An Invitation to Modern Number Theory:
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experime...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2021]
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| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext |
| Zusammenfassung: | In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 25. Feb 2021) |
| Beschreibung: | 1 online resource (528 pages) 20 line illus |
| ISBN: | 9780691215976 |
| DOI: | 10.1515/9780691215976 |
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| 520 | |a In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class | ||
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Datensatz im Suchindex
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| author | Miller, Steven J. Takloo-Bighash, Ramin |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:50:10Z |
| indexdate | 2024-07-10T09:05:21Z |
| institution | BVB |
| isbn | 9780691215976 |
| language | English |
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| spelling | Miller, Steven J. Verfasser aut An Invitation to Modern Number Theory Steven J. Miller, Ramin Takloo-Bighash Princeton, NJ Princeton University Press [2021] © 2006 1 online resource (528 pages) 20 line illus txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 25. Feb 2021) In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class In English MATHEMATICS / Number Theory bisacsh Number theory Takloo-Bighash, Ramin aut https://doi.org/10.1515/9780691215976 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Miller, Steven J. Takloo-Bighash, Ramin An Invitation to Modern Number Theory MATHEMATICS / Number Theory bisacsh Number theory |
| title | An Invitation to Modern Number Theory |
| title_auth | An Invitation to Modern Number Theory |
| title_exact_search | An Invitation to Modern Number Theory |
| title_exact_search_txtP | An Invitation to Modern Number Theory |
| title_full | An Invitation to Modern Number Theory Steven J. Miller, Ramin Takloo-Bighash |
| title_fullStr | An Invitation to Modern Number Theory Steven J. Miller, Ramin Takloo-Bighash |
| title_full_unstemmed | An Invitation to Modern Number Theory Steven J. Miller, Ramin Takloo-Bighash |
| title_short | An Invitation to Modern Number Theory |
| title_sort | an invitation to modern number theory |
| topic | MATHEMATICS / Number Theory bisacsh Number theory |
| topic_facet | MATHEMATICS / Number Theory Number theory |
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