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Mathematical Treasure: L. E. Dickson's Algebraic Invariants

Frank J. Swetz (The Pennsylvania State University)

Figure 1. Title page of Leonard Eugene Dickson's Algebraic Invariants, published as a monograph in 1914

Leonard Eugene Dickson (1874-1954) was one of America’s leading algebraists. He was the first person to earn a doctorate in mathematics from the University of Chicago. While perhaps best recognized for his three-volume History of the Theory of Numbers (1919-1923), he was a prodigious researcher and author in abstract algebra, with a particular interest in the areas of finite fields and classical groups. His Algebraic Invariants was published as a monograph in 1914; however, it had previously appeared as a contribution to a research reference, Higher Mathematics, a series that ceased publication in 1906. The chapters of this defunct book then served as subjects for a monograph series. The title page of the 1914 monograph on algebraic invariants is shown below. This monograph consists of three parts: a consideration of linear transformations; a discussion of algebraic properties of invariants and covariants; and an introduction to the notation of Siegfried Aronhold and Alfred Clebsch, then the leading researchers in the theory of invariants.

Figure 2. First page of text introducing the concept of an invariant under a linear transformation


Figure 3. Discussion of projective transformations

These three images are presented courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania. You may use them in your classroom and/or for private study. For all other purposes, please obtain permission from Archives and Special Collections, Waidner-Spahr Library, Dickinson College, Carlisle, PA.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: L. E. Dickson's Algebraic Invariants," Convergence (February 2014)