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HOMEWORK WILL BE COLLECTED ON WEDNESDAYS!

• HW1 due Oct 8: Please read through sections 1.1--1.4 from the text so you know what is there, paying special attention to the examples that are there. Then do the following problems:
  • sections 1.1/1.2: 13, 14(a)(b), 15, 21, 23, 32(a);
  • section 1.3: 5, 6, 8(a)(b)(c), 16(a)(b)(c), 17(a)(b)(c), 23(a)(b), 25(a), 27(a), 30;
  • section 1.4: 20, 21, 25.
• Here is a handout from class on October 7 explaining the formula for counting the number of compositions.
• HW2 due Oct 15: Please read sections 2.1 and 2.2. Then do the following:
  • section 1.4: 12,14,28(a);
  • review problems to Section 1: 6, 8, 16, 27;
  • section 2.1: 1, 3, 5, 8, 9, 10, 14;
• HW3 due Oct 22: You should have read sections 2.1 and 2.2 from the text already. You may want to glance over section 2.3 too but its not that important... When you think you know the logical connectives and their truth tables, and what "logically equivalent" and "logically implies" both mean, do:
  • section 2.2: 12,15,16,17.
  THEN read the proofs of Theorems 2.3, 2.4 and 2.5 from section 2.5, before attempting the following problems:
  • section 2.5: 12,13,14,15,16.
  • review problems to Section 2: 3,15,16.
  FINALLY look at Table 2.21 in section 2.4 and work it what its talking about. Then solve the following problems (mine!):
  • 1. Prove that the square root of 3 is irrational.
  • 2. Determine whether the following statements are True or False. If True you need to supply a complete proof. If False you need to give one counterexample demonstrating that it is False.
    • a) If a and b are rational then a+b is rational.
    • b) If a and b are irrational then a+b is irrational.
    • c) If a is rational and b is irrational then a+b is irrational.
  • 3. Do my question 2 again but replacing all occurences of "plus" with "multiply".
• HW4 due Oct 29: Remember there is a midterm in class on Tuesday Oct 28. Here is a practise midterm and with solutions. The real midterm will cover roughly the same topics and have a similar format. The syllabus for the midterm: all material from chapters 1,2 and 3 (up to and including the material from class on Friday Oct 24). There is also a regular homework due on Wednesday Oct 29 as usual. I'd recommend you do this *before* the midterm as the midterm includes all of chapter 3!!!
  • Read Sections 3.1, 3.2, 3.3 and 3.4.
  • Problems from section 3.1: 2,4,6,19,20.
  • Problems from section 3.2: 2,3,7,8,18,19.
  • Problems from section 3.3: 4,5,7.
  • Supplementary problems to chapter 3: 1.
• HW5 due Nov 5: Read sections 4.1 and 4.3.
  • Problems from section 3.4: 6,7,8.
  • Supplementary problems to chapter 3: 8(a)(b)(c),16.
  • Problems from section 4.1: 1,5,19,24.
  • Problems from section 4.2: 12.
• HW6 due Nov 12: Reread section 4.3 and start reading sections 4.4 and 4.5. We'll be working on those all of next week, and its helpful to have a clue in advance!
  • Problems from section 4.1: 23.
  • Problems from section 4.2: 6 (use mathematical induction!), 14.
  • Problems from section 4.3: 14,15,16,17,18 (you may need to read some of section 4.3 to work out what these questions are asking -- I'm not going to cover this in class but you should be able to work it out!)
  • Supplementary problems to chapter 4: 3,6.
• HW7 due Nov 19: There's a midterm on Tuesday next week. This will be on all the material up to and including section 4.4 in the text. Here is a practise midterm with solutions. Make sure when you are preparing for this midterm that you go over all the important definitions (including the newish definitions of "divisible by", "greatest common divisor", "prime number" from chaper 4). There will definitely be some proofs by induction on the test too! Homework is due on Wednesday as usual. Its longer than last week so start early and DO THE HOMEWORK BEFORE THE MIDTERM!
  • Problems from section 4.3: 2,3,4,5,9,12,13.
  • Problems from section 4.4: 1,4,19,21.
  • Problems from section 4.5: 1,2.
  • Supplementary problems to chapter 4: 9,10,17.
• HW8 due MONDAY Dec 1: In the last two weeks of term I'm going to change the routine slightly. On Monday and Tuesday of 9th week we'll be doing new stuff. On Wednesday of 9th week I'll devote the class to answering homework questions on this set of problems. You can either turn HW8 in on Wednesday next week OR on Monday of 10th week (after Thanksgiving). Also in 10th week I will use the Tuesday class as a regular class not as a homework-solving session.
  • For this homework (which is the last one of term!) please read Section 5.6 plus whatever you find you need from Sections 5.1--5.5 for that to make sense.
  • Problems from section 5.2: 1,15,20.
  • Problems from section 5.3: 1,2,3,4.
  • Problems from section 5.5: 2,3,4.
  • Problems from section 5.6: 1,4,8,9,10,15.
• PRACTISE FINAL and PRACTISE FINAL WITH SOLUTIONS.