Homework Exercises and Assignments

Key to ASCII notation

  • 'oo' = ∞ = "infinity"
  • '{}' = ∅ = "empty set"
  • '(-' = ∈ = "element of"
  • '(_' = ⊆ = "subset of" (not strict)
  • 'u' = ∪ = "union"
  • 'n' = ∩ = "intersection"
  • '~L' = L = "complement of L"
  • '-]' = ∃ = "there exists"
  • '\-/' = ∀ = "for all"
  • '/\' = ∧ = "and"
  • '\/' = ∨ = "or"
  • '->' = → = "implies"
  • '<->' = ↔ = "if and only if (iff)"
  • '!' = ¬ = "not", e.g., 'a != b' = a ≠ b = "a is not equal to b", 'w !(- L' = w ∉ L = "w is not an element of L", etc.
  • '\sum' = ∑ = summation sign
  • '\prod' = ∏ = product sign
  • '\Sigma' = Σ = capital greek letter Sigma, '\delta' = δ = lowercase greek letter delta, etc.
  • '|_x_|' = ⌊x⌋ = floor(x)
  • '|^x^|' = ⌈x⌉ = ceiling(x)
  • '_' indicates a subscript, e.g., 'q_1' = q1
  • '^' indicates a superscript, e.g., 'n^2' = n2
  • curly braces '{}' surround longer subscripts/superscripts, e.g., '\sum_{0 <= i <= n} 2^{i/2}' = ∑0 ≤ i ≤ n 2i/2

Exercises

Exercises are to be completed individually, to help you cement your own understanding of the course material.

Please use this Exercise Cover Sheet for all your exercises — print it double-sided and attach it to the front of your work.

Homework Exercise 1 (due Wed 17 Sep)

Exercise 1 HTML handout / Exercise 1 ASCII handout
Exercise 1 marking scheme (ASCII) — including marker's comments

Homework Exercise 2 (due Wed 24 Sep)

Exercise 2 HTML handout / Exercise 2 ASCII handout
Exercise 2 marking scheme (ASCII) — including marker's comments

Homework Exercise 3 (due Wed 15 Oct)

Exercise 3 HTML handout / Exercise 3 ASCII handout
Exercise 3 marking scheme (ASCII) — including marker's comments

Homework Exercise 4 (due Wed 22 Oct)

Exercise 4 HTML handout / Exercise 4 ASCII handout
Exercise 4 marking scheme (ASCII) — including marker's comments

Homework Exercise 5 (due Wed 12 Nov)

Exercise 5 HTML handout / Exercise 5 ASCII handout
Exercise 5 marking scheme (ASCII) — including marker's comments

Homework Exercise 6 (due Wed 19 Nov)

Exercise 6 HTML handout / Exercise 6 ASCII handout
Exercise 6 marking scheme (ASCII) — including marker's comments

Assignments

Assignments are to be completed in groups of no more than four individuals. You are strongly encouraged to find two or three partners and to work out the solutions together, rather than try to split up the work so that each person is "responsible" for one or two questions only. Remember that this is supposed to be the point of these group assignments: to give you a chance to work on problems together, so that you each learn more than by doing it yourself.
Also, splitting up the work may save time in the short term, but not in the long term: since everyone will be expected to understand how to solve each question for the term test that follows each assignment (as well as the related questions on the final exam), you will each have to go back and review each solution anyway. More importantly, as you well know, there is a big difference between reading someone else's solution and working out a solution by yourself: you learn much more by "solving" than by "reading".
Nevertheless, I leave it up to each student to decide for themselves: this is for your own benefit, and you are free to take advantage of it or not, as you see fit.

If you would like to work with someone but you don't know anybody that could be your partner, simply post a "request for partner" message on the course bulletin board — and keep an eye out for similar posts by other students.

Have a look at this article about coping with team problems, to learn some strategies you can use if you run into difficulties with your group.

Please use this Assignment Cover Sheet for all your assignments — print it double-sided and attach it to the front of your work. You should submit only one copy of your solution that lists each member of your group.

Please submit a peer evaluation report along with each assignment — each student must do this individually, as outlined in the document.

Homework Assignment 1 (due Wed 1 Oct)

Assignment 1 HTML handout / Assignment 1 ASCII handout (updated at 8:56 on Tue 23 Sep)
Assignment 1 marking scheme (ASCII) — including marker's comments

Homework Assignment 2 (due Wed 29 Oct)

Assignment 2 HTML handout / Assignment 2 ASCII handout (updated at 10:41 on Mon 20 Oct)
Assignment 2 marking scheme (ASCII) — including marker's comments

Homework Assignment 3 (due Wed 26 Nov)

Assignment 3 HTML handout / Assignment 3 ASCII handout (updated at 17:18 on Tue 18 Nov)
Assignment 3 marking scheme (ASCII) — including marker's comments (see also the counter-examples)
Assignment 3 counter-examples (PDF)