Overview

An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning-differentiation, the Riemann integral, series, and differential forms and Stokes's theorem-enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.Provides a rigorous introduction to calculus in one and several variablesIntroduces students to basic topologyCovers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappingsDiscusses differential forms and Stokes's theorem in n dimensionsAlso covers the Riemann integral, integrability, improper integrals, and series expansions

Full Product Details

9780691178790

Table of Contents

Reviews

An excellent and unusual book by an esteemed mathematician and teacher. An Introduction to Analysis is a uniquely valuable sourcebook for much of undergraduate mathematics. -John B. Garnett, University of California, Los Angeles A valuable, wonderful book. -Camil Muscalu, Cornell University Gunning's book is a great introduction to analysis that presents precisely what an honors analysis course should include. The writing is rigorous but lively, and much interesting mathematics is packed in it. -Wilhelm Schlag, University of Chicago

One would expect that this book offers a demanding, sophisticated look at this material, done rapidly and concisely. One would be correct. . . . [F]or very sophisticated honors courses with exceptionally well-prepared students who are prepared to work hard, it would certainly offer a vivid, exciting and informative introduction to this material.---Mark Hunacek, MAA Reviews An excellent and unusual book by an esteemed mathematician and teacher. An Introduction to Analysis is a uniquely valuable sourcebook for much of undergraduate mathematics. --John B. Garnett, University of California, Los Angeles A valuable, wonderful book. --Camil Muscalu, Cornell University Gunning's book is a great introduction to analysis that presents precisely what an honors analysis course should include. The writing is rigorous but lively, and much interesting mathematics is packed in it. --Wilhelm Schlag, University of Chicago

Author Information

Robert C. Gunning is professor of mathematics at Princeton University. His books include Lectures on Riemann Surfaces and Lectures on Complex Analytic Varieties (both Princeton).

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