step towards mastering real analysis with Analysis I: Third Edition - your gateway to a deeper understanding of calculus, differentiation, integration, and more. Order your copy today and unlock the secrets of analysis with this essential textbook.

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