Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest...
Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the...
History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition--one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem....
History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the de...
The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric topology and is meant for the more advanced mathematician...
The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology, combinatorial...
In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields.
In the field...
In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously...
In 1974 the editors of the present volume published a well-received book entitled Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject...
In 1974 the editors of the present volume published a well-received book entitled Latin Squares and their Applications''. It included a list of 73 uns...
The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on:
- admissible or permissible inference rules
- the derivability of the admissible inference rules
- the structural completeness of logics
- the bases for admissible and valid inference rules.
There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered.
The book...
The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is fo...
Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the...
Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, inc...
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of...
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, ...
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are...
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating space...
This series aims to cover the major aspects of numerical analysis. The volume covers the techniques of scientific computing, numerical methods for solids and solution of equations in R.
This series aims to cover the major aspects of numerical analysis. The volume covers the techniques of scientific computing, numerical methods for sol...