Mathematics

The Porous Medium Equation: Mathematical Theory by Juan Luis Vazquez

Peter H. Kropholler, Ian J. Leary, “Geometric and Cohomological Group Theory”

Te Sun Han, Kingo Kobayashi, “Mathematics of Information and Coding”

Kurt Gödel, “On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Dover Books on Mathematics)”

The Porous Medium Equation: Mathematical Theory by Juan Luis Vazquez

English | 26 Oct. 2006 | ISBN: 0198569033 | 648 Pages | PDF | 11 MB

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.

Peter H. Kropholler, Ian J. Leary, “Geometric and Cohomological Group Theory”

2017 | ISBN-10: 131662322X | 276 pages | PDF | 3 MB

This volume provides state-of-the-art accounts of exciting recent developments in the rapidly-expanding fields of geometric and cohomological group theory. The research articles and surveys collected here demonstrate connections to such diverse areas as geometric and low-dimensional topology, analysis, homological algebra and logic. Topics include various constructions of Thompson-like groups, Wise’s theory of special cube complexes, groups with exotic homological properties, the Farrell-Jones assembly conjectures and new applications of Garside structures. Its mixture of surveys and research makes this book an excellent entry point for young researchers as well as a useful reference work for experts in the field. This is the proceedings of the 100th meeting of the London Mathematical Society series of Durham Symposia.

Te Sun Han, Kingo Kobayashi, “Mathematics of Information and Coding”

2001 | pages: 302 | ISBN: 0821805347 | PDF | 14,1 mb

This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the author describes universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent, but mathematically sound manner. The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.

Kurt Gödel, “On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Dover Books on Mathematics)”

ISBN: 0486669807 | 1992 | EPUB | 80 pages | 2 MB

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.

The present volume reprints the first English translation of Giidel’s far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.

This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

Advances in Two-Dimensional Homotopy and Combinatorial Group

2018 | ISBN: 1316600904 | English | 194 pages | PDF | 2 MB

This volume presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Building on the foundations laid a quarter of a century ago in the volume Two-dimensional Homotopy and Combinatorial Group Theory (LMS 197), the editors here bring together much remarkable progress that has been obtained in the intervening years. And while the fundamental open questions, such as the Andrews-Curtis Conjecture and the Whitehead asphericity problem remain to be (fully) solved, this book will provide both students and experts with an overview of the state of the art and work in progress. Ample references are included to the LMS 197 volume, as well as a comprehensive bibliography bringing matters entirely up to date.