Since this review, Axler has released a third edition. The new edition contains substantial changes (i.e. it’s not the same book being released under “n+1 edition”): though there’s little new material, exercises appear at the end of every section, instead at the end of every chapter, and there’s many more examples given in the body of the text (a longer list of changes can be found on Dr. Axler’s website). I feel these revisions are significant improvements from a pedagogical perspective, as it gives the reader more opportunity to practice prerequisite skills before learning the next thing. The changes also lower the requisite mathematical maturity, which is a good thing (insofar as it makes the book more accessible), although it won’t push the reader to develop mathematical maturity as much. Overall: the third edition came out when I was halfway through the second edition and I felt that the improments merited switching books.
Since this review, Axler has released a third edition. The new edition contains substantial changes (i.e. it’s not the same book being released under “n+1 edition”): though there’s little new material, exercises appear at the end of every section, instead at the end of every chapter, and there’s many more examples given in the body of the text (a longer list of changes can be found on Dr. Axler’s website). I feel these revisions are significant improvements from a pedagogical perspective, as it gives the reader more opportunity to practice prerequisite skills before learning the next thing. The changes also lower the requisite mathematical maturity, which is a good thing (insofar as it makes the book more accessible), although it won’t push the reader to develop mathematical maturity as much. Overall: the third edition came out when I was halfway through the second edition and I felt that the improments merited switching books.