On the other hand, your complaints that the instructions are not clear for many of the exercises are well founded. I would like to make a list of exercises for which the instructions could be improved. Also, some way of annotating or commenting upon your papers that does not take up an unreasonable amount of the grader's time (or mine) needs to be found. For some reason that problem was not so visible when I taught the course before. I do recall that then I put generic comments, or even complete solutions, into the "lectures" for later weeks, and also that I asked students to post solutions to individual exercises on [the predecessor of] Vista when those solutions were particularly illuminating.
Please nominate your favorite exercises for either of these treatments (sharpened statements for the students of the future, or posted solutions for students of the present). I will start the process below with the Chinese remainder problems (5.19 and 5.20).
Betraying my physics background (and my years as a calculus teacher), I find the most interesting figure of this period to be Oresme, who apparently was the first to draw graphs of functions representing quantities other than positions, and had some understanding of the relations between position, velocity, and acceleration. I wish authors would tell us how his name should be pronounced -- "ORAME" like a modern French name, or what?
In Exercise 19, we first get x_1 = 0. The trouble comes in finding
x_2, where the counting board
1 3
0 4
reduces by the algorithm to
1 3
1 1 <-- LOWER LEFT IMPLIES x_2 = - 1.
and we must stop there, not go on to
4 0
1 1
Thus we can take x_2 = m_2 -1 = 3, and we get N = 0 + 1x3x3 = 9.
Alternatively, keep x_2 = -1 and compute N = 0 + 1x3x(-1) = -3,
and adding 12 we get 9.