# MATH1190.03, Winter 2000Introduction to Sets and Logic

Announcements and assignments will be posted here as they become available.

### Documents

Are now posted outside my office (N625 Ross)

### Exam

There were two questions on the exam that were meant to be challenging: problems 5 (on inverse functions) and 8b (finding all solutions to a congruence). In addition, the calculations in problem 9 (the induction) were a bit complicated (though everyone should have been able to set it up). I was pleased that each of these problems had one or two people who got them right. This material was worth a relatively high proportion of the exam, so I raised each raw final exam score by 16, before computing final grades.

The rest of the problems were essentially straight out of the homework. Though many people did fine on these questions, I was surprised by the number of people who didn't. Even after raising the exam grades the exam scores were pretty low, on average. Despite this, I think the final grades are somewhat higher than would be expected, given the level of understanding demonstrated on the exam. People can thank the relatively high midterm grades for this - see the grade distribution given below.

If people want to see where they went wrong, they are welcome to have a look at their exam, in my office, starting the last week of April (ie. once I am finished all the grading in my other courses). To arrange a time to do so, contact me by e-mail.

```A+  3
A  15
B+ 11
B  27
C+ 23
C  15
D+ 12
D   7
E   1
```

### Raw exam scores

```9 |
9 |
8 |
8 |
7 | 5
7 | 1333
6 | 668
6 | 00012224
5 | 55778999
5 | 00111223333444
4 | 56666666678888999
4 | 00001122223344444
3 | 555556666788888889999999
3 | 01111122244
2 | 57789
2 | 2
1 | 5
1 |
0 |
0 |
```

### Topics Covered

The sections of the text we covered were:
• Section 6.5 (equivalence relations)
• Section 6.1 (relations)
• Section 4.3 (permutations and combinations)
• Section 4.1 (counting)
• Section 3.2 (induction)
• Section 3.1 (direct and indirect proofs)
• Section 2.4 and bits of 2.5 (the Euclidean algorithm and applications, binary representations)
• Section 2.3 congruences
• Section 1.7 (sequences, series, cardinality)
• Section 1.6 (functions)
• Sections 1.4 and 1.5 (set theory)
• Section 1.3 (quantifiers)
• Section 1.2 (equivalences, tautologies, converses, inverses, etc.)
• Section 1.1 (logic, truth tables)