## CS 1200: Discrete Math

#### Summer 2017

This course is meant as a first introduction to discrete mathematics with emphasis on its use in computer science. Topics include: Propositional and Predicate Logic, Proof Techniques, Sequences, Mathematical Induction, Set Theory, Functions and Relations, Counting and Probability, and Graph Theory.

### Schedule

Subject Recommended Exercises
Week 1 Lecture 1
6/5
Syllabus
§1.1: Variables and Statements
§1.1: 5, 10, 12, 13
Lecture 2
6/6
§1.2, 1.3: The Language of Sets, Relations, and Functions §1.2: 1, 2b, 3, 4e, 6, 7ae, 8ad, 9b, 11
§1.3: 2, 3, 7, 8, 9, 11, 13, 19
Lecture 3
6/7
§2.1: Propositional Logic I §2.1: 1, 5a, 6, 11, 14, 15, 16, 17, 21, 25, 27, 29, 36, 37, 40, 43, 52
Lecture 4
6/8
§2.2: Propositional Logic II §2.2: 1, 5, 9, 12, 13b, 16, 20ab, 21, 22a, 23a, 24, 29, 32, 33, 34, 37, 38, 39, 40, 42, 44, 46d, 47, 49, 50a
Lecture 5
6/9
§2.3: Propositional Logic III §2.3: 3, 6, 8, 11, 12a, 14, 22, 23, 26, 28, 36, 37, 38ad, 39, 40, 41, 44
Week 2 Lecture 6
6/12
§3.1-3.2: Predicate Logic I §3.1: 1abd, 3, 4ac, 8ac, 10, 11, 18abe, 23ab, 24a, 27ab
§3.2: 1, 3c, 7, 8, 18, 19, 28, 29, 37, 38, 43, 45, 47, 48
Lecture 7
6/13
§3.3: Predicate Logic II §3.3: 3ab, 7, 10acf, 13, 16, 20ab, 24a, 27, 28, 38, 39, 40ab, 44ac, 50, 51, 55, 56, 59, 61
Lecture 8
6/14
§3.4: Predicate Logic III §3.4: 2, 6, 8, 9, 13, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 34
Lecture 9
6/15
§4.1: Proof Methods I §4.1: 2, 11, 13, 14, 16, 17, 22, 23, 31, 33, 34, 35, 41, 44, 47, 50, 55
§4.2: 4, 7, 10, 11, 18, 19, 21, 23, 24, 28, 31, 35, 38
Lecture 10
6/16
§4.2: Proof Methods I §4.2: 4, 7, 10, 11, 18, 19, 21, 23, 24, 28, 31, 35, 38
Week 3 Lecture 11
6/19
§4.3-4.4: Proof Methods II §4.3: 12, 13, 14, 15, 18, 24, 28, 34, 38, 43, 44
§4.4: 3, 7, 18, 19, 20, 22, 23, 25, 28, 32, 35, 47
Lecture 12
6/20
§4.6,4.8: Proof Methods III §4.6: 5, 7, 10, 11, 15, 17, 21, 22, 23, 34
§4.8: 4, 5, 6, 7, 9, 13, 16, 23ab, 24b, 25ac, 26
Exam 1
6/21
§1.1-1.3, 2.1-2.3, 3.1-3.4, 4.1-4.4, 4.6, 4.8
Lecture 13
6/22
§5.1: Sequences §5.1: 14, 16, 27, 28, 37, 38, 40, 41, 51, 52, 55, 58, 59, 61, 69, 70, 80ab, 81, 83, 84, 86, 88, 89
Lecture 14
6/23
§5.2: Mathematical Induction I §5.2: 1, 2, 3, 4, 5, 26
Week 4 Lecture 15
6/26
§5.2: Mathematical Induction II §5.2: 6, 7, 8, 10, 13, 14, 20, 23, 28, 29, 32
Lecture 16
6/27
§5.3: Mathematical Induction III §5.3: 1, 3, 6, 8, 10, 13, 16, 17, 24, 25, 29, 30
Lecture 17
6/28
§6.1: Set Theory §6.1: 1af, 2, 3, 6, 7c, 10, 11, 13dfi, 14b, 15, 17ad, 18, 21, 23, 27bd, 29, 31, 32ab, 35bd, 36, 37
