He received his PhD in mathematics at Harvard under Maxime Bôcher. Brenke taught at the University of Nebraska-Lincoln mathematics department from 1908 to 1944 and was chair of the department from 1934 to 1944. He retired in 1943 but his successor, Ralph Hull, was put on official leave to do war work and returned from leave in 1945.
- Brenke, W. C. (1930). "On polynomial solutions of a class of differential equations of the second order". Bull. Amer. Math. Soc. 36 (2): 77–84. doi:10.1090/s0002-9904-1930-04888-0. MR 1561893.
- Brenke, W. C. (1933). "On the summability and general sum of a series of Legendre polynomials". Bull. Amer. Math. Soc. 39 (10): 821–824. doi:10.1090/s0002-9904-1933-05753-1. MR 1562735.
- According to ancestry.com Brenke married Kate Read in 1898, had three children, and died in 1964.
- General History - Department of Mathematics - University of Nebraska-Lincoln
- William Charles Brenke at the Mathematics Genealogy Project
- NEGenWeb Project - Lancaster County Who's Who in Nebraska, 1940