The Resource Roads to infinity : the mathematics of truth and proof, John Stillwell
Roads to infinity : the mathematics of truth and proof, John Stillwell
Resource Information
The item Roads to infinity : the mathematics of truth and proof, John Stillwell represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.This item is available to borrow from 1 library branch.
Resource Information
The item Roads to infinity : the mathematics of truth and proof, John Stillwell represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.
This item is available to borrow from 1 library branch.
 Summary

 Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics.From publisher description
 "This sequel to the author's Yearning for the Impossible provides a readable survey of logicians' efforts to explicate the notions of truth, proof and undecidability, including the quest to find examples of ǹatural' undecidable statements. Leavened with historical details, it focuses on the role of infinitary considerations in the development of modern mathematics, with particular attention to the undervalued contributions of Emil Post and Gerhard Gentzen."John W. Dawson, Jr., author of Logical Dilemmas: The Life and Work of Kurt Godel 
 "Stillwell has provided an accessible, scholarly treatment of all the foundational studies today's wellrounded professional mathematician ought to know, and has managed to do so in just over 200 pages. And that includes all the relevant history. I highly recommend it."Keith Devlin, Stanford University, author of The Millennium Problems and coauthor of The Computer as Crucible: An Introduction to Experimental Mathematics 
 "Professor Stillwell ... succeeds, in every topic treated, in bringing a fresh eye to questions even mathematicians might think have been mined in the past to boring exhaustion [and] shows there is still a lot of gold to be found, if one only thinks about things in a new way. Stillwell brings new, unorthodox insights to his writing that will stimulate readers (from high schoolers to emeritus professors) to think about old topics in new, nonstale ways."SIAM Review 
 "Stillwell weaves historical details into his writing seamlessly, helping to give the reader the true feeling that mathematics is more than just a bunch of people playing games with symbols, but rather a rich and rewarding intellectual endeavor important to the human enterprise."MAA Reviews 
 While many popular books have been written on the advances in our understanding of infinity, sparked by the set theory of Georg Cantor in the 1870s and incompleteness theorems of Kurt Godel in the 1930s, such books generally dwell on a single aspect of either set theory or logic. The aim of this book is to explain the whole, in which set theory interacts with logic, and both begin to affect mainstream mathematics (the latter being quite a recent development, not yet given much space in popular accounts). 
 In Roads to Infinity, awardwinning author John Stillwell explores the consequences of accepting infinity, which are rich and surprising. The reader needs very little background beyond high school mathematics, but should have a willingness to grapple with alien ideas. Stillwell's style eases the reader into the technicalities of set theory and logic by tracing a single thread in each chapter, beginning with a natural mathematical question and following a sequence of historic responses to that question. Each response typically leads to new questions, and from them new concepts and theorems emerge. At the end of each chapter a section called "Historical Background" situates the thread in a bigger picture of mathematics and its history. 
 By following this path, key ideas are presented first, then revisited and reinforced by showing a wider view. Some readers, however, may be impatient to get to the core theorems and will skip the historical background sections, at least at first reading. Others, in search of a big picture from the beginning, may begin by reading the historical background and then come back to fill in details. Book Jacket
 Language
 eng
 Label
 Roads to infinity : the mathematics of truth and proof
 Title
 Roads to infinity
 Title remainder
 the mathematics of truth and proof
 Statement of responsibility
 John Stillwell
 Language
 eng
 Summary

 Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics.From publisher description
 "This sequel to the author's Yearning for the Impossible provides a readable survey of logicians' efforts to explicate the notions of truth, proof and undecidability, including the quest to find examples of ǹatural' undecidable statements. Leavened with historical details, it focuses on the role of infinitary considerations in the development of modern mathematics, with particular attention to the undervalued contributions of Emil Post and Gerhard Gentzen."John W. Dawson, Jr., author of Logical Dilemmas: The Life and Work of Kurt Godel 
 "Stillwell has provided an accessible, scholarly treatment of all the foundational studies today's wellrounded professional mathematician ought to know, and has managed to do so in just over 200 pages. And that includes all the relevant history. I highly recommend it."Keith Devlin, Stanford University, author of The Millennium Problems and coauthor of The Computer as Crucible: An Introduction to Experimental Mathematics 
 "Professor Stillwell ... succeeds, in every topic treated, in bringing a fresh eye to questions even mathematicians might think have been mined in the past to boring exhaustion [and] shows there is still a lot of gold to be found, if one only thinks about things in a new way. Stillwell brings new, unorthodox insights to his writing that will stimulate readers (from high schoolers to emeritus professors) to think about old topics in new, nonstale ways."SIAM Review 
 "Stillwell weaves historical details into his writing seamlessly, helping to give the reader the true feeling that mathematics is more than just a bunch of people playing games with symbols, but rather a rich and rewarding intellectual endeavor important to the human enterprise."MAA Reviews 
 While many popular books have been written on the advances in our understanding of infinity, sparked by the set theory of Georg Cantor in the 1870s and incompleteness theorems of Kurt Godel in the 1930s, such books generally dwell on a single aspect of either set theory or logic. The aim of this book is to explain the whole, in which set theory interacts with logic, and both begin to affect mainstream mathematics (the latter being quite a recent development, not yet given much space in popular accounts). 
 In Roads to Infinity, awardwinning author John Stillwell explores the consequences of accepting infinity, which are rich and surprising. The reader needs very little background beyond high school mathematics, but should have a willingness to grapple with alien ideas. Stillwell's style eases the reader into the technicalities of set theory and logic by tracing a single thread in each chapter, beginning with a natural mathematical question and following a sequence of historic responses to that question. Each response typically leads to new questions, and from them new concepts and theorems emerge. At the end of each chapter a section called "Historical Background" situates the thread in a bigger picture of mathematics and its history. 
 By following this path, key ideas are presented first, then revisited and reinforced by showing a wider view. Some readers, however, may be impatient to get to the core theorems and will skip the historical background sections, at least at first reading. Others, in search of a big picture from the beginning, may begin by reading the historical background and then come back to fill in details. Book Jacket
 Cataloging source
 DLC
 http://library.link/vocab/creatorName
 Stillwell, John
 Dewey number
 511.3/22
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA248
 LC item number
 .S778 2010
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/subjectName

 Set theory
 Infinite
 Logic, Symbolic and mathematical
 Label
 Roads to infinity : the mathematics of truth and proof, John Stillwell
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 460058722
 Dimensions
 24 cm
 Extent
 xi, 203 pages
 Isbn
 9781568814667
 Isbn Type
 (alk. paper)
 Lccn
 2010014077
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (OCoLC)460058722
 Label
 Roads to infinity : the mathematics of truth and proof, John Stillwell
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 460058722
 Dimensions
 24 cm
 Extent
 xi, 203 pages
 Isbn
 9781568814667
 Isbn Type
 (alk. paper)
 Lccn
 2010014077
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (OCoLC)460058722
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.mst.edu/portal/Roadstoinfinitythemathematicsoftruthand/06NGCiCcdw8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.mst.edu/portal/Roadstoinfinitythemathematicsoftruthand/06NGCiCcdw8/">Roads to infinity : the mathematics of truth and proof, John Stillwell</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.mst.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.mst.edu/">Missouri University of Science & Technology Library</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Roads to infinity : the mathematics of truth and proof, John Stillwell
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.mst.edu/portal/Roadstoinfinitythemathematicsoftruthand/06NGCiCcdw8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.mst.edu/portal/Roadstoinfinitythemathematicsoftruthand/06NGCiCcdw8/">Roads to infinity : the mathematics of truth and proof, John Stillwell</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.mst.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.mst.edu/">Missouri University of Science & Technology Library</a></span></span></span></span></div>