ITEC 122 2008fall ibarland

home—info—lectures—exams—archive

ITEC 122 home
2008fall

Announcements

• exam02-study-guide—exam02 info

Reading is to be completed by the beginning of the week. (Though it's okay to have read the first half of the assigned reading by Monday, and the second half by Wednesday.)

This syllabus is tentative; updates will be mentioned in class. Be sure to check back regularly. Assignments are not finalized until 1.5 weeks before the due-date.

Final exam sheduled for Dec.18 (Thu) 10:15–12:15.

Homeworks are graded on clarity of presentation, ¹ which includes use of standard notations. Short correct answers much better than long correct answers (which are, in turn, much better than long correct answers that contain both necessary and superfluous statements).
Example of some answers, from best to worst:

• Q: “Are the rational numbers Q closed under exponentiaton? Prove or disprove.”

1. “No: 2∈Q and ½∈Q, but 2^1/2 ∉ Q (from the book, §1.6 example 10).”
2. “No 2 and ½ are both rational, but 2^1/2 is irrational.
   Proof by contradiction: Suppose that 2^1/2 were rational: that is, there are integers p,q such that 2^1/2=p/q. This means 2q²=p². If we consider a prime-factorization of each side, we see that 2 must occur an even number of times on the right-hand side, but an odd number of times on the left-hand side. This is a contradiction², so our assumption that 2^1/2 is rational must have been wrong, so 2^1/2 is irrational, QED.”
3. “No; 47^2/3 is irrational.
   Proof: suppose by contradiction that 47^2/3 is rational: that is, there are integers p,q such that 47^2/3=p/q. This means 47²q³=p³. If we consider a prime-factorization of each side, we see on the right-hand-side 47 occurs a multiple of three times, while on the left it occurs 3k+2 (for some k) times. This is a contradiction, so 47^2/3 must be irrational, QED.”
4. “No. 47^2/3 is irrational: Let x=47^2/3=p/q. But then 47²q³=p³. But 47 is prime, and therefore appears 3k+2 times in the prime-factorization of the left hand side, which can't be a multiple of 3. QED.”
5. “No. 47^2/3 = 13.0236256766892..., which is irrational.”
6. “A set is closed under exponentiation if one number in the set raised to another number in the set must also be in the set. This concepts only makes sense for sets of numbers.”

• (iii) is close (the same as (ii) but with unnecessarily-complicated numbers).
• (iv) is the exact same approach as (iii), but very poorly expressed.
• (v) just claims the statement is true, without evidence. This is the most egregious answer of the lot.
• (vi) consists of several true observations, but doesn't actually answer the question.

Some extra credit will be offered for participating in Project Euler problems, based on the difficulty of the problems and the quality (and clarity) of your solution. You can submit at most two problems per week for extra-credit this way.

home—info—lectures—exams—archive

©2008, Ian Barland, Radford University Last modified 2008.Dec.15 (Mon)

Please mail any suggestions (incl. typos, broken links) to iba�rlandrad�ford.edu