Derivation And Computation

An introduction to simple type theory, containing 200 exercises with complete solutions.

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

This textbook gives a systematized and compact summary, providing the most essential types of modern models for languages and computation together with their properties and applications. Most of these models properly reflect and formalize current computational methods, based on parallelism, distribution and cooperation covered in this book. As a result, it allows the user to develop, study, and improve these methods very effectively. This textbook also represents the first systematic treatment of modern language models for computation. It covers all essential theoretical topics concerning them. From a practical viewpoint, it describes various concepts, methods, algorithms, techniques, and software units based upon these models. Based upon them, it describes several applications in biology, linguistics, and computer science. Advanced-level students studying computer science, mathematics, linguistics and biology will find this textbook a valuable resource. Theoreticians, practitioners and researchers working in today’s theory of computation and its applications will also find this book essential as a reference.

The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Derivation and Explanation in the Minimalist Program presents accessible, cutting edge research on an enduring and fundamental question confronting all linguistic inquiry – the respective roles of derivation and representation. Presents accessible, cutting edge research on the respective roles of derivation and representation in syntactic inquiry. Discusses a wide range of phenomena and also includes alternative, representational perspectives. Features papers by M. Brody, C. Collins, S. Epstein, J. Frampton, S. Gutmann, N. Hornstein, R. Kayne, H. Kitahara, J. McCloskey, N. Richards, D. Seely, E. Torrego, J. Uriagereka, C.J.W. Zwart.