Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 54-55).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 119-121).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1928. / Thesis note stamped on cover. Reprinted from the Transactions of the American mathematical society, vol. 30, no. 3. eContent provider-neutral record in process. Description based on print version record.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1940. / Typescript. eContent provider-neutral record in process. Description based on print version record.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1951. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf [47]).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1950. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--Oregon State University, 1968. / Typescript (photocopy). Includes bibliographical references (leaf 74). Also available on the World Wide Web.

It is shown that the number of classes of nonisometric lattices on the space of rational n-tuples is the same as the number of classes of n x n integral, symmetric, positive definite, unimodular matrices under integral congruence. A method is given to determine the number of classes of nonisometric lattices; this method is used to determine the number of classes for n↖ 16. A representative of each class of symmetric, integral, positive definite, unimodular 16x16 matrices is given. / Science, Faculty of / Mathematics, Department of / Graduate

A new proof is given of Newman and Taussky's result: if A is a unimodular integral n x n matrix such that A′A is a circulant, then A = QC where Q is a generalized permutation matrix and C is a circulant. A similar result is proved for unimodular integral skew circulants. Certain additional new results are obtained, the most interesting of which are: 1) Given any nonsingular group matrix A there exist unique real group matrices U and H such that U is orthogonal and H is positive definite and A = UH; 2) If A is any unimodular integral circulant, then integers k and s exist such that A′ = P(k)A and P(s)A is symmetric, where P is the companion matrix of the polynomial xⁿ-1. Finally, all the n x n positive definite integral and unimodular skew circulants are determined for values of n ≤ 6: they are shown to be trivial for n = 1,2,3 and are explicitly described for n = 4,5,6. / Science, Faculty of / Mathematics, Department of / Graduate