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Alexanderson did his undergraduate studies at the University of Oregon, graduating with a B.A. in 1955. He earned a master's degree from Stanford University in 1958, and in the same year joined the Santa Clara University faculty. At Santa Clara, he chaired the department of mathematics for 35 years, from 1967 to 2002.
He is the co-author, editor, or co-editor of 15 books, and was editor of Mathematics Magazine from 1986 to 1990. Abraham Hillman was his most frequent co-author.
with Abraham Hillman: Functional trigonometry: trigonometry integrated with vectors, complex numbers, analytic geometry, and elementary functions. 1961.
with Abraham Hillman: Algebra and trigonometry: a treatment of algebra and trigonometry integrated with vectors, complex numbers, and elementary functions. 1963. 4 editions
with Abraham Hillman: Algebra through problem solving. 1966. 7 editions
with Abraham Hillman: A first undergraduate course in abstract algebra. 1973. 16 editions
with Donald J. Albers and Constance Reid: International mathematical congresses : an illustrated history, 1893-1986. New York: Springer-Verlag. 1986; 1st edition, hbk, 63 pages; 2012 pbk reprint. 29 editions
with Abraham Hillman and Richard M. Grassi: Discrete and combinatorial mathematics. 1987. 8 editions
with Donald J. Albers: Mathematical people : profiles and interviews, with introduction by Philip J. Davis. 1985.2008 2nd edition. 26 editions
with Leonard F. Klosinski and Loren C. Larson: William Lowell Putnam Mathematical Competition : problems and solutions, 1965-1984. Washington, DC: Mathematical Association of America. 1985.2018 pbk edition. 25 editions
Pólya picture album : encounters of a mathematician by George Pólya, edited by G. L. Alexanderson. Boston: Birkhäuser. 1987. 15 editions
with Donald J. Albers and Constance Reid: More mathematical people : contemporary conversations. 1990. 13 editions
^Gillman, Leonard (1996). "Review of Lion Hunting and Other Mathematical Pursuits. A Collection of Mathematics, Verser and Stories by Ralph P. Boas, Jr., edited by Gerald L. Alexanderson and Dale H. Mugler". The American Mathematical Monthly. 103 (7): 607. doi:10.2307/2974683. ISSN0002-9890.