Homework solutions not on the TA's course page:

Errata for the text by Childs.

Complex demos:

- Summing a complex geometric series,
- Summing the exponential series,
- Spotlighting a complex differentiable (analytic) function

- 6/8/04 Office hours previously announced for Thursday, June 10 have been changed; they will be 11:00-11:30 and 12:00-12:30. Sorry for the late notice; I was asked to attend a meeting.
- 6/8/04 Solutions to the non-text homework problems of Assignment 7 are linked above. If you notice any errata, please let me know.
- 5/31/04 Solutions to Assignment #6 are ready; a link is near the top of this page.
- 5/27/04 One of you points out that in Problem M-7 part (c), the integer given is not the product of two primes as it is supposed to be. So do only parts (a) and (b) this week; I'll put a different version of (c) for next week.
- 5/26/04 On p. L 3, in Step 2(a) the rows were supposed to be rotated by different amounts. (This part was not relevant for homework.)
- 5/26/04 In Rijndael, the bits are numbered so that
**a**is the coefficient of_{7}**α**, and so on. So when you see^{7}**a**as a column vector, the bits are in the opposite order from when they are listed in a byte. Then after you do the matrix multiplication and get a column vector out, you need to put its bits back in the correct order for the byte._{0}, a_{1},...,a_{7}For finding the inverse, people are having trouble interpreting the suggestion. Just take the equation

**α**, multiply through by^{8}= α^{4}+ α^{3}+ ... + 1**α**, to get^{-1}**α**, and then solve for^{7}= α^{3}+ α^{2}+ ... + α^{-1}**α**, remembering that in the two-element field^{-1}**-1 = 1**so minus an expression is the same as plus the expression. (Of course,**α**is just one element of the field and this method of inverting applies only to**α**itself.) - 5/24/04 Erratum: p. L3, Step 1(a): should say simply "mapped to its inverse".
- 5/23/04 Office hours this week (May 24-28): Monday, May 24, 11:00-12:00; Wednesday 11:00-12:00 as usual; Thursday 1:30-2:00 (and I can't be available informally after discussion section).
- 5/21/04 I said Assignment #7 will be due in ten days, but I forgot that that's a holiday (Memorial Day)--so I'll give a shorter assignment due this coming Friday. If you're working over this weekend then you can read the Rijndael handout. (If you don't have it, see the on-line version.)
- 5/20/04 p. 206, Ex. 1 is listed as both to hand in and as not to hand in. Let's say you don't need to hand it in. Do try it, though.
- 5/20/04 In Problem H-3(b), stick to the cases where
**a**a unit or is divisible by**m**. - 5/20/04 In Problem H-4, it should say
**generators**rather than**units**. - 5/18/04 In Problem H-6, (iii)-(b): should say
**Z**._{ 151 } - 5/18/04 In Problem I-3, if you want to use a group of three people or more, you can send messages cyclically, e.g., A to B to C to A. Each two would need to establish a shared secret key.
- 5/18/04 Also in Problem I-3, please hand in a record of the numbers you calculated or observed.
- 5/17/04 In Problem I-3, in the table that says A is 1, etc., of course that should be expanded to two digits, so A is 01, B is 02, etc.
- 5/13/04 For problem 2(a) on the midterm, if you didn't give a reason for your answer and I asked you to supply one (which could be, for example, that you used trial and error), do see me about it.
- 5/13/04 Advice: For E8 p. 138, there are really two
issues: (1) Two congruences
**x ≡ y (mod r)**and**x ≡ y (mod s)**are equivalent to the single congruence**x ≡ y (mod rs)**if**r**and**s**are coprime (= relatively prime); (2) if a list**1, a, a**repeats every^{2},..., 1, a,**d**terms and a similar list repeats every**e**terms, how often do they repeat simultaneously? - 5/13/04 Advice: For E10 p. 123, you are going to need some
additive property of
**0**to start from. - 5/13/04 In E7 p. 126-7,
**1 + i**is intended in place of**i + i**. (See the errata link above.) - 5/9/04 Assignment 5 has been posted (see Handouts). Notice that for pp. 144-145 it's E13, rather than the E18 that I wrote on the board during the exam.
- 5/6/04 For Assignment 3, the solution to p. 53 E18 was omitted.
The idea is like the solution of E13 in the same section: List
the primes in
**a**, the primes in**b**(which don't overlap those for**a**) and then any additional primes that are in**n**. Write the prime factorizations of**a**,**b**, and**n**"in parallel" with exponents, some of which will be 0. Then compute the prime factorizations of**gcd(a,n)**,**gcd(b,n)**, and**gcd(ab,n)**"in parallel" also. (Thanks to ASA.) - 5/6/04 In problem C-13 and its solution, notice that the formula
in (d) involves
**ρ bar**to a positive power**n**rather than**ρ**to a negative power. The typesetting is a little confusing. (Thanks to ASA.) - 5/6/04 Here is a link to errata for the text by Childs.
- 5/5/04 at 5:52p.m. Here are links to solutions to Assignment 3 and solutions to Assignment 4 . (Both have been improved from the original postings.) For solutions to Assignments 1 and 2, see the TA's Math 117 pages, for which a link is given above.
- 4/28/04 In D-2, it should be
**π(10**and^{8}) = 5,761,455**π(10**. Use either one in your work. (Thanks to WCC.)^{9}) = 50,847,534 - 4/28/04 In D-2,
**log**means natural log, which is the usual notation in advanced math and in computer languages. Engineering, some calculators, and some calculus books use**ln**. - 4/26/04 A few people had trouble with Java on their browser. In
case you do: Check your browser version by going to the
**Help**menu and clicking on**About...**. If it's Internet Explorer 6, try this: On the**Tools**menu, select**Internet Options**and then click on the**Advanced**tab. Pull the slider half way down and look for the box**JIT compiler for virtual machine enabled**. If it's not already selected, that's your problem; select it, click**OK**at the bottom, and restart your PC. - 4/26/04 Office hours for
**Thursday, April 29**will be**11:00-12:00**. (Office hours for**Wednesday, April 28**will be**11:00-12:00**as usual. I can be there past 12:00 on request.) - 4/22/04 Here is a link to the website mentioned in D-1: Mamikon's Pascal-Sierpinski. The link given in D-1 seems not to be working. As mentioned by the TA, you can postpone this problem for a week.
- 4/21/04 A misprint early in the text: p. 26, should be gcd(15,42) = 3. (Thanks to AC.)
- 4/21/04 An additional misprint on Handout D: The problem on p. 55 was supposed to be E1. (Thanks to JL.)
- 4/19/04 There were several misprints in the first posting of Assignment 3 (Handout D); corrections have been made here and in the paper handout. (Thanks to VS.)
- 4/16/04 Office hours Monday 4/19 will be 11:30-12:30.
- 4/16/04 Assignment 3 should be posted soon and will be handed out Monday.
- 4/14/04 On Assignment 2, C-3, the symbols for 1 choose n should be n choose 1 in both parts.
- 4/7/04 On Assignment 1, p. 18, Ex. 2 was done in lecture, so you don't need to hand it in.
- 3/15/04 Enrollment is now closed.