MATH 126 Recommended Practice Problems
(7th edition of Discrete Mathematics and Its Applications by Rosen)
Sec
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2.1
2.2
8.5
2.3
2.4
2.5
3.2
4.1
4.2
4.3
5.1
5.2
5.3
6.1
6.2
6.3
6.4
6.5
7.1
8.1
8.3
10.1
10.2
10.4
10.5
Section Title
Propositional Logic
Applications of Propositional Logic
Propositional Equivalences
Predicates and Quantifiers
Nested Quantifiers
Rules of Inference
Introduction to Proofs
Proof Methods and Strategy
Sets
Set Operations
Inclusion-Exclusion
Functions
Sequences and Summations
Cardinality of Sets
The Growth of Functions
Divisibility and Modular Arithmetic
Integer Representations and Algorithms
Primes and Greatest Common Divisors
Mathematical Induction
Strong Induction and Well-Ordering
Recursive Definitions and Structural Induction
The Basics of Counting
The Pigeonhole Principle
Permutations and Combinations
Binomial Coefficients and Identities
Generalized Permutations and Combinations
An Introduction to Discrete Probability
Applications of Recurrence Relations
Divide-and-Conquer Algorithms and Recurrence Relations
Graphs and Graph Models
Graph Terminology and Special Types of Graphs
Connectivity
Euler and Hamilton Paths
Exercises
1, 3, 9, 11, 15, 17, 19, 23, 25, 27, 31(a,c,e), 33(a,c,e), 43
1, 3, 5
5, 7, 9(a,c,e), 11(a,c,e), 21, 25, 29, 31, 55
1, 5, 7, 9, 11, 13, 17(a,b,c), 23, 29(a,b), 43, 45, 53
1, 5, 9, 15(a-e), 27, 31, 39, 41
1, 3, 5, 15, 17, 29
1, 7, 11, 13, 15, 19, 21, 23, 39
1, 7, 9, 11, 13, 19, 29, 33
1, 5, 7, 9, 11, 17, 19, 21, 27, 35, 39, 41
3, 7, 17(a), 19, 23, 25, 27, 29, 31, 35, 39, 47, 49, 51, 53, 57(a,b)
1, 3, 5, 7
1, 5, 9, 13, 21, 23, 31, 33, 39, 59, 69, 79
1, 3, 9(a,d,e), 11, 13(a,c,f,h), 15(d), 19
1, 3, 11, 13, 15, 17, 21, 27
1, 3, 5, 7, 9, 13, 17, 21, 25, 27, 29(a,d,f), 33, 35, 45
1, 3, 5, 7, 9, 11, 21, 23, 25, 29, 35
1, 3, 7, 11, 17
1, 3, 11, 13, 15, 17, 25, 27, 29, 33(b,d), 39(b,e,f,i), 49
3, 7, 15, 21, 25, 31, 41, 43, 59, 67
3, 5, 7, 25
1, 3, 5(a,b), 7, 9, 11, 13, 15
1, 3, 11, 15, 17, 23, 25, 27, 29, 33, 35, 47, 49, 53, 55
1, 5, 9, 15, 19, 31, 33, 35
1, 7, 11, 15, 17, 19, 21, 25, 27, 31, 33, 39
3, 5, 7, 9, 15, 19, 31
5, 7, 11, 13, 15(a,b,c), 19, 27, 31, 37
3, 7, 13, 15, 19, 23, 27, 29, 35
3, 7, 9, 11, 19
7, 9, 11, 13, 15, 21
1, 3, 5, 7, 9, 13, 21, 27
1, 3, 5, 9, 17, 21, 23, 35, 37, 41, 43, 49, 57
1, 3, 5, 7, 11
1, 3, 5, 7, 9, 13, 15, 27, 31, 33, 35, 37, 43, 45, 47