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While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory
An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth
This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation - both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old
Introduces all major topics in nonlinear analysis and fixed point theory in a systematics way Discusses applications to a wide range of fields ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much
- Introduction. - Classes of Functions. - Fourier Series. - Fourier Transform. - Hilbert Transform. - Hardy Spaces and their Subspaces. - Hardy Inequalities. - Certain
The definitive introduction to game theory This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss
This open access textbook welcomes students into the fundamental theory of measure, integration, and real
This is the most accessible and wide-ranging introduction to critical theory currently available. Providing a comprehensive overview of the practice, role and importance of theory across the humanities and social sciences, the book not only maps a notoriously complex area, but it also enables the
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of
An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the
An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful
Giving an overview of the history of color theory from ancient and classical cultures to contemporary contexts, this book explores important critical principles and provides practical guidance on the use of color in art and design. Going beyond a simple recitation of what has historically been said
The book provides an introduction to major topics in macroeconomic theory and offers the readers three tools for comparing different models: a mathematical reformulation of Say's Law, the use of income velocity of circulation of money as a behavioural function in accordance with the Friedman
An analysis the Roman imperial succession and the failure to come up with an enduring, consistent system for selecting the next emperor with over 22 genealogical tables and 100 images illustrating the Emperors.John D Grainger analyses the Roman imperial succession, demonstrating that the empire
An Introduction to Real Estate Finance serves as the core of knowledge for a single-semester first course in real estate finance. Unlike other real estate finance textbooks, with their encyclopedic but often stale details, it combines a short traditional text with a living website. The book gives
A guide to economics, statistics and finance that explores the mathematical foundations underling econometric methods An Introduction to Econometric Theory offers a text to help in the mastery of the mathematics that underlie econometric methods and includes a detailed study of matrix algebra and
A clear and thorough introduction to meta-analysis, the process of synthesizing data from a series of separate studies. The first edition of this text was widely acclaimed for the clarity of the presentation, and quickly established itself as the definitive text in this field. The fully updated
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophyMathematics and Computation provides a broad, conceptual overview of computational complexity theory--the
A self-contained introduction to abstract interpretation-based static analysis, an essential resource for students, developers, and users.Static program analysis, or static analysis, aims to discover semantic properties of programs without running them. It plays an important role in all phases of
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the
An introduction to the theory and practice of optometry in one succinct volume. From the fundamental science of vision to clinical techniques and the management of common ocular conditions, this book encompasses the essence of contemporary optometric practice. Now in full colour and featuring over