Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
This book addresses major issues such as a growing world energy demand, environmental degradation due to anthropogenic greenhouse gas (GHG) emission, and risk management of disastrous events such as pandemics, abnormal climate, and earthquakes. Using cutting-edge analytical tools, particularly computable general equilibrium (CGE) modelling, the analyses are focused on a very wide range of policy-relevant economic questions for the Asia-Pacific region, especially for Japan, China, India, Vietnam, and smaller nations, including Brunei, Timor Leste, and Fiji. The first part considers (a) the effects of climate change on agriculture sectors, energy policies, and future GHG emission trends, (b) adaptation to climate changes in energy policy and its impacts on the economies, and (c) risk management of catastrophic events such as global pandemics. The second part examines (a) energy environmental issues, (b) economic impacts of natural disaster and depopulation, and (c) effects of informatics development on risk management, using CGE modelling and other methods in regional science fields. Contributors are internationally active leading CGE modellers and environmental economists. The book should be greatly beneficial for scholars and graduate students as well as policy makers who are interested in the economic effects and management of risks relating to climate change and disastrous events.
This collection of work reviews the results of using CGE models since the early 1970s, with an emphasis on models that encompass broad structural factors such as distribution of income and wealth, land tenancy relationships, foreign trade, production, markets, and control of the means of production that are fundamental to the behavior of developing economies. Economist Lance Taylor is an advocate of aggressive government management of developing economies. The models described in this book are are easy to set up and manipulate on microcomputers and should dominate the development debate. Taylor's detailed discussion of structuralist COE models is followed by contributions that take up their application in specific countries.This collection of work reviews the results of using CGE models since the early 1970s, with an emphasis on models that encompass broad structural factors such as distribution of income and wealth, land tenancy relationships, foreign trade, production, markets, and control of the means of production that are fundamental to the behavior of developing economies.Chapters explain the macro constraints on India's economic growth and describe Plan Austral and other heterodox shocks, describe the application of a structuralist model to Nicaragua, to Mexican food consumption policies, and to the food market in Colombia. They discuss a model with portfolio choice for Thailand, resource mobilization through administered prices, and conflicting claims and dynamic inflationary mechanisms in India, short-run energyeconomy interactions in Egypt, policy options for growth and the alleviation of poverty in Sri Lanka, currency devaluation in Mexico, and medium-term growth projections for Kuwait. The book concludes with a manual for a structuralist macro model program.
This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls. The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs. Contains software on CD ROM: The accompanying software demonstrates, through simulation and exercises, how each concept of calculus can be associated with a program for the 'ideal computer' Using this software readers will be able to write their own demonstration programs
