In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who -was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in...

-Ecclesiastes 12:12 Programs are invariably subjected to many rorms or transrormation. After an initial version of a program has been designed and developed, it undergoes debugging and certification. In addition, most long-lived pro grams have a liCe-cycle that includes modifications to meet amended specifications and extensions for expanded capabilities. Such evolution ary aspects of programming are the topic of this monograph. We present rormal methods for manipulating programs and illustrate their applica tion with numerous examples. Such methods could be incorporated in semi-automated...

Hashing algorithms scramble data and create pseudo-uniform data distribu tions. Bucket algorithms operate on raw untransformed data which are parti tioned Into groups according to membership In equl-slzed d-dlmenslonal hyperrec tangles, called cells or buckets. The bucket data structure Is rather sensitive to the distribution of the data. In these lecture notes, we attempt to explain the connection between the expected time of various bucket algorithms and the dis tribution of the data. The results are Illustrated on standard searching, sorting and selection problems, as well as on a variety...