CS/APMA 202: Problem database

Spring 2005

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The question database will be filled in as the course progresses.  Unless otherwise specified, the questions are from the course textbook.

 

Material for the first midterm

Section
 Subject
 Class problems
 Homework problems
 Additional problems
1.1
 Boolean logic
 7, 43, 51-55, 58, 59
 HW 1: 18, 48, 60 2, 4, 9, 13, 14, 19, 22, 29 a,b,c,d, 34, 40, 57
1.2
 Logical equivalences
 10, 23
 HW 2: 19, 35, 39, 50 11, 12, 14, 16, 32, 36, 37, 38, 44, 46, 48, 51
10.3 Logic gates 1, 2, 6 HW 3: 3, 4, 5, 9  
1.3
 Predicates and quantifiers
HW 5: 15, 20, 24, 41 6, 10, 15, 16, 17, 25, 28, 30, 35, 45, 46, 50, 54, 55, 58
1.4
 Nested quantifiers
 20, 24, 30, 31 HW 6: 12, 22, 33, 40 4, 10, 14, 26, 28, 29, 48
1.5
 Methods of proof
 4, 10, 20, 21, 40, 50
 HW 7: 10, 22, 34, 55 2, 6, 8, 13, 33, 38, 43, 48, 53, 60, 62, 63, 70, 72, 74, 76, 77
1.6
 Sets
  2, 4, 5, 9, 13, 14, 16, 17, 20, 21, 22, 25
1.7
 Set operations
 14, 18
 HW 4: 10, 16, 22, 34, 43 2, 4, 5, 11, 21, 23, 27, 37, 44, 46, 49
1.8 Functions 8, 32, 62 HW 8: 17, 36, 61, 64 3, 4, 12, 16, 25, 37, 44, 51, 53, 69, 70

 

Material for the second midterm (above sections are also fair game)

Section
 Subject
 Class problems
 Homework problems
 Additional problems
2.1 Algorithms   HW 11: 9, 24, 26, 34 (no additional problems for the second midterm)
2.2 Growth of Functions 1, 2 HW 12: 10, 14, 17, 20 (no additional problems for the second midterm)
2.4 Integers and division 43, 44, 45, 50, 53 HW 9: 18, 34, 40, 52 5, 7, 12, 18, 21, 28, 34, 40, 52
2.6 Applications of number theory   HW 10: 46, 47 (see note!) 46, 47, (the algorithms for generating keys, encrypting, and decrypting RSA messages)
3.1 Proof strategies 14, 15, 25, 32, 47, 49   6, 20, 22, 26, 34, 38
3.2 Sequences and summations 9, 13, 14 HW 13: 8, 9, 23, 36 6, 8, 10, 17, 19, 24, 31, 33, 34
3.3 Mathematical induction 2, 14, 31 HW 14: 12, 27, 29, 51 6, 13, 16, 28, 31, 38, 40, 48, 50, 56, 71
3.4 Recursive definitions and structural induction 1, 8, 12, 13, 22, 24, 32, 35, 38, 43 HW 15: 11, 27, 44, 59 10, 20, 26, 36, 56, 58, 64
3.6 Program correctness (covered after second midterm) (covered after second midterm) (covered after second midterm)
4.1 Basics of counting 1, 22, 37, 38, 42, 45, 48, 49   3, 7, 8, 12, 14, 16, 18, 24, 32, 34, 36, 46, 54, 56

 

Material for the final (above sections are also fair game)

Section
 Subject
 Class problems
 Homework problems
 Additional problems
3.6 Program correctness      
4.2 Pigeonhole principle 4, 10, 16, 18, 32   3, 6, 12, 14, 22, 24, 40
4.3 Permutations and combinations 3, 11, 40, 42   13, 14, 16, 17, 28, 29, 32, 34, 36, 43
4.4 Binomial coefficients 4, 19, 24, 38   6, 15, 31
5.1 Introduction to discrete probability 6, 10, 16, 28, 30, 40   13, 26, 36, 38
7.1 Relations and their properties     4, 7, 14, 20, 24, 26, 30, 40, 42, 45, 48, 52
7.3 Representing relations 31, 32   2, 7, 13, 14, 15, 22
7.4 Closures of relations 1   8, 10, 15, 19, 20, 23, 24, 26c, 29, 35
7.5 Equivalence relations 1, 5, 8, 32   14, 20, 41, 42, 47, 53
7.6 Partial orderings     1, 2, 6, 10, 16, 29, 30, 37, 41, 42, 45, 56



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