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Bronshtein and Semendyayev

(Redirected from A Guide Book to Mathematics)

Bronshtein and Semendyayev (often just Bronshtein or Bronstein,[4][3][5] sometimes BS) is the informal name of a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas originally compiled by the Russian mathematician Ilya Nikolaevich Bronshtein and engineer Konstantin Adolfovic Semendyayev.

Handbook of Mathematics
Bronshtein and Semendyayev, 13th Russian edition by Nauka (Наука), 1986
AuthorIlya Nikolaevich Bronshtein, Konstantin Adolfovic Semendyayev, et al.
LanguageRussian,[1] German,[2] Polish,[2] Hungarian,[2] French, Slovenian,[2] Croatian,[2] Serbian,[2] English,[1][2] Japanese,[1] Spanish, Chinese[2]
GenreMath
Publication date
1945[3][4]
Publication placeRussia, Germany

The work was first published in 1945 in Russia[4][3] and soon became a "standard" and frequently used guide for scientists, engineers, and technical university students. Over the decades, high popularity and a string of translations, extensions, re-translations and major revisions by various editors led to a complex international publishing history centered around the significantly expanded German version. Legal hurdles following the fall of the Iron Curtain caused the development to split into several independent branches maintained by different publishers and editors to the effect that there are now two considerably different publications associated with the original title – and both of them are available in several languages.

With some slight variations, the English version of the book was originally named A Guide-Book to Mathematics, but changed its name to Handbook of Mathematics. This name is still maintained up to the present by one of the branches. The other line is meanwhile named Users' Guide to Mathematics to help avoid confusion.

Overview

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Bronshtein and Semendyayev is a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas based on the Russian book Справочник по математике для инженеров и учащихся втузов (Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov, literally: "Handbook of mathematics for engineers and students of technical universities") compiled by the Russian mathematician Ilya Nikolaevich Bronshtein (Илья Николаевич Бронштейн)[nb 1] and engineer Konstantin Adolfovic Semendyayev (Константин Адольфович Семендяев).[4][nb 2]

The scope is the concise discussion of all major fields of applied mathematics by definitions, tables and examples with a focus on practicability and with limited formal rigour.[6][7] The work also contains a comprehensive list of analytically solvable integrals, that is, those integrals which can be described in closed form with antiderivatives.

History

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With Dmitrii Abramovich Raikov, Bronshtein authored a Russian handbook on elementary mathematics, mechanics and physics (Справочник по елементарнои математике, механике и физике), which was published in 1943.[8]

Around the same time in 1939/1940, Bronshtein, together with Semendyayev, also wrote their Russian handbook of mathematics for engineers and students of technical universities.[4] Among other sources this work was influenced by the 1936 Russian translation of the 1931 edition of the much older German Hütte - Des Ingenieurs Taschenbuch.[9][6][3] Hot lead typesetting had already started when the Siege of Leningrad prohibited further development and the print matrices were relocated.[4] After the war, they were considered lost, but could be found again years later, so that the first edition of Справочник по математике для инженеров и учащихся втузов could finally be published in 1945.[4][3]

The expanded German translation Taschenbuch der Mathematik (literally: "Pocketbook of mathematics") by Viktor Ziegler[4][3][nb 3] was first published in 1958 by B. G. Teubner in Leipzig.[4][1][3][10] It was honoured as "Schönstes Buch [de]" ("Most beautiful book") of the year 1958.[11][4][12]

Based on the German translation, an English translation became available as well under the title A Guide-Book to Mathematics in 1964, first by Pergamon Press and The Macmillan Company, later by Springer Verlag and Verlag Harri Deutsch.

In 1966, it became apparent that the title needed considerable updates to meet new requirements.[4] The original authors felt too old to continue the work and the Russian publisher Nauka (Наука) seemed to have had lost interest in the further development as well for some while.[4][3] Therefore, in 1970, a consortium of East-German mathematicians were contracted by Teubner Verlag to start to expand and revise the work.[4][3] This was coordinated by Viktor Ziegler,[nb 3] Dorothea Ziegler[nb 4] and Günter Grosche[nb 5] (University of Leipzig).[4][1] While Semendyayev contributed some work,[3] he did not want some other new chapters to be included in the manuscript in 1976, therefore they had to be split out into a new volume II.[4] Finally, after almost a decade of work, the major new revision could be published in 1979, legally as a cooperation of Teubner and Nauka.[4][3]

The reworked two-volume German edition was well received and again became a "standard" in higher mathematics education in Germany.[4][10] This led to a string of high-volume revisions[4][3][13] and translations into Russian,[1] English and Japanese[1] to meet the international demand. The English version was published by Van Nostrand Reinhold Company and Verlag Harri Deutsch as Handbook of Mathematics.

A decade later, the German 'Wende' and the later reunification led to considerable changes in the publishing environment in Germany between 1989 and 1991.[14][15][16][17][18] The East-German publisher Teubner Leipzig was integrated into the West-German publisher Teubner Stuttgart.[19][10] These changes put an end to the cooperation of the East-German Teubner Verlag with the West-German Verlag Harri Deutsch, who had been licensing this and other titles for distribution in Germany and Switzerland,[3][10][nb 6] a business model no longer working in a free market. Licensing issues caused the development to split into two independent branches by the two publishing houses:

Consequently, Verlag Harri Deutsch contracted Gerhard Musiol [de][nb 7] and Heiner Mühlig[nb 8] to start afresh and translate[3] the last non-Teubner influenced version (officially the latest revision (1977)[20] of the third Russian edition (1953),[20] which is actually the eleventh Russian edition (1967)) into German for a major rework of Taschenbuch der Mathematik as a single-volume title.[3] This was first published in 1992/1993. When Verlag Harri Deutsch closed its business two decades later, Europa-Lehrmittel took over in 2013. They continue to maintain this work up to the present (2020).[21][22] The new English translation (now by Springer Verlag) is still called Handbook of Mathematics.

