TY  - BOOK
AU  - Rosenthal,Daniel
AU  - Rosenthal,David
AU  - Rosenthal,Peter
TI  - Readable introduction to real mathematics
T2  - Undergraduate texts in mathematics
SN  - 9783319056531
U1  - 510 23
PY  - 2014///
CY  - New York
PB  - Springer
KW  - Mathematics.
KW  - Symbolic and Mathematical Logic
KW  - Mathematics
KW  - Problems
KW  - Analysis
N1  - Includes index; 1. Introduction to the natural numbers --
2. Mathematical induction --
3. Modular arithmetic --
4. The fundamental theorem of arithmetic --
5. Fermat's Theorem and Wilson's Theorem --
6. Sending and receiving secret messages --
7. The Euclidean algorithm and applications --
8. Rational numbers and irrational numbers --
9. The complex numbers --
10. Sizes of infinite sets --
11. Fundamentals of Euclidean plane geometry --
12. Constructability--
Index
N2  - 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
ER  -