Douglas S. Bridges Luminita Simona Vita D. S. Bridges
This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text covers fundamental theory of the real line and metric spaces, focusing on locatedness in normed spaces and with associated results about operators and their adjoints on a Hilbert space. The first appendix gathers together some basic notions about sets and orders, the second gives the axioms for intuitionistic logic. No background in intuitionistic logic or constructive analysis is needed in order to read the book, but some familiarity with the...
This book is an introduction to constructive mathematics with an emphasis on techniques and results obtained in the last twenty years. The text cov...
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: AMathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used...
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: AMathematical Sketchboo...
The core of this book, Chapters 3 through 5, presents a course on metric, normed, andHilbertspacesatthesenior/graduatelevel. Themotivationfor each of these chapters is the generalisation of a particular attribute of the n Euclidean spaceR: in Chapter 3, that attribute isdistance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics, . . ., this part of the book contains many results and exercises that are seldom...
The core of this book, Chapters 3 through 5, presents a course on metric, normed, andHilbertspacesatthesenior/graduatelevel. Themotivationfor each of ...
This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop??'s school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop??'s s...
The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-based theory of proximity spaces provides some guidance for the theory of apartness, the notion of nearness/proximity does not embody enough algorithmic information for a deep constructive development. The use of constructive (intuitionistic) logic in this book requires much more technical ingenuity than one finds in classical proximity...
The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being...
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as...
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The aut...
