A Companion to Analysis: A Second First and First Second Course in Analysis

by T.W. Körner

Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they work together. This book provides those students with the coherent account that they need. A Companion to Analysis explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems. Starting with the real line, the book moves on to finite-dimensional spaces and then to metric spaces. Readers who work through this text will be ready for courses such as measure theory, functional analysis, complex analysis, and differential geometry. Moreover, they will be well on the road that leads from mathematics student to mathematician. With this book, well-known author Thomas Körner provides able and hard-working students a great text for independent study or for an advanced undergraduate or first-level graduate course. It includes many stimulating exercises. An appendix contains a large number of accessible but non-routine problems that will help students advance their knowledge and improve their technique.

Genres: Mathematics, Textbooks

590 pages, Hardcover

First published January 1, 2004

About the author

Thomas William Körner (born 17 February 1946) is a British pure mathematician and the author of school books. He is titular Professor of Fourier Analysis in the University of Cambridge and a Fellow of Trinity Hall. He is the son of the philosopher Stephan Körner and of Edith Körner.

He studied at Trinity Hall, Cambridge, and wrote his PhD thesis Some Results on Kronecker, Dirichlet and Helson Sets there in 1971, studying under Nicholas Varopoulos. In 1972 he won the Salem Prize.

He has written three academic mathematics books aimed at undergraduates, and two books aimed at secondary school students, the popular 1996 title The Pleasures of Counting and Naive Decision Making (published 2008) on probability, statistics and game theory.

Reviews

[Evan · Rating 5 out of 5]

Truly great self-study guide to analysis. This guy has a great voice, but still writes clear math prose.