Education
Chisholm entered Girton in 1889, four years after she passed the senior entrance examination. At the end of their first year, when the Mays list came out, she was top of the Second class right below Isabel Maddison. In 1893, Grace passed her final examinations and scored the equivalent of a first-class degree. She also took (unofficially, on a challenge, with Isabel Maddison) the exam for the Final Honours School in mathematics at the University of Oxford on which she out-performed all the Oxford students. However, women were not awarded formal degrees at that time and Chisholm remained at Cambridge for an additional year to complete Part II of the Mathematical Tripos, which was unusual for women at this time. Chisholm was still interested in continuing her studies and since women were not yet admitted to graduate schools in England she went to the University of Göttingen in Germany to study with Felix Klein. This was one of the major mathematical centers in the world. The decision to admit her had to be approved by the Berlin Ministry of Culture. In 1895, at the age of 27, Grace became the first woman to attain a doctorate in any field in Germany. Again government approval had to be obtained to allow her to take the examination, which consisted of probing questions by several professors on sections such as geometry, differential equations, physics, astronomy, and the area of her dissertation, all in German. Along with her test she was required to take courses showing broader knowledge as well as prepare a thesis which was entitled "Algebraisch-gruppentheoretische Untersuchungen zur sphärischen Trigonometrie" (Algebraic Groups of Spherical Trigonometry.)
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