| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910483767303321 |
|
|
Autore |
Dittrich Walter |
|
|
Titolo |
Reassessing Riemann's paper : on the number of primes less than a given magnitude / / Walter Dittrich |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham, Switzerland : , : Springer, , [2018] |
|
©2018 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[Second edition.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XI, 107 p. 18 illus., 10 illus. in color.) |
|
|
|
|
|
|
Collana |
|
SpringerBriefs in History of Science and Technology |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di contenuto |
|
Preface -- Introduction -- Short Biography of Bernhard Riemann (1826 – 1866) -- Towards Euler's Product Formula and Riemann’s Extension of the Zeta Function -- Prime Power Number Counting Function -- Riemann as an Expert in Fourier Transforms -- On the Way to Riemann’s Entire Function ζ(s) -- The Product Representation of ξ(s) and ζ(s) by Riemann (1859) -- Derivation of Von Mangoldt’s Formula for ψ(x) -- The Number of Roots in the Critical Strip -- Riemann’s Zeta Function Regularization -- ζ-Function Regularization of the Partition Function of the Harmonic Oscillator -- ζ-Function Regularization of the Partition Function of the Fermi Oscillator -- The Zeta-Function in Quantum Electrodynamics (QED) -- Summary of Euler-Riemann Formulae -- Appendix. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann’s only work on prime numbers, including ideas – new at the time – such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the |
|
|
|
|
|
|
|
|
|
|
|
|
|
application of Riemann’s zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book. |
|
|
|
|
|
|
2. |
Record Nr. |
UNINA9910971499903321 |
|
|
Autore |
Bok Derek Curtis |
|
|
Titolo |
Beyond the ivory tower : social responsibilities of the modern university / / Derek Bok |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cambridge, MA, : Harvard University Press, 1982 |
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
|
|
Edizione |
[1st ed.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (318 pages) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Education, Higher - Aims and objectives - United States |
Academic freedom - United States |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Bibliographic Level Mode of Issuance: Monograph |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Frontmatter -- Contents -- Acknowledgments -- Introduction -- Part I. Basic Academic Values -- 1. Academic Freedom -- 2. Institutional Autonomy and the Demands of the State -- 3. The Purposes of the University and Its Responsibilities to Society -- Part II. Academic Responses to Social Problems -- 4. Access to the University and the Problem of Racial Inequality -- 5. The Moral Development of Students -- 6. Academic Science and the Quest for Technological Innovation -- 7. The Social Responsibilities of Research -- 8. Technical Assistance Abroad -- Part III. Addressing Social Problems by Nonacademic Means -- 9. The University and the Local Community -- 10. Taking Political Positions -- 11. Accepting Gifts -- 12. Boycotts and Other Efforts to Avoid Outside Relationships -- Conclusion -- Index |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
Derek Bok examines the complex ethical and social issues facing modern universities today, and suggests approaches that will allow the academic institution both to serve society and to continue its primary |
|
|
|
|
|
|
|
|
|
|
mission of teaching and research. |
|
|
|
|
|
| |