Avoiding the cryptic terminology of proof as far as possible, this book starts at an elementary level and displays the connections between infinitary proof theory and generalized recursion theory, especially the theory of inductive definitions. It provides an introduction to ordinal arithmetic and to the Veblen hierarchy.
This monograph covers the theory of Dirichlet forms. It examines the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Levy processes and summarizes the model-theoretic genericity of hyperfinite stochastic processes theory.
Introduces 'second generation wavelets' and the lifting transform that can be used to apply the traditional benefits of wavelets into a wide range of new areas in signal processing, data processing and computer graphics. This book details the mathematical fundamentals of the lifting transform.
These collected papers of Ernst Zermelo (1871-1953) consist of two volumes. Volume I covers set theory, the foundations of mathematics, and pure mathematics. Volume II contains his work in the calculus of variations, applied mathematics, and physics.
The concept of each toopic has been developed from primary to end stage with numerical illustrations in simple and lucid manner The definition and theorems behind each concept are supported by solved examples for better understanding A set of problems is given at the end of each chapter
Hybrid Logic and its Proof-Theory demonstrates that hybrid-logical proof-theory remedies the lack of uniformity in ordinary modal-logical proof systems. Various versions and proof systems for hybrid logic are considered, providing a detailed overview of the topic.
Describes the concepts of category, functor, natural transformation, and duality. This book focuses on adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits.
This short guide to modern error analysis is primarily intended to be used in undergraduate laboratories in the physical sciences. No prior knowledge of statistics is assumed. The necessary concepts are introduced where needed and illustrated graphically. The book emphasises the use of computers for error calculations and data fitting.
Discrete mathematics has become popular in recent decades because of its applications to computer science. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasise concepts for computer science majors.
Features Game theory and voting power, Heuristic search techniques, Quadratic fields, Reliability, and Risk analysis and decision rules. This book also features a table of solutions to Pell's equation, a table of irreducible polynomials in Z2[x], an interpretation of powers of 10, and a collection of 'proofs without words'.
Scilab is a free open-source software package for scientific computation. This is the first book to focus on simulation and modeling, and to put a major emphasis on Scicos and discuss it in depth. This new edition includes expanded chapters and major rewrites.
Providing a reference for researchers and students, this volume presents the fundamental concepts of dual tableaux, and a wide scope of applications. These include logic methods used in mathematics and philosophy, as well as applied theories of computational logic.
Written by one of the world's leading popularizers of mathematics, this book is suitable for undergraduate students of mathematics. It offers an introductory chapter on the nature of mathematics, a chapter on complex numbers, and a discussion of formal symbolic logic. It helps the students to transitioning from calculus to higher mathematics.
Gives you 2, 000 problems in discrete mathematics. This guide helps you to master various types of problems you will face on your tests, from simple questions on set theory to complex Boolean algebra, logic gates, and the use of propositional calculus.
Winner of the 1983 National Book Award, The Mathematical Experience conveyed the power and beauty of its topic to a broad audience. The study version added exercises and other classroom aids. This softcover edition includes new epilogues by the original authors.
Focusing on the foundations, this volume explores both classical and constructive mathematics. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time both subtle and more differentiated.
Enables readers to prove hundreds of mathematical results. This title presents the formal development of natural numbers from axioms, which leads into set theory and transfinite induction. It covers Peano's axioms, weak and strong induction, double induction, infinite descent downward induction, and variants of these inductions.
Self-Field Theory (SFT) is a recent development that has evolved from the classical electromagnetics of the electron's self fields that were studied by Abraham and Lorentz in 1903-4. This book deals with the topic of Self-Field Theory (SFT), a new mathematical description of physics distinct from quantum field theory.
Educates by application and real-world examples. This book offers a supplement package, and delivers matchless flexibility to both traditional and modern practitioners. It abounds with helpful exercises, including Diagnostic Tests, which assure students of a firm grasp on textbook information before they move on to the following section.
Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This textbook looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory.