|Cumulative List of Corrections:||[pdf]|
|Selected Solutions to Problems (complete list):||[pdf]|
|(By chapter):||Chapter 1 [pdf]||Chapter 5 [pdf]||Chapter 9 [pdf]|
|Chapter 2 [pdf]||Chapter 6 [pdf]||Chapter 10 [pdf]|
|Chapter 3 [pdf]||Chapter 7 [pdf]||Chapter 11 [pdf]|
|Chapter 4 [pdf]||Chapter 8 [pdf]||Chapter 12 [pdf]|
|** New Chapter **|
Introduction to Infinite Series"
||Chapter 13 [pdf]|
Available for purchase from Springer and Amazon.
Daniel Rosenthal, David Rosenthal, Peter Rosenthal
A Readable Introduction to Real Mathematics
Springer Series: Undergraduate Texts in Mathematics
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.