Lothar Collatz

Lothar Collatz ( born July 6, 1910 in Arnsberg, † September 26, 1990 in Varna ) was a German mathematician.

Life and work

In the years 1928-1933 he studied mathematics and physics at various universities in Germany (Berlin, Munich, Greifswald and Göttingen ), where he attended lectures of Erhard Schmidt, Richard von Mises, David Hilbert, Erwin Schrödinger, Richard Courant and Constantin Carathéodory.

In Schrödinger and von Mises in 1933 he laid the state exams in mathematics and physics from. Two years later he earned his doctorate work, the finite difference method with a higher approximation to linear differential equations with Alfred Klose and Erhard Schmidt. Von Mises, who had actually cared for him, had to leave because of the Nazi seizure of power Germany.

He then was an assistant at the University of Berlin, then in 1935 to move to the University of Karlsruhe and work at Theodor Pöschl and Wilhelm Quade ( 1898-1975 ) at the Institute of Engineering Mechanics. He also won the 1937 habilitation. From 1938 to 1943 he worked as a lecturer in Karlsruhe.

During the war years he was engaged in Darmstadt, Institute of Practical Mathematics. In 1943 he was appointed the Technical University of Hanover as professor of mathematics. As a professor of applied mathematics, he worked from 1952 to 1990 at the University of Hamburg. There he had founded in 1953, the Institute for Applied Mathematics, which earned him great international recognition. After his retirement in 1978, he was omnipresent as a lecturer and discussion leader mathematical conferences. He died in 1990 at a conference in the Bulgarian port city of Varna.

Since 1940, Collatz was married to Martha Togny.

He edited for many years the popular anonymous " Logeleien " the weekly newspaper "Die Zeit".

In his honor, the Collatz Prize is awarded.

Mathematical work

From his work as a mathematician is generally published in 1937, the Collatz problem is known which is unresolved. Otherwise, he was well known as an important representative of applied mathematics in the field of numerical mathematics major recognition.

Significant studies he conducted in the field of functional analysis and the theory of differential and integral equations. Began his research had already in the thirties with the finite difference method and their error estimates. He also dealt with difference schemes of higher approximations.

This was followed by work on the estimation of eigenvalues ​​of matrices and differential equations. He examined, inter alia, the structure of geometrical ornaments, periodic spline functions, bifurcations and the spectra of graphs.

He has published several standard works on numerical mathematics, which have also been translated.

See also: Collatz - graph

Writings (selection )

  • The finite difference method with a higher approximation to linear differential equations ( = writings of the mathematical seminar and the Institute for Applied Mathematics at the University of Berlin - Band 3/Heft 1 ), Leipzig 1935
  • Eigenvalue problems and their numerical treatment. Leipzig 1945
  • Eigenvalue problems with technical applications. Leipzig 1949, 1963
  • Numerical treatment of differential equations. Berlin 1951, 1955 (English 1966)
  • Differential equations for engineers. Stuttgart 1960
  • Wolfgang Wetterling optimization tasks Berlin in 1966, 1971 (English 1975)
  • Functional Analysis and Numerical Mathematics. Berlin 1964
  • Differential equations. An introduction with special emphasis on applications. Stuttgart, Teubner Verlag, 1966, 7th edition. 1990
  • With Julius Albrecht tasks of applied mathematics I. equations in one and several variables. Approximations. Berlin 1972
  • Numerical methods of approximation theory. Volume 2 lecture excerpts of the conference on Numerical methods of approximation theory of 3 - 9th June 1973 in the Mathematical Research Institute Oberwolfach, Stuttgart 1975
  • Approximation Theory: Chebyshev approximation and applications. Teubner 1973

Some online accessible essays:

  • Collatz " Theoretical foundations of numerical analysis ", Annual Report DMV 1962/3
  • Collatz " Einschliessungssatz for characteristic numbers of matrices ", Math.Zeitschrift 1942
  • Collatz " Einschliessungssatz for eigenvalues ​​of integral equations ", Math.Zeitschrift 1942
  • Collatz "On the convergence criteria for iterative methods for linear systems of equations ", Math.Zeitschrift 1950
  • Collatz, Schröder " confinement of the solution of boundary value problems ", Computational Mathematics 1959

Tribute to Dr. hc.

Membership

  • Academy of Sciences of Bologna
  • Academy of Sciences of Modena
  • German Academy of Natural Scientists Leopoldina (since 1962 )
  • Society for Applied Mathematics and Mechanics
  • Mathematical Society in Hamburg
  • The National Geographic Society
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