It will be on Wednesday, May 13, at 8:30 a.m. in S3-246. I will allow 2 ¼ hours. The exam will be comprehensive, but it will give some emphasis to the material of Chapter 10, since that was not previously tested.
Grading guidelines:
A B C D F 80-100 63-79 45-62 35-44 0-34
Grading guidelines:
A B C D F 80-100 59-79 38-58 28-37 0-27
Grading guidelines:
A B C D F 85-100 69-84 53-68 43-52 0-42
Grading guidelines:
A B C D F 119-157 93-118 68-92 53-67 0-52
In Application 9, the statement should read: "contains an increasing or a decreasing subsequence".
In the footnote, the term "not decreasing" is the wrong technical term. A correct technical term for this property is "weakly increasing" or "nondecreasing" (both are used).
In Ch.2, # 16, you should assume (as you probably did) that acquaintanceship is symmetric. That is, if A is acquainted with B, then B is acquainted with A. (I know this isn't always so in real life.)
You start with a deck of N cards, numbered from 1 to N, in any order. You play by taking the top card from the deck and putting it on the table, face up. You may either start a new pile (which you have to do with the first card, since there aren't any piles at first!), or you may put the card on top of any pile whose top card is higher than the card you're playing. You keep going until you've played the whole deck. The objective is to make the fewest piles.
All the same except that you may put the card on top of any pile whose top card is lower than the card you're playing.
This is an optional rule that you can use in the normal and reverse games. The rule: always put the card on the leftmost legal pile.
On page 345, in the table at the top, Cols. A and B should read:
48 126 48 30 18 30 18 12 6 12 6 0
On page 347, the top line should read: 16-1 = -14 = 31 in Z45.
A very minor error on page 378: In the bottom line, N(1) = infinity.
Zn, for an integer n >= 2, is the set {0, 1, ..., n-1} with arithmetic carried out modulo n. We call this system the integers modulo n.
A polynomial f(x) with coefficients in Zp is called irreducible over Zp if it cannot be factored as a product of polynomials of lower degree. (Here we treat only the coefficients as elements of Zp. x is an indeterminate, just as with ordinary polynomials.).
Fq, for a prime power q = pe (i.e., p is a prime number and e >= 1), is the set of all polynomials in i, with coefficients in Zp, that have degree < e. Calculations in Fq are carried out modulo a fixed polynomial f(x) of degree e that is irreducible over Zp. This polynomial is called a modulus polynomial for Fq. The meaning of calculating mod f(x) is that i satisfies the equation f(i) = 0. The system Fq is called a field of order q (that is, with q elements).
For a prime number p, Zp and Fp are the same. For any nonprime number, though, they are very different. (Zn is not even a field, if n is not a prime.)