Practice Problem Books

Question

The Analysis I/II/III (Differentiation and Continuity/Sequence and Series/Integration) published by AMS. The first one is this. It's a problem-solution book. I found it excellent because of the quality of questions there.

I am looking for similar book (complete problem (only) book with complete solution) in linear algebra. However, let's include following subjects too:

1. Linear Algebra

2. Abstract Algebra

3. Complex Analysis

4. Topology

Please suggest if only it is like the book i suggested in the beginning. I do not want books like exceptions in analysis/mathematics which also have significant problems which are interesting. I also do not want books that are completely aimed for competitions like putnam and are too tough.

Answer 1

Analysis

A problem Book in real analysis, Asuman G. Askoy

Problems and Solutions for Undergraduate Analysis, Rami Shakirachi based on Lang's Analysis book

Problems and Theorems in Analysis I, II and III, Polya, Szego(I think this was what you were referring)

Linear Algebra

Linear Algebra, Jim Hefferon, http://joshua.smcvt.edu/linearalgebra/ has the text book which has all problems and solutions.

Complex Analysis

Problems and Solutions for Complex Analysis, Rami Shakirachi based on Lang's complex analysis book.

Abstract Algebra

Abstract Algebra, John Beachy http://www.math.niu.edu/~beachy/abstract_algebra/study_guide/contents.html is an online text with problems and solutions.

Solution Manual for A first course in Abstract Algebra, Fraleigh . The solution manual has solutions to almost all problems if I recall and can find it online.

Answer 2

Okay, here are the few ones I know of:

• Linear Algebra: Challenging problems in linear algebra- an undergrad level problem book, whole solutions are not given but there are hints to the problems at the back. linear algebra by Friedberg,Insel- mainly a textbook, and problems are not too hard either, but I'm listing it here because it has complete solutions to every problem online in a pdf.
• Berkely problems in Mathematics- contains a lot of interesting problems on each topic like real analysis, linear algebra, complex analysis etc,etc.. Solutions are also given.