Lothar Collatz

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Lothar Collatz
Lothar Collatz (Photo courtesy MFO)
Born(1910-07-06)July 6, 1910
Arnsberg, Westphalia, German Empire
DiedSeptember 26, 1990(1990-09-26) (aged 80)
Varna, Bulgaria
NationalityGerman
Scientific career
FieldsMathematics
Doctoral advisorAlfred Klose
Erhard Schmidt
Doctoral studentsFrank Natterer

Lothar Collatz (German: [ˈkɔlaʦ]; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia.

The 3x + 1 problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.

Collatz's 1957 paper with Ulrich Sinogowitz,[1] who had been killed in the bombing of Darmstadt in World War II,[2] founded the field of spectral graph theory.

Biography

Collatz studied at universities in Germany including the University of Berlin under Alfred Klose, receiving his doctorate in 1935 for a dissertation entitled Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen (The finite difference method with higher approximation for linear differential equations).

For his many contributions to the field, Collatz had many honors bestowed upon him in his lifetime, including:

He died unexpectedly from a heart attack in Varna, Bulgaria, while attending a mathematics conference.[3]

Selected works

  • Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen (= Schriften des mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin – Band 3/Heft 1), Leipzig 1935
  • Eigenwertprobleme und ihre numerische Behandlung. Leipzig 1945
  • Eigenwertaufgaben mit technischen Anwendungen. Leipzig 1949, 1963
  • Numerische Behandlung von Differentialgleichungen. Berlin 1951,[4] 1955[5] (Eng. trans. 1966)
  • Differentialgleichungen für Ingenieure. Stuttgart 1960
  • with Wolfgang Wetterling: Optimierungsaufgaben Berlin 1966, 1971 (Eng. trans. 1975)
  • Funktionalanalysis und Numerische Mathematik. Berlin 1964
  • Differentialgleichungen. Eine Einführung unter besonderer Berücksichtigung der Anwendungen. Stuttgart, Teubner Verlag, 1966, 7th edn. 1990
  • with Julius Albrecht: Aufgaben aus der angewandten Mathematik I. Gleichungen in einer und mehreren Variablen. Approximationen. Berlin 1972
  • Numerische Methoden der Approximationstheorie. vol. 2. Vortragsauszüge der Tagung über Numerische Methoden der Approximationstheorie vom 3.-9. Juni 1973 im Mathematischen Forschungsinstitut Oberwolfach, Stuttgart 1975
  • Approximationstheorie: Tschebyscheffsche Approximation und Anwendungen. Teubner 1973

Citations

  1. ^ Von Collatz, L. and Sinogowitz, U., 1957, December. Spektren endlicher grafen. In Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (vol. 21, no. 1, pp. 63–77). Springer-Verlag.
  2. ^ Mallion, R.B., 2005. An autobiographical account of chemical graph theory in the years surrounding the launch of MATCH: An Oxford participant's highly personal and parochial reminiscence about the period 1969–1976. Match-Communications In Mathematical And In Computer Chemistry, 53(1), pp. 15–52.
  3. ^ http://www.math.technion.ac.il/hat/people/obits/collatz.pdf
  4. ^ Milne, William Edmund (1953). "Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1951". Bull. Amer. Math. Soc. 59 (1): 94–96. doi:10.1090/s0002-9904-1953-09668-9.
  5. ^ Milne, William Edmund (1956). "Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1955". Bull. Amer. Math. Soc. 62 (1): 74. doi:10.1090/s0002-9904-1956-09990-2.

Sources

  • Lothar Collatz (July 6, 1910 – September 26, 1990), Journal of Approximation Theory, vol. 65, issue 1, April 1991, page II by Günter Meinardus and Günther Nürnberger
  • Collatz, Lothar (1942), "Einschließungssatz für die charakteristischen Zahlen von Matrize", Mathematische Zeitschrift, 48 (1): 221–226, doi:10.1007/BF01180013

Further reading

  • J Albrecht, P Hagedorn and W Velte, Lothar Collatz (German), Numerical treatment of eigenvalue problems, vol. 5, Oberwolfach, 1990 (Birkhäuser, Basel, 1991), viii–ix.
  • R Ansorge, Lothar Collatz (6 July 1910 – 26 September 1990) (German), Mitt. Ges. Angew. Math. Mech. No. 1 (1991), 4–9.
  • U Eckhardt, Der Einfluss von Lothar Collatz auf die angewandte Mathematik, Numerical mathematics, Sympos., Inst. Appl. Math., Univ. Hamburg, Hamburg, 1979 (Birkhäuser, Basel-Boston, Mass., 1979), 9–23.
  • L Elsner and K P Hadeler, Lothar Collatz – on the occasion of his 75th birthday, Linear Algebra Appl. 68 (1985), vi; 1–8.
  • R B Guenther, Obituary : Lothar Collatz, 1910–1990, Aequationes Mathematicae 43 (2–3) (1992), 117–119.
  • H Heinrich, Zum siebzigsten Geburtstag von Lothar Collatz, Z. Angew. Math. Mech. 60 (5) (1980), 274–275.
  • G Meinardus, G Nürnberger, Th Riessinger and G Walz, In memoriam : the work of Lothar Collatz in approximation theory, J. Approx. Theory 67 (2) (1991), 119–128.
  • G Meinardus and G Nürnberger, In memoriam : Lothar Collatz (July 6, 1910 – September 26, 1990), J. Approx. Theory 65 (1) (1991), i; 1–2.
  • J R Whiteman, In memoriam : Lothar Collatz, Internat. J. Numer. Methods Engrg. 31 (8) (1991), 1475–1476.

External links

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