An 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 variables
Introduces students to basic topology
Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings
Discusses differential forms and Stokes's theorem in n dimensions
Also covers the Riemann integral, integrability, improper integrals, and series expansions

From the Back Cover:

"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

"A valuable, wonderful book."--Camil Muscalu, Cornell University

"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

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An Introduction to Analysis

Gunning, Robert C.

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