Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität zu Bonn, 1917. / Vita. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1963. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 50-51).

Akademisk avhandling--Uppsala. / Thesis statement from special t.p. inserted. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 165).

Thesis (Ph. D.)--University of Chicago, 1937. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Includes bibliographical references.

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

M.Sc. / Please refer to full text to view abstract

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This study was designed to determine the effectiveness of teaching symbolic logic in the high school. Three hundred eighty-seven students enrolled on the University Programme in grades nine to thirteen at Como Lake High School, in School District No. 43 (Coquitlam), took part in the investigation. The students were grouped according to the mathematics course they were studying. Answers were sought to two specific questions. Do significant differences exist between the means of the final test scores of the students in each of the groups? At which grade levels can this material be effectively mastered? As a criterion for determining this, 75 per cent of the students at a particular level were required to obtain a score of 50 per cent or better on the final test. In order to answer the first question, the results were studied by analysis of covariance with scholastic aptitude being the variable controlled. The answer to the second question was obtained by comparing the performance of each group with the standard outlined. On the basis of this information, decisions were made regarding the suitability of the material for the various grade levels. All of the differences between the means were found to be significant at the one per cent level. The highest mean score was obtained by the students in Mathematics 101, followed in order by those of Mathematics 91, 30, 20, and 10. The students of Mathematics 101, 91 and 30 satisfied the requirement that 75 per cent should obtain a score of 50 per cent or better on the final test. The students of Mathematics 20 and 10 failed to satisfy this requirement. / Education, Faculty of / Graduate

According to quantum mechanics, the pure states of a microsystem are represented by vectors in a Hilbert Space. Sentences of the form, "x є L" (where x is the state vector for a system, L a subspace of the appropriate Hilbert space), may be called Q-propositions: such sentences serve to summarise our information about the results of possible experiments on the system. Quantum logic investigates the relations which hold among the Q-propositions about a given physical sys tem. These logical relations correspond to algebraic relations among the subspaces of Hilbert space. The algebra of this set of subspaces is non-Boolean, and may be regarded either as an orthomodular lattice or as a partial Boolean algebra. With each type of structure we can associate a logic. A general approach to the semantics for such a logic is provided in terms of interpretations of a formal language within an algebraic structure; an interpretation maps sentences of the language homomorphically onto elements of the structure. When the structure in question is a Boolean algera, the resulting logic is classical; here we develop a semantics for the logic associated with partial Boolean algebras. Two systems of proof, based on the natural deduction systems of Gentzen, are shown for this logic. With respect to the given sematics, these calculi are sound and weakly complete. Strong completeness is conjectured. Quantum logic deals with the logical relations between sentences, and so is properly called a logic. However, it is the logic appropriate to a limited class of sentences: proposals that it should replace classical logic wherever the latter is used should be viewed with suspicion. / Arts, Faculty of / Philosophy, Department of / Graduate