Kategoria BISAC: Mathematics >> Geometry - General

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems - those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad.

Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a...

Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of Etienne Bezout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them.

The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in...

To quantify map construction algorithms, the authors include specific datasets and evaluation measures. The datasets, source code of map construction algorithms and evaluation measures are publicly available on...

The aim of this book is to describe the essence of fractals and multifractals dynamics in the applications of bioscience and engineering, bioinformatics, and financial time series. To reach these aims, the book covers the basic idea, history, structure, methodology and analysis of fractals, the relationship between fractals and nonlinear dynamics, the applications of fractal and multifractal analysis in biomedical science, and how fractal signals and images are modelled by Iterated Function system. Illustrations and practical applications are given throughout the text to provide clear...

In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems.

The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators...

All real life mathematics is problem solving. And all those fascinated by puzzles are problem solvers at heart. But thinking mathematically is a skill we have to learn and one which it is easy to forget. Recreational mathematicians and students can practise problem solving in different ways. In this book solving puzzles is practised in a different way from most books they will have seen before:
# Readers get no clues to what the puzzle is about
# They may take hours or even days to work out what is being asked of them
# Even after that, some problems may have no solution
The...

This professional treatise on engineering graphics emphasizes engineering geometry as the theoretical foundation for communication of design ideas with real world structures and products. It considers each theoretical notion of engineering geometry as a complex solution of direct- and inverse-problems of descriptive geometry and each solution of basic engineering problems presented is accompanied by construction of biunique two- and three-dimension models of geometrical images. The book explains the universal structure of formal algorithms of the solutions of positional, metric, and...

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure.

The first part of the book introduces the definitions and notations of the universal...

This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.
Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important...