Diffusion, Quantum Theory, and Radically Elementary Mathematics
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| Title: | Diffusion, Quantum Theory, and Radically Elementary Mathematics |
|---|---|
| Description: | Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes. |
| Authors: | William G. Faris |
| Resource Type: | eBook. |
| Subjects: | Diffusion, Mathematical physics, Quantum theory |
| Categories: | MATHEMATICS / Geometry / Algebraic, SCIENCE / Physics / Quantum Theory, MATHEMATICS / Probability & Statistics / Stochastic Processes |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
|---|---|
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| Items | – Name: Title Label: Title Group: Ti Data: Diffusion, Quantum Theory, and Radically Elementary Mathematics – Name: Abstract Label: Description Group: Ab Data: Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22William+G%2E+Faris%22">William G. Faris</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Diffusion%22">Diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+physics%22">Mathematical physics</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+Algebraic%22">MATHEMATICS / Geometry / Algebraic</searchLink><br /><searchLink fieldCode="ZK" term="%22SCIENCE+%2F+Physics+%2F+Quantum+Theory%22">SCIENCE / Physics / Quantum Theory</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Probability+%26+Statistics+%2F+Stochastic+Processes%22">MATHEMATICS / Probability & Statistics / Stochastic Processes</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 530.15 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Diffusion Type: general – SubjectFull: Mathematical physics Type: general – SubjectFull: Quantum theory Type: general Titles: – TitleFull: Diffusion, Quantum Theory, and Radically Elementary Mathematics Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: William G. Faris – PersonEntity: Name: NameFull: William G. Faris IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2014 – D: 22 M: 09 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9780691125459 – Type: isbn-electronic Value: 9781400865253 Titles: – TitleFull: Diffusion, Quantum Theory, and Radically Elementary Mathematics Type: main |
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