This textbook takes physics and engineering undergraduates through the mathematics they need in the first years of study. It offers an accessible approach which is characterized by the combination of the textbook with a detailed study guide. This study guide, supplied as freely accessible downloads for each chapter, divides the whole learning task into small units. You will read and study a limited section of the textbook and then return to the study guide afterwards. Learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. The degree of difficulty slowly rises, which will let you gain confidence and experience your own progress, thus fostering motivation. The sequence of studies can be individualized according to performance and can be regarded as a full tutorial course. This combination of a textbook with a detailed study guide is a powerful means to meet the rising importance of learning outside of lectures at home and will be of great benefit, especially to students learning remotely.
Information theory and cybernetics have developed along somewhat different lines in Europe and in the U. S. A. This book is to be seen as a contribution towards bridging the gap. Anyone who seeks to apply information theory in the fields of education and psychology very soon comes up against a central diffi culty: in the form in which it was developed by Shannon information theory excludes the semantic aspect. This problem is fundamental for in education, as in psychology, the semantic aspect is the very heart of the matter. Thus, while Attneave, Miller and Quastler, among others, successfully employed the concepts and units of measurement of in formation theory in the interpretation of the findings of experimental psychology, they were obliged to restrict their work to its syntactic and statistical aspects. Before we can make use of the methods and results of information we have to solve the central problem: How can theory in actual teaching, we measure the semantic information of a verbal message? The only way to do this is by extending the theory. A special concept has been deve loped for this purpose: subjective information. In place of an objectively measurable quantity (frequency of sign sequences) we set an empirically determined one: the subjective probability with which the recipient expects a certain sign sequence.
Information theory always has the dual appeal of bringing important concepts to the study of communication in society, and of providing a calculus for information flows within systems. This book introduces readers to basic concepts of information theory, extending its original linear conception of communication to many variables, networks, and higher-order interactions (including loops) and developing it into a method for analyzing qualitative data. It elaborates on the algebra of entropy and information, shows how complex models of data are constructed and tested, describes algorithms for exploring multivariate structures using such models, and gives illustrative applications of these techniques. The book is designed as a text but it can also serve as a handbook for social researchers and systems theorists with an interest in communication.
Mathematics is the basic language in physics and engineering. This textbook offers an accessible and highly-effective approach to mathematics which is characterised by the combination of the textbook with a detailed study guide on an accompanying CD.
Information theory and cybernetics have developed along somewhat different lines in Europe and in the U. S. A. This book is to be seen as a contribution towards bridging the gap. Anyone who seeks to apply information theory in the fields of education and psychology very soon comes up against a central diffi culty: in the form in which it was developed by Shannon information theory excludes the semantic aspect. This problem is fundamental for in education, as in psychology, the semantic aspect is the very heart of the matter. Thus, while Attneave, Miller and Quastler, among others, successfully employed the concepts and units of measurement of in formation theory in the interpretation of the findings of experimental psychology, they were obliged to restrict their work to its syntactic and statistical aspects. Before we can make use of the methods and results of information we have to solve the central problem: How can theory in actual teaching, we measure the semantic information of a verbal message? The only way to do this is by extending the theory. A special concept has been deve loped for this purpose: subjective information. In place of an objectively measurable quantity (frequency of sign sequences) we set an empirically determined one: the subjective probability with which the recipient expects a certain sign sequence.
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