In a parallel development, Eberhard Zeidler,[nb 9] who had contributed to the Grosche and Ziegler editions already, became editor for the continuation of the latest existing German edition by Teubner (1990),[3] the version which had previously also been distributed by Verlag Harri Deutsch, and updated it significantly to become the Teubner-Taschenbuch der Mathematik[13][1] (literally: "Teubner pocketbook of mathematics") for Teubner.[5] This was first published in 1995/1996 – still as a two-volume work. The work was continued by Vieweg+Teubner Verlag after the merger with Vieweg Verlag [de] in 2003. When Vieweg+Teubner was bought by Springer and renamed Springer Vieweg Verlag, several new chapters were added and some more advanced contents stripped out for the single-volume Springer-Taschenbuch der Mathematik (literally: "Springer pocketbook of mathematics") in 2012/2013.[3] This is now accompanied by a completely reworked and considerably expanded four-volume series named Springer-Handbuch der Mathematik (literally: "Springer handbook of mathematics") by Zeidler also based on the former Bronshtein and Semendyayev.[1][3][5] So far, this latest revision of the alternative development branch isn't available in English, but volume I of the former Teubner-Taschenbuch der Mathematik has been translated and published by Oxford University Press as Oxford Users' Guide to Mathematics already.[1][5]

Editions

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1945–1978: Bronshtein and Semendyayev editions

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Russian editions (1945–1977, 1998–2009)

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Authors: Bronshtein, Ilya Nikolaevich (Бронштейн, Илья Николаевич); Semendyayev, Konstantin Adolfovic (Семендяев, Константин Адольфович).[4]

  • Nauka (Наука) Moscow Sprawotschnik po matematike dlja inschenerow i utschaschtschichsja wtusow Справочник по математике для инженеров и учащихся втузов:
    • 1st edition, 1945 (556 pages, print run of 50 000):[7][4][3]
    • 2nd edition, 1948 (556 pages, print run of 83 000 units):[3]
    • 3rd revised edition, 1953 (chapter IV by Shura-Bura, Mikhail Romanovich [ru] (Шура-Бура, Михаил Романович) rewritten and chapters 8–10 added):[3][20]
    • 4th edition, 1954: (Gostekhizdat)
    • 5th edition, 1955
    • 6th edition, 1956 (ii+608 pages):[4][3]
    • 7th edition, 1957 (609 pages)[23]
    • 8th edition, 1959
    • 9th edition, 1962, Gosudarstvennoe Izdatel'stvo Fiziko-Matematicheskoy Literatury (Государственное издательство физико-математической литературы) (Fizmatgiz / Физматгиз).
    • 10th edition, 1964 (614 pages): ISBN 5-458-31226-0, 978-5-458-31226-4 (reprint 2013, paperback, Book on Demand Ltd.)
    • 11th edition, 1967 (608 pages + 1 inlet, last Russian edition of this series, as Nauka published in a print run of 100 000 units a translation of Mathematical Handbook for Scientists and Engineers by Granino and Theresa M. Korn instead in 1968)[4][3]
    • 1977 (end of production?)[20]
See also: Subsequent Russian editions
  • Nauka (Наука) / Fizmatlit (Физматлит) Справочник по математике для инженеров и учащихся втузов
  • Lan (Лань) Sprawotschnik po matematike dlja inschenerow i utschaschtschichsja wtusow Справочник по математике для инженеров и учащихся втузов:

German editions (1958–1978)

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Authors: Bronshtein, Ilya Nikolaevich; Semendyayev, Konstantin Adolfovic; Miller, Maximilian.[nb 11]
Translator: Ziegler, Viktor.[4][13][nb 3]

  • BSB B. G. Teubner Verlagsgesellschaft Taschenbuch der Mathematik:[4][13]
    • 1st expanded edition, 1958 (xii+548 pages + 1 inlet sheet, based on 4th or 6th Russian edition, ca. 1954, with a chapter by Miller added)[4][3][10][nb 11]
    • 2nd edition, 1959 (xii+548 pages + 1 inlet sheet):[4][3]
    • 3rd further expanded edition, 1960 (xiii+584 pages + 1 inlet sheet, with another chapter by Miller added):[4][3][nb 11]
    • 1st edition, 1961 (xiii+584 pages + 1 inlet sheet):[24][10]
    • 2nd edition, 1961 (xiii+584 pages + 1 inlet sheet):[10]
    • 2nd edition, 1962 (xiii+584 pages + 1 inlet sheet):[10]
    • 3rd edition, 1962 (xiii+584 pages):[10]
    • 4th edition, 1964 (xiii+584 pages):[10]
    • ? edition, 1965 (xiii+584 pages + 1 inlet sheet):[10]
    • 5th edition, 1965 (xiii+584 pages + 1 inlet sheet):[10][nb 6]
    • 6th unchanged edition, 1st printing, 1963 (xiii+584 pages): (soft plastic cover)[10]
    • 6th edition, 2nd printing, 1965 (xiii+584 pages): (soft plastic cover)[10]
    • 6th edition, 1966 (xiii+585 pages + 1 inlet sheet): (soft plastic cover)[10]
    • 6th edition, 1966 (xiii+584 pages + 1 inlet sheet):[10][nb 6]
    • 7th reviewed and corrected edition, 1967 (xiii+585 pages + 1 inlet sheet):[10]
    • 8th edition, 1967 (xiii+585 pages + 1 inlet sheet): (soft plastic cover)[10]
    • 8th unchanged edition, 1967 (xiii+585 pages): (soft plastic cover)[10]
    • 8th edition, 1968 [1967] (xiii+585 pages + 1 inlet sheet):[10]
    • 9th edition, 1969 (xiii+585 pages + 1 inlet sheet):[10]
    • 10th edition, 1969 (xiii+585 pages + 1 inlet sheet): (soft plastic cover)[10]
    • 10th edition, 1969 (xiii+585 pages + 1 inlet sheet): (soft plastic cover)
    • 10th edition, 1970 (xiii+585 pages + 1 inlet sheet):
    • 11th edition, 1971 (xiii+585 pages + 2 inlet sheets):
    • 12th edition, 1973 (xiii+585 pages + 1 inlet sheet)
    • 12th edition, 1973 (xiii+585 pages + 2 inlet sheets):
    • 13th edition, 1973 (xiii+585 pages + 2 inlet sheets): ISBN 3-87144-016-7, 978-3-87144-016-8
    • 14th edition, 1974
    • 15th edition, 1975 (xiii+585 pages + 2 inlet sheets)
    • 15th edition, 1975 (xiii+585 pages + 2 inlet sheets): ISBN 3-87144-016-7, 978-3-87144-016-8
    • 16th edition, 1976 (xiii+585 pages + 2 inlet sheets)
    • 16th edition, 1976 (xiii+585 pages + 2 inlet sheets): ISBN 3-87144-016-7, 978-3-87144-016-8
    • 17th edition, 1977 (xiii+585 pages + 2 inlet sheets):
    • 17th edition, 1977 (xiii+585 pages + 2 inlet sheets): ISBN 3-87144-016-7, 978-3-87144-016-8
    • 18th edition, 1978 (xiii+585 pages)[4][1][3]
See also: Subsequent German editions

