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Look Inside Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass

Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass

Part of Cambridge Library Collection - Mathematics

  • Date Published: October 2013
  • availability: Available
  • format: Paperback
  • isbn: 9781108059350


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About the Authors
  • Great mathematicians write for the future and Georg Friedrich Bernhard Riemann (1826–66) was one of the greatest mathematicians of all time. Edited by Heinrich Martin Weber, with assistance from Richard Dedekind, this edition of his collected works in German first appeared in 1876. Riemann's interests ranged from pure mathematics to mathematical physics. He wrote a short paper on number theory which provided the key to the prime number theorem, and his zeta hypothesis has given mathematicians the most famous of today's unsolved problems. Moreover, his famous 1854 lecture 'On the hypotheses which underlie geometry' set in motion studies which culminated in Einstein's general theory of relativity. Even Riemann's over-optimistic use of the Dirichlet principle to prove the conformal mapping theorem turned out to be immensely fruitful. The alert reader will further profit from finding here the seeds of modern distribution theory, algebraic topology and measure theory.

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    Product details

    • Date Published: October 2013
    • format: Paperback
    • isbn: 9781108059350
    • length: 540 pages
    • dimensions: 244 x 170 x 28 mm
    • weight: 0.85kg
    • contains: 5 b/w illus.
    • availability: Available
  • Table of Contents

    Part I:
    1. Grundlagen für eine allgemeine Theorie der Functioneneiner veränderlichen complexen Grösse
    2. Ueber die Gesetze der Vertheilung von Spannungselectricität in ponderablen Körpen
    3. Zur Theorie der Nobili'schen Farbenringe
    4. Beiträge zur Theorie der durch die Gauss'sche Reihe
    5. Selbstanzeige der vorstehenden Abhandlung
    6. Theorie der Abel'schen Functionen
    7. Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse
    8. Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite
    9. Selbstanzige der vorstehenden Abhandlung
    10. Ein Beitrag zu den Untersuchungen über die Bewegung eines flüssigen gleichartigen Ellipsoides
    11. Ueber das Verschwinden der Theta-Functionen
    Part 2:
    12. Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe
    13. Ueber die Hypothesen, welche der Geometrie zu Grunde liegen
    14. Ein Beitrag zur Electrodynamik
    15. Beweis des Satzes, dass eine einwerthige mehr als 2 n fach periodische Function von n Veränderlichen unmöglich ist
    16. Estratto di una lettera scritta in lingua italiana il di 21 gennaio 1864
    17. Ueber die Fläche vom kleinsten Inhalt bei gegebener Begrenzung
    18. Mechanik des Ohres
    Part III:
    19. Versuch einer allgemeinen Auffassung der Integration und Differentiation
    20. Neue Theorie des Rückstandes in electrischen Bindungsapparaten
    21. Zwei allgemeine Lehrsätze über äre Differentialgleichungen mit algebraischen Coefficienten
    22. Commentatio mathematica
    23. Sullo svolgimento del quoziente di due serie ipergeometriche in frazione continua infinita
    24. Ueber das Potential eines Ringes
    25. Gleichgewicht der Electricität auf Cylindern mit kreisförmigen Querschnitt und parallelen Axen
    26. Beispiele von Flächen kleinsten Inhalts bei gegebener Begrenzung
    27. Fragmente über die Grenzfälle der elliptischen Modulfunctionen
    28. Fragment aus der Analysis Situs
    29. Convergenz der p-fach unendlichen Theta-Reihe
    30. Zur Theorie der Abel'schen Functionen für den Fall p = 3
    Anhang: Fragmente philosophischen Inhalts
    Bernhard Riemann's Lebenslauf.

  • Author

    Bernhard Riemann


    Richard Dedekind

    Heinrich Martin Weber

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