Designed for an undergraduate course or for independent study, this
text presents sophisticated mathematical ideas in an elementary and
friendly fashion. The fundamental purpose of this book is to engage
the reader and to teach a real understanding of mathematical
thinking while conveying the beauty and elegance of mathematics.
The text focuses on teaching the understanding of mathematical
proofs. The material covered has applications both to mathematics
and to other subjects. The book contains a large number of
exercises of varying difficulty, designed to help reinforce basic
concepts and to motivate and challenge the reader. The sole
prerequisite for understanding the text is basic high school
algebra; some trigonometry is needed for Chapters 9 and 12. Topics
covered include: mathematical induction - modular arithmetic - the
fundamental theorem of arithmetic - Fermat's little theorem - RSA
encryption - the Euclidean algorithm -rational and irrational
numbers - complex numbers - cardinality - Euclidean plane geometry
- constructability (including a proof that an angle of 60 degrees
cannot be trisected with a straightedge and compass). This textbook
is suitable for a wide variety of courses and for a broad range of
students in the fields of education, liberal arts, physical
sciences and mathematics. Students at the senior high school level
who like mathematics will also be able to further their
understanding of mathematical thinking by reading this book.
General
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