Polish editions (1959–2019)

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  • Poradnik encyklopedyczny matematyka
    • 1959 (696 pages)
  • Państwowe Wydawnictwo Naukowe (PWN), Warsaw: Matematyka Poradnik encyklopedyczny
    • 1968
    • 1973
    • 1986
    • 1996
    • 1997
    • 2004
  • Wydawnictwo Naukowe PWN, Warsaw: Matematyka poradnik encyklopedyczny
See also: Subsequent Polish editions

Hungarian editions (1963–1987)

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Translator: György, Bizám

See also: Subsequent Hungarian editions

French editions (1963–1990)

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Translator: Lefort, Henri

  • Edition Eyrolles [fr], Paris: aide-mémoire de mathématiques : à l'usage des ingénieurs et des élèves des grandes écoles[nb 12]
    • 1st edition, based on 8th Russian edition (935 pages + inlet "parties proportionnelles"), 1963
    • 2nd edition, 1967
    • 1976
    • 9th edition, 1990 (935 pages)

Slovenian editions (1963–1994)

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Book Matematični priročnik, 4th reprint, 1975
 
Page in Matematični priročnik, 4th reprint, 1975
 
Book Matematični priročnik, 5th reprint, 1978

Translator: Žabkar, Albin [sl]

See also: Subsequent Slovenian editions

Yugoslav (Bosnian-Croatian-Serbian language) editions (1964–1975)

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Editor: Blanuša, Danilo.
Translators: Vistrička, Zvonko; Uremović, Ivan

  • Tehnička knjiga, Zagreb Matematički priručnik za inženjere i studente:
    • 1st edition, 1964 (695 pages, based on 9th Russian edition, 1962)
    • 1975 (696 pages)
See also: Subsequent Croatian and Serbian editions

English editions (1964–1973, 2013)

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Translators: Jaworowski, Jan W.; Bleicher, Michael N.

See also: Subsequent English editions

Spanish editions (1971–1988, 2001–2004)

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Editor: Aparicio Bernardo, Emiliano.
Translator: Harding Rojas, Inés.

  • Cultura popular, Mexico Manual de matemáticas para ingenieros y estudiantes
    • 1st edition, 1971 (696 pages)
  • Editorial MIR, Moscow Manual de Matemáticas para ingenieros y estudiantes (based on Russian edition, 1973):
  • Rubiños-1860, S.A., Madrid / Editorial MIR, Moscow Manual de Matemáticas Para Ingenieros y Estudiantes:
  • Quinto Sol Manual de Matemáticas para ingenieros y estudiantes:

1979–1991: Grosche and Ziegler editions

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German editions (1979–1991)

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Books Volume I 19th edition (1979), Volume II 3rd edition (1984), Volume II 7th edition (1995)

Editors: Grosche, Günter;[nb 5] Ziegler, Viktor;[nb 3] Ziegler, Dorothea.[nb 4]
Authors: Beckmann, Peter [de]; Belger, Martin; Benker, Hans; Denkmann, Norbert; Deweß, Monika; Erfurth, Horst; Gentemann, Helmut; Göthner, Peter; Gottwald, Siegfried; Grosche, Günter; Hilbig, Harald; Hofmann, Reinhard; Kästner, Herbert [de]; Purkert, Walter; vom Scheidt, Jürgen [de]; Semendjajew, Konstantin Adolfowitsch; Vettermann, Theodor; Wünsch, Volkmar; Zeidler, Eberhard.[4][13]

See also: Subsequent German editions

Editors: Grosche, Günter; Ziegler, Viktor; Ziegler, Dorothea.
Authors: Bär, Gunter; Deweß, Günter; Deweß, Monika; Gerber, Siegmar [de]; Göhde, Dietrich; Jentsch, Lothar; Miller, Maximilian; Piehler, Joachim; Zeidler, Eberhard.[13]

See also: Subsequent German editions

Russian editions (1980–1986)

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Editors: Grosche, Günter; Ziegler, Viktor; Ziegler, Dorothea.

  • Nauka (Наука) / Tec-Theor-Lit Spravočnik po matematike: dlja inženerov i učaščichsja vtuzov:
    • 12th completely revised edition, 1980 (retranslation from 19th German edition)[3]
    • 12th edition, 1981 (718 pages, retranslation from 19th German edition, 1979)[1]
  • Nauka (Наука), Moscow[3] / GFML (ГФМЛ) Sprawotschnik po matematike dlja inschenerow i utschaschtschichsja wtusow Справочник по математике для инженеров и учащихся втузов:
See also: Subsequent Russian editions

English editions (1985, 1998)

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Editor: Beckmann, Peter [de].
Translator: Hirsch, Kurt August

See also: Subsequent English editions

Japanese editions (1985–1987)

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Translators: Miyamoto, Toshio (宮本 敏雄); Matsuda, Nobuyuki (松田 信行).

1995–2013: Zeidler editions

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German editions (1995–2013)

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Editor (part I): Zeidler, Eberhard.[nb 9]
Authors (part I): Hackbusch, Wolfgang; Schwarz, Hans Rudolf; Zeidler, Eberhard.[3][13]

Editors (part II): Grosche, Günter; Ziegler, Viktor; Ziegler, Dorothea; Zeidler, Eberhard.
Authors (part II): Claus, Volker [de]; Deweß, Günter; Deweß, Monika; Diekert, Volker; Fuchssteiner, Benno; Gottwald, Siegfried; Gündel, Susanne; Hoschek, Josef; Olderog, Ernst-Rüdiger; Richter, Michael M.; Schenke, Michael; Widmayer, Peter; Zeidler, Eberhard.[3][13]

Editors: Zeidler, Eberhard.
Authors: Hackbusch, Wolfgang; Hromkovič, Juraj; Luderer, Bernd [de]; Schwarz, Hans Rudolf; Blath, Jochen; Schied, Alexander; Dempe, Stephan; Wanka, Gert [de]; Gottwald, Siegfried; Zeidler, Eberhard.

