Series: Dolciani Mathematical Expositions
Hardback (ISBN-13: 9780883853481)
269 b/w illus. 3 tables 149 exercises
Page extent: 160 pages
Size: 228 x 152 mm
Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and
proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with
inevitability and economy'. Charming Proofs presents a collection of remarkable proofs in elementary mathematics that are
exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual
representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, and to develop the
ability to create proofs themselves. The authors consider proofs from topics such as geometry, number theory, inequalities,
plane tilings, origami and polyhedra. Secondary school and university teachers can use this book to introduce their students
to mathematical elegance. More than 130 exercises for the reader (with solutions) are also included.
* Over 130 challenges (and their solutions) draw the reader into the process
of creating proofs for themselves * Suitable as
a supplementary text for an introductory course on proofs, mathematical
reasoning, or problem solving * Over 250 figures are
used to facilitate both the proofs themselves and the reader's understanding
Preface; Introduction; 1. A garden of integers; 2. Distinguished numbers; 3. Points in the plane; 4. The polygonal
playground; 5. A treasury of triangle theorems; 6. The enchantment of the equilateral triangle; 7. The quadrilaterals'
corner; 8. Squares everywhere; 9. Curves ahead; 10. Adventures in tiling and coloring; 11. Geometry in three dimensions; 12.
Additional theorems, problems and proofs; Solutions to the challenges; References; Index; About the authors.
Series: Cambridge Library Collection - Mathematics
Paperback (ISBN-13: 9781108013109)
Page extent: 228 pages
Size: 216 x 140 mm
John Leigh Smeathman Hatton (1865-1933) was a British mathematician and
educator. He worked for 40 years at a pioneering
educational project in East London that began as the People's Palace and eventually became Queen Mary College in the
University of London. Hatton served as its Principal from 1908 to 1933. This book, published in 1920, explores the
relationship between imaginary and real non-Euclidean geometry through graphical representations of imaginaries under a
variety of conventions. This relationship is of importance as points with complex determining elements are present in both
imaginary and real geometry. Hatton uses concepts including the use of co-ordinate methods to develop and illustrate this
relationship, and concentrates on the idea that the only differences between real and imaginary points exist solely in
relation to other points. This clearly written volume exemplifies the type of non-Euclidean geometry research current at the
time of publication.
Preface; 1. Imaginary points and lengths on real straight lines. Imaginary straight lines. Properties of semi-real figures;
2. The circle with a real branch. The conic with a real branch; 3. Angles between imaginary straight lines. Measurement of
imaginary angles and of lengths on imaginary straight lines. Theorems connected with projection. 4. The general conic; 5. The
imaginary conic; 6. Tracing of conics and straight lines; 7. The imaginary in space; Indexes.
Series: Classroom Resource Materials
Hardback (ISBN-13: 9780883857700)
68 b/w illus. 15 colour illus. 7 tables 181 exercises
Page extent: 230 pages
Size: 254 x 178 mm
Rediscovering Mathematics is principally a guide to effective mathematical education. However, its collection of topics and
puzzles will also inspire a renewed interest in mathematics among students and enthusiasts. The book focuses on problem
solving and understanding, and discourages learning by rote memorization. Its topics include number theory and its
applications to secure communication over the Internet, and applications of probability to sports and gambling. The topics
are linked by the common theme of mathematical learning through investigation and discovery. It is suitable for anyone who
wants to expand their view of mathematics. It can be used as a text for training math teachers at all levels, and is
recommended for anyone interested in mathematics and how mathematics should be taught. Rediscovering Mathematics provides a
fresh view of mathematics for those who already like the subject, and offers
a second chance for those who think they hate it.
* Nearly 200 end-of-chapter exercises * Frequent challenges with hints
and solutions throughout * A focus on learning through
problem-solving and understanding is enhanced by linking mathematical topics to everyday-life scenarios
Preface - a guide for the reader; Introduction - how to read mathematics; 1. Mathematical discovery in the classroom; 2.
Don't reach for your calculator (yet); 3. Have another piece of pie, Zeno*;
4. Thinking like a mathematician - lessons from a
medieval Rabbi; 5. What's mathematics good for*; 6. Three averages; 7.
Algorithms - the unexpected role of pure mathematics;
8. Pythagoras' Theorem and math by pictures; 9. Memorizing versus understanding; 10. Games and gambling; 11. Soccer balls and
counting tricks; 12. Pizza Pi and area; 13. Back to the classroom; Resources for rediscovering mathematics; Further reading.
Series: Carus Mathematical Monographs
Paperback (ISBN-13: 9780883850428)
26 b/w illus. 33 colour illus. 1 table 92 exercises
Page extent: 260 pages
Size: 210 x 138 mm
The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Godel's
incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience
in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of
mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than
standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about
the subject.
* An emphasis on possible interpretations of certain results and concepts,
and their connections to author areas of inquiry,
gives the reader a depth of understanding * Includes both 'Exercises' and
'Investigations': the former emphasise more
technical questions concerning the ideas, while the latter are more open, allowing scope for student initiative and further
research * Notes at the end of each part set the mathematical ideas in
their historical background
1. Predicate logic; 2. Set theory; 3. Recursion theory and computability; 4. Model theory; 5. Independence results in set
theory; 6. Nonstandard analysis; 7. Constructive mathematics; Appendix A. A deductive system for first-order logic; Appendix
B. Relations and orderings; Appendix C. Cardinal arithmetic; Bibliography; Index.