### Students

Thomas Milton Putnam :Concerning the linear fractional group on three variables with coefficients in the Galois field of order \( p^n \) University of Chicago, Ph.D. 1901 |

Herbert Edwin Jordan :Group characters of various types of linear groups University of Chicago, Ph.D. 1904 |

William Henry Bussey :Generational relations for the abstract group, simply isomorphic with the linear fractional group University of Chicago, Ph.D. 1904 |

Arthur Ranum :On a new kind of congruence groups University of Chicago, Ph.D. 1906 |

Robert Lacey Börger :On the determination of ternary linear groups in a Galois field of order \( p^2 \) University of Chicago, Ph.D. 1907 |

Albert Harris Wilson :The canonical types of nets of quadratic forms in the Galois field of order \( p^n \) University of Chicago, Ph.D. 1911 |

Mildred Leonora Sanderson :Formal modular invariants with an application to binary modular covariants University of Chicago, Ph.D. 1913 |

Olive Clio Hazlett :On the classification and invariantive characterization of nilpotent algebras University of Chicago, Ph.D. 1915 |

William Lloyd Garrison Williams :Fundamental systems of formal modular seminvariants of the binary cubic University of Chicago, Ph.D. 1920 |

Mayme Irwin Logsdon :Equivalence and reduction of pairs of Hermitian forms University of Chicago, Ph.D. 1921 |

Cyrus Colton MacDuffee :Invariantive characterizations of linear algebras with the associative law not assumed University of Chicago, Ph.D. 1921 |

Claiborne Green Latimer :Arithmetic of generalized quaternion algebras University of Chicago, Ph.D. 1924 |

Frederick Stanley Nowlan :Arithmetics of rational division algebras of order nine University of Chicago, Ph.D. 1925 |

Echo Dolores Pepper :Theory of algebras over a quasi-field University of Chicago, Ph.D. 1925 |

Albert Everett Cooper :A topical history of the theory of quadratic residues University of Chicago, Ph.D. 1926 |

Raymond Joseph Garver :I: On Tschirnhausen transformations. II: Division algebras of order sixteen University of Chicago, Ph.D. 1926 |

Joel Samuel Georges :Associativity conditions for division algebras corresponding to any Abelian group University of Chicago, Ph.D. 1926 |

Marion Elizabeth Stark :A self-adjoint boundary-value problem associated with a problem of the Calculus of Variations University of Chicago, Ph.D. 1926 |

Ralph George Archibald :Diophantine equations in division algebras University of Chicago, Ph.D. 1927 |

Lois Wilfred Griffiths :Certain quaternary quadratic forms and Diophantine equations by generalized quaternion algebras University of Chicago, Ph.D. 1927 |

John Williamson :Conditions for associativity of division algebras connected with non-Abelian groups University of Chicago, Ph.D. 1927 |

Burton Wadsworth Jones :Representation by positive ternary quadratic forms University of Chicago, Ph.D. 1928 |

Abraham Adrian Albert :Algebras and their radicals and division algebras University of Chicago, Ph.D. 1928 |

Earl L. Thompson :Systems of two differential equations from the Lie group standpoint University of Chicago, Ph.D. 1928 |

David Clarence Morrow :The determination of all quaternary quadratic forms which represent every positive integer University of Chicago, Ph.D. 1928 |

Ko-chuen Yang :Various generalizations of Waring’s problem University of Chicago, Ph.D. 1928 |

Samuel Silberfarb :Representation by indefinite ternary quadratic forms University of Chicago, Ph.D. 1929 |

Gordon Pall :Problems in additive theory of numbers University of Chicago, Ph.D. 1929 |

Orley Edward Brown :The equivalence of triples of bilinear forms and sets of integers with equal sums of like powers University of Chicago, Ph.D. 1929 |

Alexander Victor Oppenheim :The minima of indefinite quaternary quadratic forms University of Chicago, Ph.D. 1930 |

Ralph Sylvester Underwood :On universal quadratic null forms in five variables University of Chicago, Ph.D. 1930 |

Fred Winchell Sparks :Universal quadratic zero-forms in four variables University of Chicago, Ph.D. 1931 |

Mina Spiegel Rees :Division algebras associated with an equation whose group has four generators University of Chicago, Ph.D. 1931 |

Arnold Ephraim Ross :On representation of integers by indefinite ternary quadratic forms University of Chicago, Ph.D. 1931 |

Emily McCoy Chandler :Waring’s theorem for fourth powers University of Chicago, Ph.D. 1931 |

Ruth Glidden Mason :Studies in the Waring problem University of Chicago, Ph.D. 1932 |

Ralph Hull :The numbers of solutions of congruences involving only \( k \)-th powers University of Chicago, Ph.D. 1932 |

Ralph Ernest Huston :Asymptotic generalizations of Waring’s theorem University of Chicago, Ph.D. 1932 |

Ralph Duncan James :Analytical investigations in Waring’s theorem University of Chicago, Ph.D. 1932 |

Marie Paula Litzinger :A Basis for Residual polynomials in \( n \) variables University of Chicago, Ph.D. 1934 |

Frances Ellen Baker :A contribution to the Waring problem for cubic functions University of Chicago, Ph.D. 1934 |

George Cuthbert Webber :Waring’s problem for cubic functions University of Chicago, Ph.D. 1934 |

Robert Clarence Shook :Concerning Waring’s problem for sixth powers University of Chicago, Ph.D. 1934 |

Kenneth Smith Ghent :On sums of values of a polynomial multiplied by constants University of Chicago, Ph.D. 1935 |

Mabel Gweneth Humphreys :On the Waring problem with polynomial summands University of Chicago, Ph.D. 1935 |

Mae Ruth Anderson :Representation as a sum of multiples of polygonal numbers University of Chicago, Ph.D. 1936 |

Stanmore Brooks Townes :Reduced positive quaternary quadratic forms University of Chicago, Ph.D. 1936 |

John Clark Brixey :The null forms \( ax^2 + by^2 + cz^2 + du^2 \) which represent all integers University of Chicago, Ph.D. 1936 |

Dora McFarland :Division algebras defined by non-Abelian groups University of Chicago, Ph.D. 1936 |

Harold Chatland :The asymptotic Waring problem for homogeneous polynomial summands University of Chicago, Ph.D. 1937 |

Mary Barbara Haberzetle :Two new universal Waring theorems University of Chicago, Ph.D. 1938 |

Margaret Evelyn Mauch :Extensions of Waring’s theorem on seventh powers University of Chicago, Ph.D. 1938 |

Ivan Morton Niven :A Waring problem University of Chicago, Ph.D. 1938 |