Editors: Zeidler, Eberhard.
Authors: Hackbusch, Wolfgang; Hromkovič, Juraj; Luderer, Bernd [de]; Schwarz, Hans Rudolf; Blath, Jochen; Schied, Alexander; Dempe, Stephan; Wanka, Gert [de]; Gottwald, Siegfried; Zeidler, Eberhard.

See also: Alternative German branch

English editions (2004–2013)

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Editor: Zeidler, Eberhard.
Authors: Hackbusch, Wolfgang; Schwarz, Hans Rudolf; Zeidler, Eberhard.
Translator: Hunt, Bruce.

See also: Alternative English branch

Chinese edition (2012)

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Editor: Zeidler, Eberhard (埃伯哈德·蔡德勒)
Translator: Li Wenlin (李文林)

See also: Alternative Chinese branch

1992–2020: Musiol and Mühlig editions

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German editions (1992–2020)

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Editors: Musiol, Gerhard [de];[nb 7] Mühlig, Heiner.[20][nb 8]
Authors: Baumann, Ulrike; Brunner, Jürgen; Flach, Günter [de]; Fleischer, Norbert Mozesovich (Флайшер, Норберт Мозесович); Grauel, Adolf; Reif, Roland; Reitmann, Volker (Райтманн, Фолькер); Steinert, I.; Marsolek, Lothar; Musiol, Gerhard [de]; Mühlig, Heiner; Nickel, Heinz; Weber, Matthias; Ziesche, Paul [de].[20]

Editors: Musiol, Gerhard [de];[nb 7] Mühlig, Heiner.[nb 8]
Authors: Baumann, Ulrike; Bernstein, Swanhild; Brand, Joachim; Brunner, Jürgen; Buchleitner, Andreas (CD-ROM only); Flach, Günter [de]; Fleischer, Norbert Mozesovich (Флайшер, Норберт Мозесович); Grauel, Adolf; Reif, Roland; Reitmann, Volker (Райтманн, Фолькер); Rumpf, Benno (CD-ROM only); Steinert, I.; Tiersch, Markus (CD-ROM only); Marsolek, Lothar; Mulansky, Bernd; Musiol, Gerhard [de]; Mühlig, Heiner; Nickel, Heinz; Weber, Matthias; Wellens, Thomas (CD-ROM only); Ziesche, Paul [de].

See also: Alternative German branch

Slovenian editions (1997–2020)

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Contributors: Barbič, Janez; Dolinar, Gregor; Jurčič-Zlobec, Borut; Mramor Kosta, Neža.
Translator: Barbič, Janez.

Hungarian editions (2000–2009)

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English editions (2002–2015)

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Editors: Musiol, Gerhard [de];[nb 7]Mühlig, Heiner.[nb 8]
Authors: Baumann, Ulrike; Brunner, Jürgen; Flach, Günter [de]; Fleischer, Norbert Mozesovich (Флайшер, Норберт Мозесович); Grauel, Adolf; Reif, Roland; Reitmann, Volker (Райтманн, Фолькер); Steinert, I.; Marsolek, Lothar; Musiol, Gerhard [de]; Mühlig, Heiner; Nickel, Heinz; Weber, Matthias; Ziesche, Paul [de].
Translator: Szép, Gabriella.

Editors: Musiol, Gerhard [de];[nb 7] Mühlig, Heiner.[nb 8]
Authors: Baumann, Ulrike; Bernstein, Swanhild; Brand, Joachim; Brunner, Jürgen; Buchleitner, Andreas (CD-ROM only); Flach, Günter [de]; Fleischer, Norbert Mozesovich (Флайшер, Норберт Мозесович); Grauel, Adolf; Reif, Roland; Reitmann, Volker (Райтманн, Фолькер); Rumpf, Benno (CD-ROM only); Steinert, I.; Tiersch, Markus (CD-ROM only); Tóth, János; Marsolek, Lothar; Mulansky, Bernd; Musiol, Gerhard [de]; Mühlig, Heiner; Nickel, Heinz; Weber, Matthias; Wellens, Thomas (CD-ROM only); Ziesche, Paul [de].

See also: Alternative English branch

Croatian edition (2004)

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Translator: Uremović, Ivan

Serbian edition (2004)

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Translators: Šućur, Miljenko; Valčić Trkulja, Milena.

Polish editions (2007–2020)

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  • Wydawnictwo Naukowe PWN, Warsaw: Nowoczesne kompendium matematyki

Chinese edition (2020)

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Editors: Bronstein (布龙施泰因), Semendyayev (谢缅佳耶夫), Musiol (穆西奥尔), Mühlig (米利希)
Translators: Li Wenlin (李文林) et al.

See also: Alternative Chinese branch

Bronshtein-integrability

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Due to Bronshtein and Semendyayev containing a comprehensive table of analytically solvable integrals, integrals are sometimes referred to as being "Bronshtein-integrable" in German universities if they can be looked up in the book (in playful analogy to terms like Riemann-integrability and Lebesgue-integrability).[36][37][38][39][40]

