Discrete Mathematics: A Brief Introduction (for Salisbury CC) 1st edition

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Kathleen Shannon
Publisher: Custom Labs

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  • Chapter 0: What is Discrete Mathematics with Examples
    • 0.0: What is Discrete Mathematics?
    • 0.1: Logistic Population Models and the Interplay between Discrete and Continuous Systems and Models (3)
    • 0.2: The Königsburg Bridge Problem and the Party Problem
    • 0.3: Some Useful Definitions (2)

  • Chapter 1: Preliminaries 1: Sets
    • 1.0: Sets, subsets and set operations: Unions, Intersections, Complements (14)
    • 1.1: Set Equality: Truth Tables, Venn Diagrams and Element Chasing (12)
    • 1.2: Set Identities: Associate, Commutative, Absorptive; Identity Laws; DeMorgan's Laws (11)
    • 1.3: Functions and Relations (10)
    • 1.4: Relations on a set A and their properties (15)
    • 1.5: Equivalence Relations and modular arithmetic (16)
    • 1.6: Partial Orderings and Hasse Diagrams (21)
    • 1: Chapter 1 Review

  • Chapter 2: Preliminaries 2: Logic and Proof
    • 2.0: What is Proof; Conditional Connectives, Converses and Contrapositives (25)
    • 2.1: Mathematical Induction (16)
    • 2.2: More Mathematical Induction and Strong Induction (20)
    • 2.3: Universal and Existential Quantifiers (4)
    • 2.4: Recurrence Relations (42)
    • 2: Chapter 2 Review

  • Chapter 3: Counting (with Discussions of Discrete Probability)
    • 3.0: Introduction: What is counting? (22)
    • 3.1: Ordered Samples with and without Repetition, Permutations (20)
    • 3.2: Unordered Samples without Repetition: Subsets, Pascal's Triangle and the Binomial Theorem (14)
    • 3.3: Unordered Samples with Repetition: Multisets (Optional) (15)
    • 3.4: The Principle of Inclusion and Exclusion (12)
    • 3.5: Wrap up on Discrete Probability (3)
    • 3: Chapter 3 Review

  • Chapter 4: Trees and Other Graphs
    • 4.0: Some Definitions and Uses: Graphs, Multigraphs, Network Problems, Transportation Problems (3)
    • 4.1: Graphs and Cycles: Adjacency Matrices, the Königsburg Bridge Problem and Euler Cycles (6)
    • 4.2: Trees and Spanning Trees: Spanning Tree Algorithm and the Daisy Chain Theorem (9)
    • 4.3: Greedy Algorithms: Minimal spanning trees, shortest paths, Prim's Algorithm, and Dijkstra's Algorithm (17)
    • 4.4: Binary Trees: Search Algorithms, Reverse Polish Notation (28)
    • 4.5: Planar Graphs and Euler's Theorem (7)
    • 4: Chapter 4 Review

  • Chapter 5: Introduction to Propositional Calculus, Boolean Algebra and Digital Logic Gates
    • 5.0: Set Theory, Propositional Calculus and Boolean Algebra, what's the difference?
    • 5.1: Propositional Calculus (28)
    • 5.2: Boolean Algebra (18)
    • 5.3: Digital Logic Gates (11)
    • 5.4: Karnaugh Maps: Simplifying Boolean Expressions (15)
    • 5: Chapter 5 Review