Lecture 18
6/29
§6.2: Set Properties §6.2: 1, 3, 4, 6, 7, 8, 11, 15, 18, 19, 20, 21, 22, 26, 34, 36
Lecture 19
6/30
§7.1-7.2: Functions §7.1: 1, 3, 4a, 5abd, 6, 7, 9, 11ab, 12, 14, 15, 18, 21, 25a, 26a, 28ab, 29a, 30, 33, 35, 37, 38, 43, 44, 51abc
§7.2: 1, 6, 7a, 8, 9, 10, 12, 13ab, 15, 21, 22, 28, 29, 36, 37, 38, 42, 43, 44, 45, 49
Week 5 Lecture 20
7/3
§8.1-8.2: Relations §8.1: 1a, 3, 4ab, 5ab, 8c, 9, 10, 12, 14, 15, 19, 20, 21, 23
§8.2: 1, 3, 5, 6, 9, 10, 11, 12, 14, 23, 25, 26, 28, 34, 35, 37, 43, 44, 51, 53
Holiday
7/4
Lecture 21
7/5
§8.3: Equivalence Relations §8.3: 1, 3, 5, 6, 7, 8, 9, 10, 15, 18, 19a, 21, 22, 23, 24, 25, 28, 29, 30, 34, 36, 37, 39, 44abd
Lecture 22
7/6
§8.5: Partial Order Relations §8.5: 1ab, 2, 3, 4, 5, 6, 8, 9, 10, 11abd, 13, 14a, 16a, 17ab, 18, 19, 21, 22, 24, 25, 26, 27, 30, 31, 32, 35, 37, 38, 39, 42, 44, 46, 47, 49, 50a
Review
7/7
Week 6 Exam 2
7/10
§5.1-5.3, 6.1, 7.1-7.2, 8.1-8.3, 8.5
Lecture 23
7/11
§8.4: Modular Arithmetic and the RSA Algorithm
Lecture 24
7/12
§9.1-9.2 Counting & Probability I §9.1: 2, 3, 5, 7, 12, 13ab, 14, 16, 18, 19, 20, 21, 24, 25, 26, 28, 29, 31, 32
§9.2: 1, 4, 6, 7, 8, 9, 10, 11ab, 12, 13ab, 14, 15, 16, 18, 19, 22, 24, 27, 28, 32, 34, 37a, 38, 39, 47
Lecture 25
7/13
§9.3-9.4 Counting & Probability II §9.3: 1, 3, 4, 6, 8, 9, 11, 13, 14, 15, 16, 25, 29, 31, 32, 33, 34, 35, 37
Lecture 26
7/14
§9.4 Counting & Probability III §9.4: 1, 3, 5, 9, 12, 13, 14, 17, 19, 22, 23, 26, 28, 29, 31
Lecture 27
7/17
§9.5-9.6 Counting & Probability IV §9.5: 1, 3, 5ab, 6, 7, 9, 12, 13ad, 15, 16, 19, 21, 22, 23, 24, 25, 27
§9.6: 1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 18, 20
Lecture 28
7/18
§10.1-10.2 Graph Theory I §10.1: 1, 3, 6, 8, 9, 12, 13, 15, 17, 18, 22, 23, 27, 28, 29, 36, 37abef, 39, 40b, 42
§10.2: 1, 3, 4, 6, 8ac, 9, 12, 17, 18, 19, 22, 23, 24, 26, 30, 31, 33, 36
Lecture 29
7/19
§10.3, 10.5 Graph Theory II §10.3: 1a, 2a, 3, 4acd, 6, 7, 8a, 9, 10abfi, 12, 19, 20
§10.5: 1a, 2a, 3, 4, 7a, 8-16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30
Lecture 30
7/20
§10.6-10.7 (not Dijkstra's algorithm) Graph Theory III §10.6: 1, 3-12, 15, 16, 18, 20ac
§10.7: 1, 3, 5-8, 9, 21, 29
Review
7/21
Exam 3
7/24
§9.1-9.6, 10.1-10.3, 10.5-10.7 (not Dijkstra's algorithm)
Review
7/25
Review
7/26
Final Exam
7/27
§1.1-1.3, 2.1-2.3, 3.1-3.4, 4.1-4.4, 4.6, 4.8, 5.1-5.3, 6.1, 7.1-7.2, 8.1-8.3, 8.5, 9.1-9.6, 10.1-10.3, 10.5-10.7 (not Dijkstra's algorithm)