See also

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Notes

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  1. ^ Ilya Nikolaevich Bronshtein (Илья Николаевич Бронштейн) (1903–1976, GND 104989742, 1089147996) worked on the state's technical university MAMI in Moscow, History of chair of mathematics at MAMI, in Russian
  2. ^ Konstantin Adolfovic Semendyayev (Константин Адольфович Семендяев) (*1908-12-09, Simferopol to †1988-11-15, GND 104989750) worked in the department of applied mathematics of the Steklov Institute in Moscow. He carried out pioneering work in the area of numerical weather forecasting in Russia. Russian biography: [1][2][3][4]
  3. ^ a b c d Viktor Ziegler (1922-02-10, Kurschani to 1980-10-06, Leipzig, Germany). German mathematician and lecturer. [5]
  4. ^ a b Dorothea Ziegler née Hüttner (1924-06-26, Leipzig to 2013-01-18, Frauwalde), Germany. German lecturer. [6] [7]
  5. ^ a b Günter Grosche (–1997?), GND 1014419204, MGP-ID 151792, MR author ID 264328, Leipzig, Germany. [8][9][10]
  6. ^ a b c According to DNB-IDN 572534310, 572534353 the distribution license for Verlag Harri Deutsch was for the Federal Republic of Germany (FRG) including Berlin (West), as well as for Switzerland, but not for Austria and other German-speaking regions. According to Hans-Joachim Girlich and Anna-Maria Seemann, Edition Leipzig was responsible for distribution to Austria.
  7. ^ a b c d e Gerhard Musiol [de] (*1930-11-26, Deutzen, Germany) Dresden, Germany. GND 106735462, 160023831. German physicist. [11][12]
  8. ^ a b c d e Heiner Mühlig (1933–) Burgstädt, Germany. Dresden, Germany. GND 106922890, 1025708008. German numerical mathematician. [13]
  9. ^ a b Eberhard Zeidler (*1940-10-06 to †2016-11-18) Leipzig, Germany. GND 121295869, 1090654693.[14][15][16]
  10. ^ a b c The 13th Russian edition was published in 1986 (based on the 12th Russian edition as of 1980, which in turn was a retranslation from the 19th German edition by Grosche and Ziegler in 1979). The 15th Russian edition (which was a reprint of the 11th genuinely Russian edition (and non-Teubner influenced), originally published in 1967) was published in 1998. So far, a 14th Russian edition based on either of these two development branches could not be identified and is likely to not have existed.
  11. ^ a b c Maximilian Miller [de] (1903-11-05, Lenggries, Germany to 1980-01-16, Dresden, Germany), GND 118733966).
  12. ^ Besides the translation of the work of I. N. Bronstejn and K. A. Szemengyajev, there are several other French books titled Aide-mémoire de mathématiques as well.
  13. ^ a b Springer-Handbuch der Mathematik I includes chapters 0–1 of Springer-Taschenbuch der Mathematik plus additional material.
  14. ^ a b Springer-Handbuch der Mathematik II includes chapters 2–4 of Springer-Taschenbuch der Mathematik plus additional material.
  15. ^ a b Springer-Handbuch der Mathematik III includes chapters 5–9 of Springer-Taschenbuch der Mathematik plus additional material.
  16. ^ a b Springer-Handbuch der Mathematik IV chapters 10–19 include additional material not covered by Springer-Taschenbuch der Mathematik at all.
  17. ^ Besides the translation of the work of I. N. Bronstejn, K. A. Szemengyajev, G. Musiol and H. Mühlig, there are several other Hungarian books titled Matematikai kézikönyv as well, including an unrelated work by Merta Ildikó and a translation of Granino and Theresa Korn's work named Matematikai kézikönyv műszakiaknak, which served as kind of a predecessor on the Hungarian market.

