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Abstrak :
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.

Abstrak :
Dalam analisis regresi, terdapat dua pendekatan, yaitu pendekatan regresi parametrik dan pendekatan regresi nonparametrik. Dalam regresi parametrik, bentuk dari kurva regresi sudah diasumsikan, sedangkan dalam regresi nonparametrik, bentuk dari kurva regresi tidak diketahui. Salah satu regresi nonparametrik yang dapat digunakan adalah regresi spline dengan menggunakan truncated power basis. Regresi spline adalah suatu polinomial sepotong-sepotong yang dihubungkan oleh titik-titik bersama yang disebut dengan knot. Pada regresi spline, estimasi parameter dilakukan dengan menggunakan metode OLS (Ordinary Least Square). Namun, dengan metode OLS akan menyebabkan overparameterized dan pada plot taksiran kurva regresi akan terjadi fluktuatif apabila pemilihan jumlah knot terlalu banyak. Untuk itu, diperlukan suatu tambahan kendala yang didalamnya mengandung smoothing parameter sehingga diperoleh taksiran yang ideal. Metode estimasi parameter ini dikenal dengan metode PLS (Penalized Least Square). Regresi spline yang menggunakan estimasi parameter PLS (Penalized Least Square) disebut dengan regresi penalized spline. Pada contoh penerapan data, model terbaik dipilih untuk regresi penalized spline truncated power basis linier dengan 23 buah knot dan smoothing parameter sebesar 2.44. ......In analysis regression, there are two approach, that is parametric regression approach and nonparametric regression approach. In parametric regression, the shape of regression curve is assumed, whereas in the nonparametric regression, the shape of curve is unknown. One of the nonparametric regression can be used is spline regression using truncated power basis. Spline regression is piecewise polynomials that connect at join points called knots. In spline regression, parameter estimation were fit by OLS (Ordinary Least Square) method. However, the OLS method will lead to overparameterized and in the plot of estimated regression curve will be fluctuative when using too much knots. Therefore, it needs an additional constraint which contain smoothing parameter, so that will result an ideally fit. This parameter estimation method known as PLS (Penalized Least Square) method. Spline regression that using PLS method is called by penalized spline regression. In the example application of data, the best model is choosen for penalized spline regression truncated power basis linear with 23 knots and smoothing parameter at 2.44.

Abstrak :
New approaches to knot insertion and deletion are presented in this unique, detailed approach to understanding, analyzing, and rendering B-spline curves and surfaces. Computer scientists, mechanical engineers, and programmers and analysts involved in CAD and CAGD will find innovative, practical applications using the blossoming approach to knot insertion, factored knot insertion, and knot deletion, as well as comparisons of many knot insertion algorithms. This book also serves as an excellent reference guide for graduate students involved in computer aided geometric design.