Abstract
There is a growing belief among educators that university undergraduate teaching in mathematics needs improvement. They contend that college instruction in mathematics should be an exciting and rewarding process of communicating ideas and it should be treated with the same consideration as the research carried on by various college mathematics professors. Many capable students take the Ph.D. degree because it is the only advanced mathematics degree of quality available to them. Furthermore, universities and other employers of mathematical talent hire Ph.D.s for positions which require teaching ability and breadth of mathematical knowledge rather than research ability because the only available talent is in the Ph.D. pool. Our present production of talent is not giving us the high caliber product our complex society demands. Many Ph.D.s never make a creative contribution to mathematics or the teaching of mathematics beyond their doctoral dissertation [1]. The dropout rate among graduate students in mathematics is far too high, the dropouts complaining in many instances of the narrowness of the preparation for the Ph.D. degree. A goodly number of them would prefer an advanced degree in mathematics which stresses teaching expertise and breadth of knowledge in mathematics.
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