References

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  1. ^ a b c d e f g h i j k l m n o p q r Zeidler, Eberhard; Schwarz, Hans Rudolf; Hackbusch, Wolfgang; Luderer, Bernd [in German]; Blath, Jochen; Schied, Alexander; Dempe, Stephan; Wanka, Gert; Hromkovič, Juraj; Gottwald, Siegfried (2013) [2012]. Zeidler, Eberhard (ed.). Springer-Handbuch der Mathematik I (in German). Vol. I (1 ed.). Berlin / Heidelberg, Germany: Springer Spektrum, Springer Fachmedien Wiesbaden. p. vii. doi:10.1007/978-3-658-00285-5. ISBN 978-3-658-00284-8. ISBN 3-658-00284-0. […] Das "Springer-Handbuch der Mathematik" knüpft an eine lange Tradition an. Das "Taschenbuch der Mathematik" von I. N. Bronstein und K. A. Semendjajew wurde von Dr. Viktor Ziegler aus dem Russischen ins Deutsche übersetzt. Es erschien 1958 im Verlag B. G. Teubner in Leipzig, und bis zum Jahre 1978 lagen bereits 18 Auflagen vor. Unter der Herausgabe von Dr. Günter Grosche und Dr. Viktor Ziegler und unter wesentlicher redaktioneller Mitarbeit von Frau Dorothea Ziegler erschien 1979 die völlig überarbeitete 19. Auflage, an der Wissenschaftler der Leipziger Universität und anderer Hochschulen des mitteldeutschen Raumes mitwirkten. [Bis 1995 erschienen sieben weitere Auflagen.] Diese Neubearbeitung wurde ins Russische übersetzt und erschien 1981 im Verlag für Technisch-Theoretische Literatur in Moskau. Ferner wurde eine englische´und eine japanische Übersetzung publiziert. Motiviert durch die stürmische Entwicklung der Mathematik und ihrer Anwendungen erschien in den Jahren 1995 und 1996 ein völlig neuverfasstes, zweibändiges "Teubner-Taschenbuch der Mathematik" im Verlag B. G. Teubner Stuttgart und Leipzig. [Die englische Übersetzung des ersten Bandes erschien 2003 im Verlag Oxford University Press, New York, als "Oxford Users' Guide to Mathematics".] Das daraus entstandene vorliegende "Springer-Handbuch der Mathematik" enthält zwei völlig neu geschriebene Kapitel über Wirtschafts- und Finanzmathematik sowie über Algorithmik und Informatik. […] (xii+635 pages)
  2. ^ a b c d e f g h i j k l m "2015/2016 Catalogue English version" (PDF). Haan-Gruiten, Germany: Verlag Europa-Lehrmittel Nourney, Vollmer GmbH & Co. KG. 2016-03-31. pp. preface, 43. Archived (PDF) from the original on 2016-04-04. Retrieved 2016-04-04. Taschenbuch der Mathematik (Bronstein); Pocket Book of Mathematics; 9th ed, 1280 pp, softcover; Europa-No. 56702; Language: German; Translations available in: Chinese, Croatian, English, Hungarian, Polish, Serbian, Slovenian.
  3. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao Girlich, Hans-Joachim [in German] (March 2014). "Von Pascals Repertorium zum Springer-Taschenbuch der Mathematik – über eine mathematische Bestsellerserie" [From Pascal's finding aid to Springer's pocketbook of mathematics – about a bestseller series in mathematics] (PDF) (in German) (preprint ed.). Leipzig, Germany: University of Leipzig, Mathematisches Institut. DNB-IDN 1052022731. Archived (PDF) from the original on 2016-04-06. Retrieved 2016-04-06.
  4. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah Ziegler, Dorothea (2002-02-21). "Der "Bronstein"". Archiv der Stiftung Benedictus Gotthelf Teubner, Leipzig (in German). Frauwalde, Germany. Archived from the original on 2016-03-25. Retrieved 2016-03-25.
  5. ^ a b c d Jost, Jürgen (2017-11-30). "Eberhard Zeidler 1940–2016". Obituary. Jahresbericht der Deutschen Mathematiker-Vereinigung. 2018 (3 #120). Springer: 221–228. doi:10.1365/s13291-017-0175-4. Archived from the original on 2022-01-16. Retrieved 2022-01-16. p. 223: […] He also took over the classical "Taschenbuch der Mathematik", which had been founded by I.N. Bronstein and K.A. Semendjaew in the Soviet Union. A German translation was published in the GDR by Teubner, with a licensed edition also in West Germany. Originally, this book, known as the "Bronstein", was a basic and widely used reference work for mathematical formulas, but Eberhard Zeidler transformed it over the years into a compendium of modern mathematics, with the help of several collaborators […]. A first translation into English appeared at Oxford University Press in 2004, as "Oxford users' guide to mathematics". Subsequent stages then saw the "Taschenbuch der Mathematik" as well as the 4-volume "Handbuch der Mathematik", published by Springer. — His various books were so successful and popular that most of them saw several editions in close succession. […] [17]
  6. ^ a b Bronshtein (Бронштейн), Ilya Nikolaevich (Илья Николаевич); Semendyayev (Семендяев), Konstantin Adolfovic (Константин Адольфович) (1948). Sprawotschnik po matematike dlja inschenerow i utschaschtschichsja wtusow Справочник по математике для инженеров и учащихся втузов [Handbook of mathematics for engineers and students of technical universities] (in Russian) (2 ed.). Moscow / Leningrad: Nauka (Наука). p. 530. p. foreword of 1st edition: Задача, которая стояла перед нами — дать в небольшом по объёму справочнике основные сведения по математике, необходимые в учебной и практической работе инженерам и студентам втузов,— была чрезвычайно трудной. Стремясь к краткости изложения, мы всё же пытались сделать справочник доступным, удобным для пользования и, по возможности, математически строгим (в той мере, в которой эту строгость следует предъявлять к инженерам).
  7. ^ a b Efimov (Ефимов), Nikolai Vladimirovich (Николай Владимирович) (1947). И. Н. Бронштейн и К. А. Семендяев, “Справочник по математике для инженеров и учащихся втузов” (рецензия) [I.  N. Bronshtein, K.  A. Semendyaev, "Handbook of mathematics for engineers and students of higher technical schools" (review)]. Criticism and bibliography. Uspekhi Matematicheskikh Nauk Успехи математических наук (УМН) (review) (in Russian). 2 (1(17)): 236–237. Mi umn6932. Archived from the original on 2020-12-04. Retrieved 2021-12-30. [18]
  8. ^ Bronshtein (Бронштейн), Ilya Nikolaevich (Илья Николаевич); Raikov (Райков), Dmitrii Abramovich (Дмитрий Абрамович) (1943). Spravochnik po elementarnoi matematike, mekhanike i fizike Справочник по елементарнои математике, механике и физике [Handbook of elementary mathematics, mechanics and physics] (in Russian). Moscow: Tekhizdat (Техиздат). OCLC 641446206. (200 pages)
  9. ^ Hütte: Справочник для инженеров, техников и студентов (in Russian). Vol. 1 (16 ed.). Объединённое научно-техническое издательство (ОНТИ). 1936. (NB. This is a Russian translation of the 26th German edition of Hütte - Des Ingenieurs Taschenbuch as of 1931.)