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Group Quantity Questions
Chapter 0: What is Discrete Mathematics with Examples
0.1 3 PR.001 PR.001a PR.003
0.3 2 PE.002 PR.001
Chapter 1: Preliminaries 1: Sets
1.0 14 PE.001 PE.002 PE.002a PE.003 PE.004 PE.005 PE.006 PE.007a PE.007b PE.007c PE.007d PE.008 PE.015-018 WCDE.002
1.1 16 PE.000 PE.000a PE.000a.z PE.000b PE.001a PE.001a.z PE.001b PE.001b.z PE.001f PE.001f.z PE.002a PE.002b PE.002f PE.003a PE.003b PE.003f
1.2 11 PE.000 PE.002f PE.003 PE.003a PE.003b PE.003c PE.003d PE.003e PE.003v PE.005a PE.005b
1.3 10 PE.001 PE.002a PE.003 PE.005 PE.005a PE.005b PE.006 PE.007 PE.008 PE.009
1.4 15 PE.001a PE.001b PE.001c PE.001d PE.001e PE.001f PE.001g PE.001h PE.001i PE.001j PE.001k PE.002 PE.002a WCDE.001 WCDE.002
1.5 16 PE.001a PE.001b PE.001c PE.001d PE.001d.alt PE.002a PE.002b PE.003 PE.004 PE.005 PE.006 PE.007 PE.008 PE.009 PE.010 PE.011
1.6 21 PE.001 PE.002 PE.002.both PE.002.hasse PE.003 PE.004 PE.004a PE.005 PE.005.both PE.006 PE.006.both PE.006.hasse PE.007 PE.008 PE.009 PE.010 PE.010.both PR.002 PR.003 PR.006 PR.007
Chapter 2: Preliminaries 2: Logic and Proof
2.0 25 PE.001a PE.001b PE.001c PE.001d PE.001e PE.001f PE.001g PE.001h PE.001i PE.001j PE.001k PE.001l PE.001m PE.001n PE.002 PE.003 PE.006 PE.007 PE.008 PE.009 PE.010 PR.001 PR.002 PR.003 PR.004
2.1 16 PE.001 PE.002 PE.003 PE.004 PE.005 PE.006 PE.007 PE.008 PE.009 PE.010 PE.011 PE.012 PE.013 PE.014 PR.001 PR.002
2.2 20 PE.001a PE.001b PE.001b.rand PE.001c PE.001d PE.001e PE.001f PE.001f.rand PE.001g PE.001h PE.002 PE.003 PE.004 PE.005 PE.006 PR.001 PR.002 PR.003 PR.004 PR.005
2.3 4 PE.001 PE.002 PE.003 PE.003.mc
2.4 43 PE.000 PE.000 PE.000a PE.000b PE.000c PE.001 PE.001a PE.001b PE.001c PE.001d PE.001e PE.001f PE.002 PE.002.rand PE.003 PE.003.rand PE.004 PE.004.rand PE.005 PE.005.rand PE.006 PE.006.rand PE.007 PE.007.rand PE.008 PE.009 PE.011 PE.013 PE.015 PE.017 PE.019 PE.021 PR.001 PR.002 PR.003 PR.004 PR.005 PR.006 PR.007 PR.008 PR.010 PR.011 PR.012 PR.013
Chapter 3: Counting (with Discussions of Discrete Probability)
3.0 22 PE.001 PE.002 PE.003 PE.005 PE.006 PE.007 PE.008 PE.008-009 PE.008-009.numerical PE.010 PE.011 PE.012 PR.001 PR.002 PR.003 WCDE.001 WCDE.002 WCDE.003 WCDE.004 WCDE.005 WCDE.006 XP.001
3.1 20 PE.001 PE.002 PE.003 PE.004 PE.005 PE.006 PE.007 PE.008 PE.009 PE.010 PE.011-018 PE.012 PE.013 PE.015 PE.017 PE.019 PE.021 PE.023 PE.024 PE.026
3.2 14 PE.001 PE.003 PE.003and012r PE.003r PE.004 PE.005 PE.006 PE.009 PE.009and011 PE.011 PE.012r PE.015 PR.001 XP.001
3.3 15 PE.001 PE.001-004 PE.002 PE.005 PE.005-006 PE.007 PE.008 PE.009 PE.010 PE.012 PE.013 PR.001 PR.001-002 PR.002-003 PR.003
3.4 12 PE.000 PE.002 PE.002a PE.002l PE.002r PE.003 PE.004 PE.005 PE.006r PE.008r PE.012r PR.003
3.5 3 PE.003 PE.004 PE.005
Chapter 4: Trees and Other Graphs
4.0 3 PE.002 PE.003 PE.004
4.1 6 PE.001 PE.002 PE.003 PE.004 PE.005 WCDE.003
4.2 9 PE.004 PE.005 PE.006 PE.007 PE.008 PE.009 PE.010 PE.011 PR.003
4.3 17 PE.001a PE.001b PE.001c PE.002a PE.002b PE.002c PE.003d PE.003e PE.003f PE.004d PE.004e PE.004f PE.005a PE.005b PE.006d PE.006e PE.007b
4.4 28 PE.001a PE.001b PE.001c PE.001d PE.002a PE.002b PE.002c PE.002d PE.003a PE.003b PE.003c PE.003d PE.004a PE.004b PE.004c PE.004d PE.005 PE.006 PE.007 PE.009a PE.009b PE.009c PR.001 PR.002 PR.003 PR.005 PR.006 PR.007
4.5 7 PE.001 PE.002 PE.003 PE.003.explanation PE.004 PR.001 PR.002
Chapter 5: Introduction to Propositional Calculus, Boolean Algebra and Digital Logic Gates
5.1 28 PE.001 PE.002 PE.003 PE.004 PE.005 PE.007 PE.008 PE.009 PE.010 PE.011 PE.014b PE.027 PE.027.explanation PE.028 PE.028.explanation PE.029 PE.029.explanation PE.030 PE.030.explanation PE.031.explanation PE.032 PE.032.explanation PE.033 PE.034 PE.035 PE.036 PE.16a PE.17a
5.2 18 PE.001a PE.002 PE.003 PE.004 PE.005 PE.006 PE.007 PE.026 PE.027 PE.14b PE.14b.italics PE.16a PE.17a PR.001 PR.002 PR.002a PR.003 PR.006
5.3 11 PE.001a PE.001a.ms PE.001b PE.001b.ms PE.001c PE.001c.ms PR.002a PR.002b PR.002c PR.002d PR.004
5.4 15 PE.000 PE.011 PE.011.implicants PE.012 PE.012.implicants PE.013 PE.013.implicants PE.014 PE.014.implicants PE.015 PE.015.implicants PE.016 PE.016.implicants PE.018 PE.018.implicants
Total 444 (1)