Syllabus and Assignments 

Fall 2007

 

Section Name Problems

1.1

Logic 8(b,d,f), 10, 30(c,f), 32(c,f), 38(b,d)
1.2 Propositional Equivalences 6, 10(b,d), 14, 18, 20
1.3 Predicates and Quantifiers 5, 9, 32, 60; 16, 28, 40,
1.4 Nested Quantifiers 4, 6, 10, 28, 30; 16, 20
1.5 Rules of Inference 4, 6, 10, 19; 2, 13, 16, 20
1.6 Introduction to Proofs 2, 3, 6, 8,  16, 18
1.7 Proof Methods and Strategy 28, 29, 37, 38,
2.1 Sets 1, 5, 7, 17, 18, 21, 23, 28
2.2 Set Operations 4, 6, 8, 10, 18(a, c, e), 29, 30, 32, 37, 38, 51, 53; 25, 50
2.3 Functions 2, 3, 4(b, d), 8, 10, 12, 18, 26, 32, 54, 56, 57; 34
2.4 Sequences and Summations 2, 4, 6, 14, 16;  10, 17, 27
3.1 Algorithms 2, 3, 11, 12, 16, 24
3.2 The Growth of Functions 2, 4, 6, 8, 14, 20, 34, 46, 48, 50
3.3 Complexity of Algorithms 1, 7, 8, 10
3.4 The Integers and Division 9, 16, 17, 26, 31, 32
3.5 Primes and Greatest Common Divisors 4, 10, 13, 15, 16, 20
3.6 Integers and Algorithms 2, 4, 5, 8, 24, 25, 30, 32, 46, 49, 50
3.8 Matrices 1 - 10 (inclusive), 18, 19, 29
4.1 Mathematical Induction 7, 8, 11; 3, 4, 5, 6, 15, 21
4.2 Strong Induction and Well-Ordering 3, 4, 6, 10, 11, 12
4.3 Recursive Definitions and Structural Induction 2, 4, 8, 10, 12, 14, 17, 18, 34, 35, 59
4.4 Recursive Algorithms 8, 10, 14, 26, 29, 37
4.5 Program Correctness 1, 3, 4
5.1 The Basics of Counting 1 - 6 (inclusive), 11, 16, 24, 28, 33, 38
5.2 The Pigeonhole Principle 2, 3, 4, 5, 14, 26
5.3 Permutations and Combinations 1, 4, 7, 10, 15, 20, 27, 30, 33
5.5 Generalized Permutations and Combinations 2, 4, 5, 9, 12, 16, 18, 30, 38, 40
8.1 Relations and their Properties 1, 3, 7, 9, 16, 28; 32
8.2 n-ary Relations and Their Applications 2, 7, 8, 10, 16, 17, 19, 28, 29
8.3 Representing Relations 1, 3, 7, 13, 14, 15, 22, 26, 31
8.4 Closure or Relations (optional) 6, 11, 16, 17, 18, 25, 26 - 29