  10. ^ a b c d e f g h i j k l m n o p q r s t u v Seemann, Anna-Maria (2018-12-18) [2017]. Parallelverlage im geteilten Deutschland - Entstehung, Beziehungen und Strategien am Beispiel ausgewählter Wissenschaftsverlage [Parallel publishers in the divided Germany - Emergence, relationships and strategies on the example of selected scientific publishers]. Schriftmedien – Kommunikations- und buchwissenschaftliche Perspektiven (in German). Vol. 6 (1 ed.). Berlin, Germany: Walter de Gruyter GmbH. pp. 390, 409–410 [409]. ISBN 978-3-11-054091-8. ISSN 2364-9771. Retrieved 2022-02-04. pp. 409–410: […] 1961 verlegte Edition Leipzig das Taschenbuch der Mathematik von Ilja Bronstein und Konstantin Semendjajew in deutscher Übersetzung. Das Buch war in erster Auflage 1958 bei B. G. Teubner in Leipzig herausgekommen. Es erschien 1961 gleichzeitig bei Harri Deutsch in Frankfurt am Main als Lizenzausgabe der Edition Leipzig. Davon erhielt der B. G. Teubner Verlag in Stuttgart im November 1960 Kenntnis. Darauf angesprochen, "tat [Deutsch] so, als ob er darüber, daß das Taschenbuch der Mathematik in der 1. und 2. Auflage in unserem Leipziger Verlag erschienen ist, nicht näher unterrichtet sei." Das sich bald zum Standardwerk entwickelnde Buch wurden in den folgenden Jahrzehnten weiterhin von Teubner in Leipzig und Deutsch in Frankfurt am Main herausgebracht, wobei die Ausgaben verschiedene Bearbeiter hatten und sich inzwischen deutlich unterschieden. Edition Leipzig publizierte bis 1969 ebenfalls weitere Auflagen, die allerdings nur für den Vertrieb in Österreich bestimmt waren. Spätere Verträge zwischen Teubner Leipzig und Harri Deutsch weisen eine Teilung der Vertriebsgebiete auf. Harri Deutsch durfte Mitdrucktitel in Westdeutschland, West-Berlin und der Schweiz vertreiben, alle übrigen Länder waren Teubner vorbehalten. [...] Die Edition Leipzig vertrieb [...] die Bücher der Parallelverlage teilweise nicht selbst in der Bundesrepublik, sondern vergab Lizenzen an westliche Verlage [...] Wie der Fall von Harri Deutsch zeigt, war es diesen leichter möglich, sich ahnungslos zu geben, als dies der DDR-Verlag vermocht hätte, der die Lizenz direkt von einem der Parallelverlage erhalten hatte. [...] (x+595+5 pages) (NB. This work is based on the thesis of the author at Friedrich-Alexander-Universität Erlangen-Nürnberg in 2016.)
  11. ^ Spiegel Deutscher Buchkunst 1958 - Die schönsten Bücher des Jahres 1958 (in German). Börsenverein der Deutschen Buchhändler zu Leipzig [de]. 1958. 45: I. N. Bronstein und K. A. Semendjajew: Taschenbuch der Mathematik für Ingenieure und Studenten der Technischen Hochschulen. B.G. Teubner Verlagsgesellschaft, Leipzig [19]
  12. ^ Eisenburger, Peter (2019-04-06) [2015-01-21]. "Schönste Bücher der DDR" (in German). Archived from the original on 2022-02-08. Retrieved 2022-02-08.
  13. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa Weiß, Jürgen (2002-03-21). "Teubner-Einzeltitel" [Individual Teubner titles] (in German). Leipzig, Germany: Edition am Gutenbergplatz Leipzig (EAGLE). Archived from the original on 2016-03-31. Retrieved 2016-03-31. (NB. Some of the total page numbers have been found not to be accurate.)
  14. ^ de Frondeville, Elisabeth (1992). Die Auswirkungen der deutschen Wiedervereinigung auf die Buchverlage der ehemaligen DDR (1.1.1990–1.9.1991) [Consequences of the German reunification for the publishing houses of the former GDR (1990-01-01 to 1991-09-01)] (Thesis) (in German) (1 ed.). Paris, France: Université de Paris VIII, Département d'Etudes Germaniques. OCLC 489866216. SUDOC 011493771. DNB-IDN 1045409294. Retrieved 2016-03-31. (NB. This publication is the author's master thesis under Le Rider, Jacques [fr] and Mortier, Jean at the Université de Paris VIII in 1992.)
  15. ^ Rumland, Marie-Kristin (1993) [1992]. Veränderungen im Verlagswesen und Buchhandel der ehemaligen DDR 1989–1991 [Changes in the publishing and bookselling business of the former GDR 1989–1991]. Deutsches Bucharchiv München (Thesis). Buchwissenschaftliche Beiträge aus dem Deutschen Bucharchiv München (in German). Vol. 44. Foreword by Swierk, Alfred Gerard [de] (1 ed.). Wiesbaden, Germany: Otto Harrassowitz Verlag. ISBN 3-447-03419-X. ISSN 0724-7001. OCLC 30837656. ISBN 978-3-447-03419-7. DNB-IDN 931326907. Retrieved 2016-03-28. (NB. This book is based on the author's magister thesis (OCLC 758411591) at the Friedrich-Alexander-Universität Erlangen-Nürnberg in 1992. According to Christoph Links this work contains a number of factual errors.)
  16. ^ Elteste, Babette (1994). Die Neugestaltung des Verlagswesens in den Neuen Bundesländern [Reshaping of the publishing business in the new federal states of Germany] (Thesis) (in German) (1 ed.). Munich, Germany. OCLC 724083472. DNB-IDN 1000126986. (NB. This publication is the author's diplom thesis at the Ludwig-Maximilians-Universität München.)
  17. ^ Reich, Regine (1997-06-08) [1996]. Zur Konkurrenzfähigkeit ostdeutscher Buchverlage auf dem gesamtdeutschen Markt: Eine Untersuchung der Verlage Aufbau, Reclam Leipzig und Fachbuchverlag [On the competitiveness of East-German book publishing houses on the total German market: Research on publishing houses Aufbau, Reclam Leipzig and Fachbuchverlag] (Thesis) (in German) (1 ed.). diplom.de [de] (Diplomica Verlag [de]) / Bod Third Party Titles. ISBN 3-8324-0065-6. ISBN 978-3-8324-0065-1 (diplom.de). ISBN 3-8386-0065-7 / ISBN 978-3-8386-0065-9 (Bod Third Party Titles). DNB-IDN 1051604672. Retrieved 2016-03-31. [20] (NB. This book is based on the author's magister thesis at Leuphana Universität Lüneburg in 1996.)
  18. ^ Krämer, Heinrich (2003-03-17) [2003-02-21]. "Die Wiedervereinigung der Verlagsfirmen B. G. Teubner in Stuttgart und Leipzig 1991: "Sonderlösung Teubner"" [The reunification of the publishers B. G. Teubner in Stuttgart and Leipzig 1991: "Special solution Teubner"]. Archiv der Stiftung Benedictus Gotthelf Teubner, Leipzig (in German). Schwieberdingen, Germany. Archived from the original on 2016-04-03. Retrieved 2016-04-02.
