The Mathematics Of Generalization
DOWNLOAD
Download The Mathematics Of Generalization PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Mathematics Of Generalization book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Mathematics Of Generalization
DOWNLOAD
Author : David. H Wolpert
language : en
Publisher: CRC Press
Release Date : 2018-03-05
The Mathematics Of Generalization written by David. H Wolpert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
This book provides different mathematical frameworks for addressing supervised learning. It is based on a workshop held under the auspices of the Center for Nonlinear Studies at Los Alamos and the Santa Fe Institute in the summer of 1992.
Approaches To Algebra
DOWNLOAD
Author : N. Bednarz
language : en
Publisher: Springer
Release Date : 1996-06-30
Approaches To Algebra written by N. Bednarz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-30 with Education categories.
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Mathematical Logic
DOWNLOAD
Author : J.D. Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Logic written by J.D. Monk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
Advanced Mathematical Thinking
DOWNLOAD
Author : David Tall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Advanced Mathematical Thinking written by David Tall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking – what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students – has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: • the nature of advanced mathematical thinking, • cognitive theory, and • reviews of the progress of cognitive research into different areas of advanced mathematics.
Conflicts Between Generalization Rigor And Intuition
DOWNLOAD
Author : Gert Schubring
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-10
Conflicts Between Generalization Rigor And Intuition written by Gert Schubring and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-10 with Mathematics categories.
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
Learning And Generalisation
DOWNLOAD
Author : Mathukumalli Vidyasagar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Learning And Generalisation written by Mathukumalli Vidyasagar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Technology & Engineering categories.
Learning and Generalization provides a formal mathematical theory addressing intuitive questions of the type: • How does a machine learn a concept on the basis of examples? • How can a neural network, after training, correctly predict the outcome of a previously unseen input? • How much training is required to achieve a given level of accuracy in the prediction? • How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite time? The second edition covers new areas including: • support vector machines; • fat-shattering dimensions and applications to neural network learning; • learning with dependent samples generated by a beta-mixing process; • connections between system identification and learning theory; • probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithms. It also contains solutions to some of the open problems posed in the first edition, while adding new open problems.
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models
DOWNLOAD
Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 2000-01-11
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-11 with Mathematics categories.
This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Differential Geometry
DOWNLOAD
Author : R.W. Sharpe
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-11-21
Differential Geometry written by R.W. Sharpe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-21 with Mathematics categories.
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Generalized Lie Theory In Mathematics Physics And Beyond
DOWNLOAD
Author : Sergei D. Silvestrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-18
Generalized Lie Theory In Mathematics Physics And Beyond written by Sergei D. Silvestrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-18 with Mathematics categories.
This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.
The Oxford Handbook Of Generality In Mathematics And The Sciences
DOWNLOAD
Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
This collection of original essays aims to inquire into the diversity of Generality. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts.