Note: The date for the third midterm has been changed from Friday, May 4 to Wednesday, May 2. The homework that was due on May 2 will be due on Monday, April 30.

Professor: Peter Pacheco
Office: Harney 540
Phone: 422-6630
Email: domain: math.usfca.edu, user: peter
Office Hours: MWF 1:30-2:30, and by appointment

Class mailing list: To sign up click here and type in your preferred email address. The mailing list will then send you an email asking you to confirm that you want to join the list. In order to join, you must reply. You can post messages by sending email to user math300 in domain math.usfca.edu

Course Syllabus

Homework Assignments

1. Homework Assignment 1.
   • Part 1:
     • pp. 7-9: 1abcde, 2bde, 3bcdg, 6ac
     • pp. 15-17: 15bc, 16a, 17, 18af, 19, 21, 22ad, 23bc, 24b
     There is no part (e) for number 6. So you should just do 6ac. Part 1 is due at the beginning of class on Friday, January 26. Here's a key.
   • Part 2:
     • pp. 15-17: 25bc (simplify your answer), 26fg, 27ab, 28b, 32i (don't use a truth table), 33a, 34a (don't use a truth table), 36a, 37a.
     For 32i and 34a, you can use any of the tautologies in section 1.2 and any of the tautologies we proved in class (except, of course, those that you need to prove). Part 2 is due at the beginning of class on Monday, January 29. Here's a key.
   • Part 3:
     • pp. 23-24: 41abce, 50abc, 51, 54ab
     Part 3 is due at the beginning of class on Wednesday, January 31. Here's a key.
2. Homework assignment 2.
   • Read the discussion of hidden quantifiers which runs from the middle of page 19 to the top of page 20. Note the list of errata contains a change to page 19.
   • Part 1:
     • pp. 23-24: 42, 43, 45, 47, 52ace
     This is due on Friday, February 2. Here's a key.
   • Part 2:
     • pp. 30-31: 56, 57, 58 (the definition of divides is on p. 22), 59ab, 60 (you can use the fact that if 2 divides mn, then 2 divides m or 2 divides n).
     Your answers should be written in idiomatic English. Make sure you use complete sentences. This is due on Monday, February 5. Here's a key.
   • Part 3:
     • Prove that the integer n is even iff -n is even.
     • Prove that if n is an integer, then there exists an integer k such that n = 2k+1 iff there exists an integer m such that n = 2m - 1.
     • pp. 30-31: 62, 63, 67, 70
     • pp. 33-34: 78, 79
     Your answers should be written in idiomatic English. Make sure you use complete sentences. This is due on Wednesday, February 7. Here's a key.
3. Homework Assignment 3
   • Part 1:
     • pp. 33-34: 80, 82, 84, 88
     For the problems that require a proof, use proof by contradiction. For this assignment and all future assignments, your answers should be written in idiomatic English. Make sure you use complete sentences. This is due on Friday, February 9. Here's a key.
   • Part 2:
     • Prove that multiplication of rational numbers is well-defined.
     • pp. 33-34: 89
     • pp. 39-40: 94, 95, 96ab
     These are due on Monday, February 12. Here's a key.
   • Part 3:
     • pp. 39-40: 99, 101, 102
     These are due on Wednesday, February 14. Here's a key.
4. Homework Assignment 4
   • Part 1. Here's a key.
   • Part 2. Here's a key.
5. Homework Assignment 5:
   • pp. 44-45: 5, 7, 8, 9, 10abefi, 11e
   • pp. 52-54: 21aei, 26, 27, 28ab
   These are due on Wednesday, February 28. Here's a key.
6. Homework Assignment 6:
   • Part 1:
     • pp. 44-45: 17, 20
     • pp. 52-54: 22, 23, 29b, 30, 39
     These are due on Friday, March 2. Here's a key.
   • Part 2:
     • pp. 52-54: 31, 32a, 35b, 40a
     • pp. 59-60: 53, 54, 55, 56
     These are due on Monday, March 5. Here's a key.
   • Part 3. Here's a key
7. Homework Assignment 7:
   • Part 1:
     • pp. 52-54: 44c, 45b, 46a
     • pp. 59-60: 61, 68, 71
     Here's a key
   • Part 2:
     • pp. 73-76: 1aegkq
     These are due on Wednesday, March 21 (not Monday, March 19, as originally scheduled). Here's a key
8. Homework Assignment 8:
   • Part 1:
     • pp. 73-76: 2, 8, 10, 11, 12
     These are due on Friday, March 23. Here's a key
   • Part 2. Here's a key
   • Part 3:
     • pp. 82-83: 22, 26, 30, 36
     Here's a key
9. Homework Assignment 9:
   • Part 1:
     • pp. 82-83: 24, 25, 37ab
     These are due on Friday, March 30. Here's a key
   • Part 2:
     • pp. 82-83: 17, 20, 23, 29ab
     These are due on Monday, April 2. Here's a key
   • Part 3:
     • pp. 90-92: 41, 54, 55, 57
     These are due on Wednesday, April 11. Here's a key
10. Homework Assignment 10:
    • Part 1:
      • pp. 90-92: 51, 52, 53, 67
      • pp. 107-108: 4abc, 5abc, 6
      These are due on Friday, April 13. Here's a key
    • Part 2:
      • pp. 107-108: 7abc, 8, 16
      • pp. 114-116: 17abc, 18ab, 24ae
      These are due on Monday, April 16. Here's a key
    • Part 3. Here's a key
11. Homework Assignment 11
    • Part 1. Here's a key
    • Part 2. Here's a key
    • Part 3. Here's a key
12. Homework Assignment 12
    • Part 1. Here's a key
    • Part 2. Here's a key
13. Homework Assignment 13
    • Part 1. Here's a key
    • Part 2. Here's a key
14. Some recommended homework problems. Here's a key

Additional Information

• A table of tautologies and contradictions (updated 2/7)
• A list of errata. This will be updated when I find an error.
• A key to the first midterm
• A key to the second midterm
• A key to the third midterm
• A list of topics for the final exam