She earned her Ph.D. from UIUC in 1967, under the supervision ofRichard L. Bishop, with a thesis entitledReducibility of Euclidean Immersions of Low Codimensions.[5] After joining the UIUC faculty as a half-time instructor, she became a regular faculty member in 1972.[3] She retired in 2009[6] and died in 2023.[4]
Alexander's most significant achievements were in relation to the study of metric spaces with curvature bounds. Of particular importance was her work with Bishop to establish a concept of curvature bounds in the style of Alexandrov geometry forsemi-Riemannian manifolds andLorentzian manifolds, an early step towards the development ofsynthetic geometry in a Lorentzian setting.[7]
At Illinois, Alexander won the Luckman Distinguished Undergraduate Teaching Award and the William Prokasy Award for Excellence in Undergraduate Teaching in 1993.[6]
In 2014 she was elected as afellow of theAmerican Mathematical Society "for contributions to geometry, for high-quality exposition, and for exceptional teaching of mathematics."[8]
