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This book is the result of a joint venture between Professor Akio
Kawauchi, Osaka City University, well-known for his research in
knot theory, and the Osaka study group of mathematics education,
founded by Professor Hirokazu Okamori and now chaired by his
successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The
seven chapters address the teaching and learning of knot theory
from several perspectives. Readers will find an extremely clear and
concise introduction to the fundamentals of knot theory, an
overview of curricular developments in Japan, and in particular a
series of teaching experiments at all levels which not only
demonstrate the creativity and the professional expertise of the
members of the study group, but also give a lively impression of
students learning processes. In addition the reports show that
elementary knot theory is not just a preparation for advanced knot
theory but also an excellent means to develop spatial thinking. The
book can be highly recommended for several reasons: First of all,
and that is the main intention of the book, it serves as a
comprehensive text for teaching and learning knot theory. Moreover
it provides a model for cooperation between mathematicians and
mathematics educators based on substantial mathematics. And finally
it is a thorough introduction to the Japanese art of lesson studies
again in the context of substantial mathematics.
Knot theory is a rapidly developing field of research with many
applications not only for mathematics. The present volume, written
by a well-known specialist, gives a complete survey of knot theory
from its very beginnings to today's most recent research results.
The topics include Alexander polynomials, Jones type polynomials,
and Vassiliev invariants. With its appendix containing many useful
tables and an extended list of references with over 3,500 entries
it is an indispensable book for everyone concerned with knot
theory. The book can serve as an introduction to the field for
advanced undergraduate and graduate students. Also researchers
working in outside areas such as theoretical physics or molecular
biology will benefit from this thorough study which is complemented
by many exercises and examples.
Knot theory is a rapidly developing field of research with many
applications not only for mathematics. The present volume, written
by a well-known specialist, gives a complete survey of knot theory
from its very beginnings to today's most recent research results.
The topics include Alexander polynomials, Jones type polynomials,
and Vassiliev invariants. With its appendix containing many useful
tables and an extended list of references with over 3,500 entries
it is an indispensable book for everyone concerned with knot
theory. The book can serve as an introduction to the field for
advanced undergraduate and graduate students. Also researchers
working in outside areas such as theoretical physics or molecular
biology will benefit from this thorough study which is complemented
by many exercises and examples.
The series is aimed specifically at publishing peer reviewed
reviews and contributions presented at workshops and conferences.
Each volume is associated with a particular conference, symposium
or workshop. These events cover various topics within pure and
applied mathematics and provide up-to-date coverage of new
developments, methods and applications.
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