MAU23203 - Analysis in Several Real Variables Dr. David R. Wilkins Suggestions for Problems and Further Reading

Suggestions for Further Reading

Those enrolled in this module are not required, or expected, to acquire any printed textbook. Nevertheless those who seek a (fairly demanding) textbook to accompany the real analysis modules that they take as an undergraduate might consider acquiring Principles of Mathematical Analysis by Walter Rudin (ISBN 007054235X). This textbook has been recommended reading in real analysis courses worldwide for many decades.

Sources for Problems

Those looking for problems related to the module content might consider reviewing some of the continuous assessment tests taken by students of Course 121 (a course in real analysis taken by Junior Fresh students) in earlier years earlier years. Some of the definitions and results examined are not included in the current version of module MAU23203. In particular, the definition of homeomorphism is not included in the first six sections of the current version of MAU23203: a function between subsets of Euclidean spaces is said to be a homeomorphism if it is an invertible function satisfying the additional requirement that the function itself and its inverse should both be continuous. For problems relevant to the first six sections of MAU23203 in 2021/22, see for example, the following Course 121 continuous assessment tests: Course 121, Test V in 1990/91; Course 121, Test V in 1992/93; Course 121, Test V in 1993/94. See also problems 3, 4, 5 included on the first problem set for Course 212 in 1998/99.

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Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.