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Max also contributed by far the larger part of the exercises. Rather than a literal reproduction of the course, they should be regarded as its skeleton they were supplemented by references to stan­ dard text-books on algebra. Edwin Clark, University of South Florida, 2002-Dec. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. A revision by Jim Hefferon, St Michaels College, 2003-Dec of notes by W.

Being alien to the local tradition, it did not work out as well as I had hoped, and student attendance at the problem sessions so on became desultory. This idea was borrowed from the "Praktikum" of German universi­ ties. asked to solve under Max's supervision and (when necessary) with his help. The course consisted of two lectures a week, supplemented by a weekly "laboratory period" where students were given exercises which they were. According to his recollection, "this was the first and last time, in the his tory of the Chicago department of mathematics, that an assistant worked for his salary". What made it possible, in the form which I had planned for it, was the fact that Max Rosenlicht, now of the University of California at Berkeley, was then my assistant. In mathematics, the notion of a set is a primitive notion. 114 PART I I : Optimization Theory and Methods To UNDERSTAND THE strategy of optimization procedures, certain basic concepts must be described. Prime number, composite numbers, squares) were distinguished the structure of perfect numbers (cf.In the summer quarter of 1949, I taught a ten-weeks introductory course on number theory at the University of Chicago it was announced in the catalogue as "Alge­ bra 251". Set Theory and Logic: Fundamental Concepts (Notes by Dr. If a and b are integers and there is some integer c such that a b c, then we say that b divides a or is a factor or divisor of a and write ba. In Ancient Greece (6th century B.C.) divisibility of integers was studied, and particular subclasses of integers (such as prime numbers, cf. Number theory arose from problems in arithmetic connected with the multiplication and division of integers. Integers, together with the simplest geometrical figures, were the first and the most ancient mathematical concepts.