  19. ^ a b c d e f g h i Bronstein, Ilja Nikolajewitsch (Бронштейн, Илья Николаевич); Semendjajew, Konstantin Adolfowitsch (Семендяев, Константин Адольфович); Baumann, Ulrike; Brunner, Jürgen; Flach, Günter [in German]; Fleischer, Norbert Mozesovich (Флайшер, Норберт Мозесович); Grauel, Adolf; Reif, Roland; Reitmann, Volker (Райтманн, Фолькер); Steinert, I.; Marsolek, Lothar; Musiol, Gerhard [in German]; Mühlig, Heiner; Nickel, Heinz; Weber, Matthias; Ziesche, Paul [in German] (1993). "Foreword". In Musiol, Gerhard [in German]; Mühlig, Heiner (eds.). Taschenbuch der Mathematik [Pocketbook of mathematics] (in German) (1st completely revised ed.). Verlag Harri Deutsch. ISBN 3-8171-2001-X. ISBN 978-3-8171-2001-7. [...] Warum also eine Neubearbeitung auf der Basis der letzten russischen Ausgabe(∗), die bis 1977 erschien? Abgesehen von verlagsrechtlichen Gründen wird mit der vorliegenden Neubearbeitung vor allem das Ziel verfolgt, dem "Bronstein" einen zeitgerechten praxisnahen Bezug zu geben, wie ihn zahlreiche befragte Nutzer sich wünschen. Besonderer Dank gilt dem russischen Originalverlag FIZMATLIT und den Rechtsnachfolgern der Originalautoren dafür, dass sie die Zustimmung zur notwendigen Anpassung an die heutigen Ansprüche des Nutzerkreises und der damit verbundenen freien Überarbeitung gaben. [...] (*)Fußnote: Der Neuübersetzung des russischsprachigen Originals liegt die 3. Auflage (Moskau 1953) zu Grunde.{{cite book}}: CS1 maint: multiple names: authors list (link)
  20. ^ "Verlag Harri Deutsch gibt aktives Verlagsgeschäft auf / Europa Lehrmittel übernimmt" [Verlag Harri Deutsch stops active publishing business / Europa Lehrmittel takes over]. BuchMarkt (in German). BuchMarkt Verlag K. Werner GmbH. 2013-05-17. Archived from the original on 2016-03-28. Retrieved 2016-03-28.
  21. ^ "Harri Deutsch Verlag beendet Verlagsgeschäft – Europa-Lehrmittel übernimmt Verlagsrechte" [Verlag Harri Deutsch stops publishing activities – Europa-Lehrmittel takes over publishing rights]. Börsenblatt (in German). Börsenverein des Deutschen Buchhandels. 2013-05-21. Archived from the original on 2016-03-25. Retrieved 2016-03-25.
  22. ^ a b c Steen, Lynn Arthur (October 1986). "Central section: General, L**. Handbook of Mathematics". Telegraphic Reviews – The American Mathematical Monthly. 93 (8). Mathematical Association of America: C65–C72. JSTOR 2322325. Handbook of Mathematics. I. N. Bronshtein, K. A. Semendyayev. Transl: K. A. Hirsch. Van Nostrand Reinhold, 1985, xv+973 pp, $37.95 (P). ISBN 0-442-21171-6. English translation of a 1978 East German revision of a 1957 Russian handbook.
  23. ^ Giesecke, Martin [in German] (1960-11-08). "Nr. 80". 22199 B.G. Teubner Verlag, Stuttgart (Notice) – via Sächsisches Staatsarchiv Leipzig (SStAL) [de]. (NB. Company archive of B. G. Teubner Verlag, Stuttgart.)
  24. ^ Ostebee, Arnold (December 1997). "Reference, P, L. Handbook of Mathematics". Telegraphic Reviews – The American Mathematical Monthly. 104 (10). Mathematical Association of America: 992–997. JSTOR 2974497. Handbook of Mathematics. I. N. Bronshtein, K. A. Semendyayev. Transl: K. A. Hirsch. Springer-Verlag, 1997, xv+973 pp, $57. ISBN 3-540-62130-X Reprint of the revised third edition (TR, October 1986).
  25. ^ Handbook of Mathematics (PDF) (reprint of the 3rd ed.). Springer-Verlag Berlin Heidelberg GmbH. January 1997 [December 1978]. p. preface. Archived (PDF) from the original on 2016-04-04. Retrieved 2016-04-04. Preface of the Reprint of the 3rd edition. The book is in such high demand that the publisher decided to reprint the 3rd edition published in 1997. January 1997 Springer-Verlag
  26. ^ "Taschenbuch der Mathematik, 1998" [Pocketbook of mathematics] (in German). Verlag Harri Deutsch. 1999-06-09. ISBN 3-8171-2004-4. Archived from the original on 1999-11-10.
  27. ^ "Taschenbuch der Mathematik mit Multiplattform-CD-ROM, 1998" [Pocketbook of mathematics with multi-platform CD-ROM] (in German). Verlag Harri Deutsch. 1999-06-09. ISBN 3-8171-2014-1. Archived from the original on 1999-08-23.
  28. ^ "Taschenbuch der Mathematik" [Pocketbook of mathematics] (in German). Verlag Harri Deutsch. 2000-10-05. ISBN 3-8171-2005-2. Archived from the original on 2000-10-21.
  29. ^ "Taschenbuch der Mathematik mit Multiplattform-CD-ROM, 2000" [Pocketbook of mathematics with multi-platform CD-ROM] (in German). Verlag Harri Deutsch. 2000-10-05. ISBN 3-8171-2015-X. Archived from the original on 2000-10-21.
  30. ^ "Taschenbuch der Mathematik, 2005" [Pocketbook of mathematics] (in German). Verlag Harri Deutsch. 2005-09-30. ISBN 3-8171-2006-0. Archived from the original on 2005-10-14.
  31. ^ "Taschenbuch der Mathematik mit Multiplattform-CD-ROM, 2005" [Pocketbook of mathematics with multi-platform CD-ROM] (in German). Verlag Harri Deutsch. 2005-08-01. ISBN 3-8171-2016-8. Archived from the original on 2005-10-14.
  32. ^ "Taschenbuch der Mathematik, 2008" [Pocketbook of mathematics] (in German). Verlag Harri Deutsch. 2008-07-25. ISBN 978-3-8171-2007-9. Archived from the original on 2009-09-05.
  33. ^ "Taschenbuch der Mathematik mit Multiplattform-CD-ROM, 2008" [Pocketbook of mathematics with multi-platform CD-ROM] (in German). Verlag Harri Deutsch. 2008-07-25. ISBN 978-3-8171-2017-8. Archived from the original on 2009-11-25.
  34. ^ "Fachwissen für die Hochschule – Gesamtverzeichnis – Edition Harri Deutsch – Mathematik, Physik, Chemie, Biologie, Technik Sachbuch" (PDF) (Catalog) (in German). Europa-Lehrmittel. 2015-04-30. Archived (PDF) from the original on 2016-03-27.
  35. ^ Paul, Dietrich (2011). Was ist an Mathematik schon lustig? Ein Lesebuch rund um Mathematik und Kabarett, Musik und Humor [What is funny about mathematics? A reading book about mathematics and cabaret, music and humour.] (in German) (1 ed.). Vieweg+Teubner Verlag. p. 32. doi:10.1007/978-3-8348-9852-4. ISBN 978-3-8348-0466-2. (xii+236 pages)
  36. ^ Rädler, Joachim (ed.). 0.1 Biophysics of Molecules - Exercise 5 (PDF) (Tutorial exercise). Biophysics of macromolecules (in German and English). University of Munich. p. 2. Archived (PDF) from the original on 2016-04-18. Retrieved 2020-06-27. (2 pages)
  37. ^ Beetz, Jürgen (2013). 1+1=10: Mathematik für Höhlenmenschen (in German). Berlin / Heidelberg, Germany: Springer Spektrum. p. 259. ISBN 978-3-8274-2927-8.
  38. ^ "[German] Bronstein-integrabel adj., a function whose integral can be found in a formulary". DoesNotTranslate. February 2016. Archived from the original on 2016-04-04. Retrieved 2016-04-04.
  39. ^ Heim, Sabine; Heim, Gunter. "Bronstein integrierbar". WH54-Fachwort-Lexikon Mathematik (in German). Mathe-AC Lernwerkstatt. Archived from the original on 2020-06-27. Retrieved 2020-04-20.
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