Math 29 Homework #17 It is difficult to give an idea of the extent of modern mathematics. The word 'extent' is not the right one: I mean extent crowded with beautiful detail - not an extent of mere uniformity such as an objectless plain, but of a tract of country seen at first at a distance, but which will bear to be rambled through and studied in every detail of hillside and valley, stream, rock, wood, and flower. But, as for everything else, so for mathematical theory - beauty can be perceived but not explained. Arthur Cayley

	Reading Read what we covered in today's class: 6.1, 6.2 Read what we will cover in the next class: 6.2, 3, 4, 5 When reading 6.1 pay special attention to the following concepts: Thereoms 1.1 and 1.3 are the key to almost all of the results in the remainder of this section. Theorems 1.4,1.5, 1.6, 1.7. Notice how each of these problems reduces to the halting problem. When reading 6.2, 6.3 pay special attention to the following concepts: the description of the word problem for groups and the decision problem for diophantine equations. When reading 6.3,4,5 pay special attention to the following concepts: Make sure that you understand the statement of the decidability problems presented in these sections.

	Problems The following problems are due by the beginning of class on Friday 5/7. Define each of the following: word generated diophantine equation p. 106, # 6.1.8.1 c, d, f, g, h