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Includes entries for maps and atlases.
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Metabolic Flux Analysis: Methods and Protocols opens up the field of metabolic flux analysis to those who want to start a new flux analysis project but are overwhelmed by the complexity of the approach. Metabolic flux analysis emerged from the current limitation for the prediction of metabolic fluxes from a measured inventory of the cell. Divided into convenient thematic parts, topics in this essential volume include the fundamental characteristics of the underlying networks, the application of quantitative metabolite data and thermodynamic principles to constrain the solution space for flux balance analysis (FBA), the experimental toolbox to conduct different types of flux analysis experiments, the processing of data from 13C experiments and three chapters that summarize some recent key findings. Written in the successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible protocols and notes on troubleshooting and avoiding known pitfalls. Authoritative and easily accessible, Metabolic Flux Analysis: Methods and Protocols presents protocols that cover a range of relevant organisms currently used in the field, providing a solid basis to anybody interested in the field of metabolic flux analysis.
Plant neurobiology is a newly emerging field of plant sciences. It covers signalling and communication at all levels of biological organization – from molecules up to ecological communities. In this book, plants are presented as intelligent and social organisms with complex forms of communication and information processing. Authors from diverse backgrounds such as molecular and cellular biology, electrophysiology, as well as ecology treat the most important aspects of plant communication, including the plant immune system, abilities of plants to recognize self, signal transduction, receptors, plant neurotransmitters and plant neurophysiology. Further, plants are able to recognize the identity of herbivores and organize the defence responses accordingly. The similarities in animal and plant neuronal/immune systems are discussed too. All these hidden aspects of plant life and behaviour will stimulate further intense investigations in order to understand the communicative plants in their whole complexity.
This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.