McHarg studied at the Glasgow High School for Girls and then the University of Glasgow, earning a master's degree with first class honours in mathematics and natural philosophy in 1943. The university awarded her the Thomas Logan Medal and a George A Clark scholarship, funding her as a researcher at Girton College, Cambridge. At Girton, she studied nonlinear partial differential equations with Mary Cartwright, and completed her Ph.D. in 1948.
McHarg returned to the University of Glasgow as a lecturer in 1948. There, she became an expert in special functions. She also translated the text Differential Equations by Francesco Tricomi from Italian into English; her translation was published in 1961 by Hafner and republished in 2012 by Dover Publications.
- Martin, Dan (7 May 1999), "Dr Elizabeth McHarg", The Herald (Glasgow). Reprinted as "Elizabeth A. McHarg", Glasgow Mathematical Journal, 42 (3): 487–488, September 2000, doi:10.1017/s0017089500030159
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