Maria Hasse

Maria-Viktoria Hasse (May 30, 1921 – January 10, 2014) was a German mathematician who became the first female professor in the faculty of mathematics and science at TU Dresden.[1] She wrote books on set theory and category theory,[2] and is known as one of the namesakes of the Gallai–Hasse–Roy–Vitaver theorem in graph coloring.

Education and career

Hasse was born in Warnemünde. She went to the gymnasium in Rostock, and after a term in the Reich Labour Service from 1939 to 1940, studied mathematics, physics, and philosophy at the University of Rostock and University of Tübingen from 1940 to 1943, earning a diploma in 1943 from Rostock. She continued at Rostock as an assistant and lecturer, earning a doctorate (Dr. rer. nat.) in 1949 and a habilitation in 1954.[2][1] Her doctoral dissertation, Über eine singuläre Intergralgleichung 1. Art mit logarithmischer Unstetigkeit [On a singular integral equation of the 1st kind with logarithmic discontinuity], was supervised by Hans Schubert;[3] her habilitation thesis was Über eine Hillsche Differentialgleichung [On Hill's differential equation]. She worked as a professor of algebra at TU Dresden from 1954 until her 1981 retirement.[4]

Contributions

With Lothar Michler, Hasse wrote Theorie der Kategorien [Category Theory] (Deutscher Verlag, 1966).[5] She also wrote Grundbegriffe der Mengenlehre und Logik [Basic Concepts of Set Theory and Logic] (Harri Deutsch, 1968).[6]

In the theory of graph coloring, the Gallai–Hasse–Roy–Vitaver theorem provides a duality between colorings of the vertices of a graph and orientations of its edges. It states that the minimum number of colors needed in a coloring equals the number of vertices in a longest path, in an orientation chosen to minimize the length of this path. It was stated in 1958 in a graph theory textbook by Claude Berge, and independently published by Hasse, Tibor Gallai, B. Roy, and L. Vitaver. Hasse's publication of this result was the second chronologically, in 1965.[7]

References

1. Voss, Waltraud (2016), Lieselott Herforth: Die erste Rektorin einer deutschen Universität, Gender studies (in German), transcript Verlag, pp. 127–128, ISBN 9783839435458
2. "Hasse, Maria-Viktoria", Catalogus professorum rostochienium, University of Rostock, retrieved 2018-02-25
3. Maria Hasse at the Mathematics Genealogy Project
4. Voss (2016) The Rostock CPR gives the date of her start at Dresden as 1964, but this would leave a ten-year gap in her work life, and Voss is clear that she arrived before the 1962 start of Lieselott Herforth.
5. Isbell, J. R., "Review of Theorie der Kategorien", Mathematical Reviews, MR 0213411
6. MR0215725
7. Independent publications of the Gallai–Hasse–Roy–Vitaver theorem:
   • Gallai, Tibor (1968), "On directed graphs and circuits", Theory of Graphs (Proceedings of the Colloquium Tihany 1966), New York: Academic Press, pp. 115–118
   • Витавер, Л. М. (1962), "Нахождение минимальных раскрасок вершин графа с помощью булевых степеней матрицы смежностей [Determination of minimal coloring of vertices of a graph by means of Boolean powers of the incidence matrix]", Doklady Akademii Nauk SSSR (in Russian), 147: 758–759, MR 0145509
   • Hasse, Maria (1965), "Zur algebraischen Begründung der Graphentheorie. I", Mathematische Nachrichten (in German), 28 (5–6): 275–290, doi:10.1002/mana.19650280503, MR 0179105
   • Roy, B. (1967), "Nombre chromatique et plus longs chemins d'un graphe" (PDF), Rev. Française Informat. Recherche Opérationnelle (in French), 1 (5): 129–132, doi:10.1051/m2an/1967010501291, MR 0225683
   For an overview of the theorem and its history, see Nešetřil, Jaroslav; Ossona de Mendez, Patrice (2012), "Theorem 3.13", Sparsity: Graphs, Structures, and Algorithms, Algorithms and Combinatorics, 28, Heidelberg: Springer, p. 42, doi:10.1007/978-3-642-27875-4, ISBN 978-3-642-27874-7, MR 2920058.