"Theory of Recursive Functions and Effective Computability" by Hartley Rogers, Jr., published in 1957 by Stevens & Co., is a foundational text in the study of recursive functions and effective computability. The book provides a comprehensive exploration of the theoretical underpinnings of computation, focusing on the concepts of recursion and computability. It delves into the nature of algorithms, the definition of recursive functions, and the principles of effective computation. The work is structured to present the essential ideas of recursive function theory, including the notions of Turing machines, recursive sets, and the hierarchy of computable functions. Rogers' treatment is both rigorous and accessible, making it a key resource for students and researchers in computer science and mathematical logic. The book is divided into chapters that build upon each other, starting with the basic definitions and moving towards more complex topics such as the Church-Turing thesis, the classification of computable functions, and the limits of computation. It also discusses the relationship between recursive functions and other models of computation, such as the lambda calculus and the Post machine. The text is notable for its clarity and logical progression, which helps in understanding the deep connections between different models of computation. Overall, "Theory of Recursive Functions and Effective Computability" remains an important reference in the field, offering a thorough and systematic approach to the study of computability theory."Theory of Recursive Functions and Effective Computability" by Hartley Rogers, Jr., published in 1957 by Stevens & Co., is a foundational text in the study of recursive functions and effective computability. The book provides a comprehensive exploration of the theoretical underpinnings of computation, focusing on the concepts of recursion and computability. It delves into the nature of algorithms, the definition of recursive functions, and the principles of effective computation. The work is structured to present the essential ideas of recursive function theory, including the notions of Turing machines, recursive sets, and the hierarchy of computable functions. Rogers' treatment is both rigorous and accessible, making it a key resource for students and researchers in computer science and mathematical logic. The book is divided into chapters that build upon each other, starting with the basic definitions and moving towards more complex topics such as the Church-Turing thesis, the classification of computable functions, and the limits of computation. It also discusses the relationship between recursive functions and other models of computation, such as the lambda calculus and the Post machine. The text is notable for its clarity and logical progression, which helps in understanding the deep connections between different models of computation. Overall, "Theory of Recursive Functions and Effective Computability" remains an important reference in the field, offering a thorough and systematic approach to the study of computability theory.