Students of mathematical biology discover modern methods of taxonomy with this text, which introduces taxonomic characters, the measurement of similarity, and the analysis of principal components. Other topics include multidimensional scaling, cluster analysis, identification and assignment techniques, more. A familiarity with matrix algebra and elementary statistics are the sole prerequisites.
How do we group different subjects on a variety of variables? Should we use a classification procedure in which only the concepts are classified (typology), one in which only empirical entities are classified (taxonomy), or some combination of both? In this clearly written book, Bailey addresses these questions and shows how classification methods can be used to improve research. Beginning with an exploration of the advantages and disadvantages of classification procedures including those typologies that can be constructed without the use of a computer, the book covers such topics as clustering procedures (including agglomerative and divisive methods), the relationship among various classification techniques (including the relationship of monothetic, qualitative typologies to polythetic, quantitative taxonomies), a comparison of clustering methods and how these methods compare with related statistical techniques such as factor analysis, multidimensional scaling and systems analysis, and lists classification resources. This volume also discusses software packages for use in clustering techniques.
I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in this book is quite interesting and stimulating in paradigms, clustering and optimization. On the other hand, it has a substantial application appeal. The book will be useful both to specialists and students in the fields of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. Panos Pardalos, Series Editor.
This second edition of Modern Bacterial Taxonomy has been completely revised and expanded to include detailed coverage of molecular systematics including relevant aspects of nucleic acid sequences, the construction of phylogenetic trees, typing of bacteria by restriction fragment length polymorphisms, DNA hybridization probes and the use of the polymerase chain reaction in bacterial systematics.
This is an examination of the relationship between classification and evolutionary theory, with reference to the competing schools of taxonomic thinking. Emphasis is placed on one of these schools, the transformed cladists who have attempted to reject all evolutionary thinking in classification and to cast doubt on evolution in general. The author examines the limits to this line of thought from a philosophical and methodological perspective. He concludes that transformed cladistics does not achieve what it claims and that it either implicitly assumes a Platonic World View, or is unintelligible without taking into account evolutionary processes--the very processes it claims to reject. Through this analysis the author attempts to formulate criteria of an objective and consistent nature that can be used to judge competing methodologies and theories. Philosophers of science, zoologists interested in taxonomy, and evolutionary biologists will find this a compelling study.
Taxonomy comprises a broad variety of activities related to the construction of classificatory systems. Over the past several years, the development of numerical and mathematical techniques designed to produce more objective results has transformed the field. This text offers students of mathematical biology an introduction to modern methods of taxonomy. Starting with an introduction to the philosophy and aims of numerical taxonomy, the text considers taxonomic characters and the measurement of similarity. An analysis of principal components presents geometric and mathematical interpretations; other chapters explore multidimensional scaling, cluster analysis, identification and assignment techniques, and the construction of evolutionary trees. Each of the eight major sections concludes with a helpful summary of its contents. In addition to its value to undergraduates, this text should also prove practical for postgraduate students and researchers interested in taxonomy and in the use of numerical methods in evolutionary studies. A familiarity with matrix algebra and elementary statistics are the sole prerequisites. Book jacket.
Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.
Taxonomy is an ever-changing, controversial and exCitmg field of biology. It has not remained motionless since the days of its founding fathers in the last century, but, just as with other fields of endeavour, it continues to advance in leaps and bounds, both in procedure and in philosophy. These changes are not only of interest to other taxonomists, but have far reaching implications for much of the rest of biology, and they have the potential to reshape a great deal of current biological thought, because taxonomy underpins much of biological methodology. It is not only important that an ethologist. physiologist. biochemist or ecologist can obtain information about the identities of the species which they are investigating; biology is also uniquely dependent on the comparative method and on the need to generalize. Both of these necessitate knowledge of the evolutionary relationships between organisms. and it is the science of taxonomy that can develop testable phylogenetic hypotheses and ultimately provide the best estimates of evolutionary history and relationships.
Addressing NCTM standards, this second edition offers a wide range of practical writing strategies to help students deepen their understanding of mathematical concepts and theories.
