Classical Recursion Theory

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

This book presents and applies a framework for studying the complexity of algorithms. It is aimed at logicians, computer scientists, mathematicians and philosophers interested in the theory of computation and its foundations, and it is written at a level suitable for non-specialists. Part I provides an accessible introduction to abstract recursion theory and its connection with computability and complexity. This part is suitable for use as a textbook for an advanced undergraduate or graduate course: all the necessary elementary facts from logic, recursion theory, arithmetic and algebra are included. Part II develops and applies an extension of the homomorphism method due jointly to the author and Lou van den Dries for deriving lower complexity bounds for problems in number theory and algebra which (provably or plausibly) restrict all elementary algorithms from specified primitives. The book includes over 250 problems, from simple checks of the reader's understanding, to current open pr

The third volume in Leonard Susskind's one-of-a-kind physics series cracks open Einstein's special relativity and field theory In the first two books in his wildly popular The Theoretical Minimum seri

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This textbook introduces key ideas in sociological theory, with a focus on contemporary relevance and applicability. It explains theories and theorists of sociology’s classical age, including Émile

Social Theory provides a sophisticated yet highly accessible introduction to classical and contemporary social theories. The author’s concise presentation allows students and instructors to focus on c

A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the f

This volume focuses on the relevant general theory and presents some first applications, namely those based on classical shell theory. After a brief introduction, during which the history and state-of

Scott Appelrouth and Laura Edles' Classical and Contemporary Sociological Theory, 3rd edition is a hybrid text/reader that offers the best of both worlds for instructors and students. It incl

This book emphasizes three very important concepts: computability, as opposed to recursion or induction; classical computability, i.e., algorithmic functions on certain countable structures in the ori

The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical ph

First published in 1960, this seminal work illuminates the interrelations of the various approaches to the theory of economic growth. Professor Meade seeks to understand the factors which determine th

Explores the gamut of social theory Classical and Contemporary Social Theory: Investigation and Application, 1/e, is the most comprehensive, informative social theory book on the market. The

"This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classic

The sixth edition of Peter Kivisto’s popular anthology, Illuminating Social Life, continues to demonstrate to students how social theories can help them make sense of the swirling events and perplexin

The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight ne

This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in

This set contains the two authoritative textbooks Contemporary Sociological Theory, 3rd Edition and Classical Sociological Theory, 3rd Edition.The third edition of Contemporary Sociological Theory is

In Key Concepts in Classical Social Theory individual entries introduce, explain and contextualize the key topics within classical social theory. Definitions, summaries and key words are developed th

In Key Concepts in Classical Social Theory individual entries introduce, explain and contextualize the key topics within classical social theory. Definitions, summaries and key words are developed th

* Offers a rigorous mathematical treatment of mechanics as a text or reference* Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Eart

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introducti

This authoritative and reader-friendly anthology will help you think through some of humanity's most persistent questions regarding right and wrong, good and bad. ETHICAL THEORY: CLASSICAL AND CONTEMP

This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of math

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of math

This textbook is uniquely written with dual purpose. It covers core material in the foundations of computing for graduate students in computer science and also provides an introduction to some more a

This book is a complete account of the predicate transformation calculus semantics of sequential programs, including repetitions, recursive procedures, computational induction and unbounded nondeterminacy. Predicate transformation semantics are the best specification method for the development of correct and well-structured computer programs. The author develops this theory to a greater depth than has been achieved before, and describes it in a way that makes it readily compatible with programming rules for partial and total correctness of repetitions and recursive procedures, supplies new rules for proving incorrectness, and a stronger rule for proving that two programs satisfy the same specifications. Finally, the semantics are extended so that non-terminating programs can be specified as well. This will be essential reading for all computer scientists working in specification and verification of programs.

Based on the theme that the authors call "rediscovering the promise of sociology," CLASSICAL SOCIOLOGICAL THEORY covers the period from the early 19th century and the emergence of the distinct field o

Hurst (College of Wooster) explains to undergraduate students how classical social theories articulated a hundred years old can be applied to contemporary society. He discusses Karl Marx, Emile Durkhe

This text goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. This third revised edition features a new section on constants