The book contains chapters of structured approach to problem
solving in mathematical analysis on an intermediate level. It
follows the ideas of G.Polya and others, distinguishing between
exercises and problem solving in mathematics. Interrelated concepts
are connected by hyperlinks, pointing toward easier or more
difficult problems so as to show paths of mathematical reasoning.
Basic definitions and theorems can also be found by hyperlinks from
relevant places. Problems are open to alternative formulations,
generalizations, simplifications, and verification of hypotheses by
the reader; this is shown to be helpful in solving problems. The
book presents how advanced mathematical software can aid all stages
of mathematical reasoning while the mathematical content remains in
foreground. The authors show how software can contribute to deeper
understanding and to enlarging the scope of teaching for students
and teachers of mathematics.
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