Lecture Schedule

DATE WEEK LEC TOPIC(S)
TEXTBOOK
8/31
1
1
 Course Intro. Logical statements. Truth tables. De Morgan’s Law. ch. 4.1 & 4.5
9/02
1
2
 Contrapositive. Tautology. Contradiction. Logical equivalences
Goodaire & Parmenter		 ch. 4.5 & 4.7
9/04
1
3
 DNF, CNF and SAT. Quantifiers. ch. 4.6, 4.3
9/07
2
 No class – Labor Day
9/09
2
4
 Quantifiers. ch. 4.3 & 4.4
9/11
2
5
 Operations on sets. De Morgan’s Law of Sets. Venn diagrams. ch. 3.3 – 3.7
9/14
3
6
 Proving set identities. ch.3.9
9/16
3
7
 Proof techniques: direct proof, contradiction, contrapositive. ch. 4.9
9/18
3
8
 The Principle of Induction. ch. 5.1 & 5.2
9/21
4
9
 The Principle of Induction. ch. 5.1 & 5.2
9/23
4
10
 The Principle of Strong Induction. ch. 5.3 – 5.5
9/25
4
11
 The Principle of Strong Induction. ch. 5.4 & 5.5
9/28
5
 Midterm I

Practice Exam solutions
9/30
5
12
 Surjective, injective and bijective functions. ch. 7.2 – 7.4
10/02
5
13
 Composition of functions. Inverse functions. ch. 7.5
10/05
6
14
 Infinite sets. ch. 7.6
10/07
6
15
 Countable sets. Cardinality. ch. 7.6
10/09
6
16
 Uncountable sets. ch. 7.6
10/12
7
17
 A partition of a set. The Rule of Sum. The Rule of Product. ch. 8.2
10/14
7
18
 Permutations and combinations. ch. 8.3
10/16
7
19
 Repetitions. ch. 8.5
10/19
8
20
 The Binomial Theorem and Pascal’s Triangle. ch. 8.4
10/21
8
21
 Combinatorial Proofs. ch. 8.4
10/23
8
 No classes – mid-semester break
10/26
9
22
 Combinatorial Proofs. ch. 8.4
10/28
9
 Midterm II

Practice Exam solutions
10/30
9
23
 The Pigeonhole Principle. ch. 8.6
11/02
10
24
 The Principle of Inclusion-Exclusion. ch. 8.7
11/04
10
25
 The Principle of Inclusion-Exclusion. ch. 8.7
11/06
10
26
 Greatest common divisor. The Euclidean Algorithm. ch. –
11/09
11
27
 Diophantine equations. ch. –
11/11
11
28
 Relations. Equivalence relations. ch. 6.4
11/13
11
29
 Equivalence classes. ch. 6.5
11/16
12
 Review for the exam
11/18
12
 Midterm III

Practice Exam solutions
11/20
12
30
 Congruence classes. Modular Arithmetic. ch. 6.5
11/23
13
31
 Using congruence classes to solve divisibility problems. ch. –
11/25
13
 No classes – Thanksgiving break
11/27
13
 No classes – Thanksgiving break
11/30
14
32
 Fermat’s Little Theorem. ch. –
12/02
14
33
 Fast Exponentiation ch. –
12/04
14
34
 The Chinese Remainder Theorem. ch. –
12/07
15
35
 RSA ch. –
12/09
15
37
 Supremum and infimum of a set. Density of the rational numbers. ch. –
12/11
15
38
 The real numbers. ch. –
12/15 Final Exam, 8:30-11:30am