Bøger af Mark Burgin

Postgraduate Certificate in Medical Education (PGCME) is a postgraduate qualification that prepares healthcare professionals to teach and train others. This book is an introductory guide to the PGCME, covering the basic skills and knowledge you need to know, using the best available techniques to engage your learning. The author has used AI to generate and refine the content of the book, sharing insights and experiences with the reader along the way. This makes the book more than just a textbook; it's an experiment in using AI to learn. Whether you're new to the PGCME, teaching it, or simply want to understand how AI can boost learning, this book is an essential resource.

The main part of the book consists of the dialogue between physicist Otto Rössler, and artist and AI researcher Bill Seaman with the commentaries disclosing information perspective by information scientist Mark Burgin and Bill Seaman. In this dialogue, Rössler and Seaman discuss concepts surrounding Rössler's major research over his lifetime. Additionally, each research topic is linked to the set of papers and books published by Rössler and other related collaborative researchers. The goal is to delineate an intellectual directory for future researchers. The discussed topics being transdisciplinary in nature cross many fields in science and technology. A comprehensive historical bibliography is also included. The work explores many fields germane to theoretical science as Rössler was often quite early in developing these fields and interacting with many famous scientists. This work pertains to information theory, which has often been left out of the historical literature.Burgin as an expert in information theory is providing an information perspective on this dialogue adding historical discussion and relevant scientific and mathematical underpinnings of the discussed ideas. His observations are complemented by Seaman, who presents the synthesis of artistic and scientific outlook.Addendum contains articles describing Rössler's relationships to colleagues from multiple fields, a parable by Rössler and papers related to Rössler's research and theoretical models of processes in the universe.

"Hypernumbers and Extrafunctions" presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions  in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.

Set theory has become one of the most respected fields in mathematics due to the situation in which sets are used to build mathematical structures, pervading the whole of modern mathematics, and objects. This book presents and discusses research in the study of set theory, as well as their role and place in mathematics.

Presents an examination of the theory of super-recursive algorithms and its ramifications for the computer industry, networks, artificial intelligence, embedded systems, and the Internet. This book demonstrates how these algorithms are more appropriate as mathematical models for modern computers.

Computers, their software and their networks are among the most complicated systems of our time. Science is the only efficient tool for dealing with this overwhelming complexity. One of the methodologies developed in science is the axiomatic approach. This book developes an axiomatic approach in computer science.