The present volume originated in a desire on the part of the authors to furnish a text of Course I. as was previously mapped out by the department of mathematics at the University of Wisconsin. The orginal intent was to produce a syllabus for the use of students in this institution, but it was subsequently thought that a work which would be useful here might also be found useful elsewhere, and hence it was decided to give the work more the character of a treatise than a syllabus. To insure the best results it was thought desirable to print the present preliminary edition and put it to the test of class room work, and at the same time to invite criticism and suggestions from teachers and others interested in mathematics, and then from the results of the authors' tests, and from the experience of others, to rewrite the work, changing it freely. For these reasons the treatment of many subjects in the following pages should be understood as merely tentative. The final form will depend entirely upon the results of experience. An examination of the text will reveal many deviations from the beaten path, but the idea was not to deviate simply for the sake of being different from others; on the contrary the authors have freely drawn from other works. The sources from which material has been most largely drawn are the following: For problems, Christie's Test Questions and Wolstenholm's Collection; for various matters in the text, Kempt's Lehrbuch in die Moderne Algebra, and the algebras of Chrystal; Aldis; Hall and Knight; Oliver, Wait and Jones; and Todhunter; for historical notes, Marie's Histoire des Sciences Mathematiques et Physiques, and Matthiesen's Grundzuge der Antiken und Modernen Algebra. |