Knapp Anthony W. Basic Real Analysis

2005 г.
The books are written as textbooks, and their primary audience is students who
are learning the material for the first time and who are planning a career in which
they will use advanced mathematics professionally. Much of the material in the
books corresponds to normal course work. Nevertheless, it is often the case that
core mathematics curricula, time-limited as they are, do not include all the topics
that one might like. Thus the book includes important topics that may be skipped
in required courses but that the professional mathematician will ultimately want
to learn by self-study.
The content of the required courses at each university reflects expectations of
what students need before beginning specialized study andwork on a thesis. These
expectations vary from country to country and from university to university. Even
so, there seems to be a rough consensus about what mathematics a plenary lecturer
at a broad international or national meeting may take as known by the audience.
The tables of contents of the two books represent my own understanding of what
that degree of knowledge is for real analysis today.