the banach tarski paradox encyclopedia of mathematics and its applications

Download Book The Banach Tarski Paradox Encyclopedia Of Mathematics And Its Applications in PDF format. You can Read Online The Banach Tarski Paradox Encyclopedia Of Mathematics And Its Applications here in PDF, EPUB, Mobi or Docx formats.

The Banach Tarski Paradox

Author : Stan Wagon
ISBN : 0521457041
Genre : Mathematics
File Size : 51. 81 MB
Format : PDF, ePub, Mobi
Download : 525
Read : 1174

Get This Book


This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up to date proofs and discusses many unsolved problems.

The Banach Tarski Paradox

Author : Grzegorz Tomkowicz
ISBN : 9781107042599
Genre : Mathematics
File Size : 58. 52 MB
Format : PDF, ePub, Docs
Download : 191
Read : 470

Get This Book


The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.

Permanents

Author : Henryk Minc
ISBN : 0521302269
Genre : Mathematics
File Size : 34. 30 MB
Format : PDF, ePub
Download : 588
Read : 1296

Get This Book


The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
ISBN : 1447121732
Genre : Mathematics
File Size : 50. 51 MB
Format : PDF, ePub
Download : 720
Read : 1134

Get This Book


This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Combinatorial Group Theory And Applications To Geometry

Author : D.J. Collins
ISBN : 3540637044
Genre : Mathematics
File Size : 32. 8 MB
Format : PDF, Kindle
Download : 217
Read : 841

Get This Book


This book consists of two parts. The first part provides a comprehensive description of that part of group theory which has its roots in topology. The second more advanced part deals with recent work on groups relating to topological manifolds. It is a valuable guide to research in this field. The text contains numerous examples, sketches of proofs and open problems.

Model Theory

Author : Wilfrid Hodges
ISBN : 0521304423
Genre : Mathematics
File Size : 52. 65 MB
Format : PDF, ePub, Docs
Download : 112
Read : 341

Get This Book


Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.

The Joys Of Haar Measure

Author : Joe Diestel
ISBN : 9781470409357
Genre : Mathematics
File Size : 46. 31 MB
Format : PDF
Download : 772
Read : 1187

Get This Book


From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general. Presenting existence proofs in special cases, such as compact metrizable groups, highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject. After presenting the compact case, applications indicate how these tools can find use. The generalisation to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage's approach to the general problem of homogeneous action in the locally compact setting shows how Banach's approach and that of Cartan and Weil can be unified with good effect. Finally, the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated. The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables, although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.

Philosophy Of Mathematics

Author :
ISBN : 0080930581
Genre : Philosophy
File Size : 23. 58 MB
Format : PDF, Mobi
Download : 215
Read : 1168

Get This Book


One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Studia Universitatis Babe Bolyai

Author :
ISBN : UVA:X002005705
Genre : Mathematics
File Size : 23. 7 MB
Format : PDF
Download : 887
Read : 742

Get This Book



Mathematica In Action

Author : Stan Wagon
ISBN : 0387754776
Genre : Mathematics
File Size : 44. 78 MB
Format : PDF
Download : 551
Read : 549

Get This Book


Plenty of examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting. Emphasizes the breadth of Mathematica and the impressive results of combining techniques from different areas. Whenever possible, the book shows how Mathematica can be used to discover new things. Striking examples include the design of a road on which a square wheel bike can ride, the design of a drill that can drill square holes, and new and surprising formulas for p. Visualization is emphasized throughout, with finely crafted graphics in each chapter.

Top Download:

Best Books