Discrete Mathematics with Applications 5th edition

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Susanna S. Epp
Publisher: Cengage Learning

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  • Chapter 1: Speaking Mathematically
    • 1.1: Variables (4)
    • 1.2: The Language of Sets (4)
    • 1.3: The Language of Relations and Functions (5)
    • 1.4: The Language of Graphs (3)

  • Chapter 2: The Logic of Compound Statements
    • 2.1: Logical Form and Logical Equivalence (12)
    • 2.2: Conditional Statements (13)
    • 2.3: Valid and Invalid Arguments (9)
    • 2.4: Application: Digital Logic Circuits (6)
    • 2.5: Application: Number Systems and Circuits for Addition (9)

  • Chapter 3: The Logic of Quantified Statements
    • 3.1: Predicates and Quantified Statements I (7)
    • 3.2: Predicates and Quantified Statements II (9)
    • 3.3: Statements with Multiple Quantifiers (9)
    • 3.4: Arguments with Quantified Statements (6)

  • Chapter 4: Elementary Number Theory and Methods of Proof
    • 4.1: Direct Proof and Counterexample I: Introduction (8)
    • 4.2: Direct Proof and Counterexample II: Writing Advice (6)
    • 4.3: Direct Proof and Counterexample III: Rational Numbers (12)
    • 4.4: Direct Proof and Counterexample IV: Divisibility (20)
    • 4.5: Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem (16)
    • 4.6: Direct Proof and Counterexample VI: Floor and Ceiling (11)
    • 4.7: Indirect Argument: Contradiction and Contraposition (10)
    • 4.8: Indirect Argument: Two Famous Theorems (4)
    • 4.9: Application: The Handshake Theorem (13)
    • 4.10: Application: Algorithms (15)

  • Chapter 5: Sequences, Mathematical Induction, and Recursion
    • 5.1: Sequences (15)
    • 5.2: Mathematical Induction I: Proving Formulas (7)
    • 5.3: Mathematical Induction II: Applications (7)
    • 5.4: Strong Mathematical Induction and the Well-Ordering Principle for the Integers (4)
    • 5.5: Application: Correctness of Algorithms (2)
    • 5.6: Defining Sequences Recursively (9)
    • 5.7: Solving Recurrence Relations by Iteration (7)
    • 5.8: Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients (6)
    • 5.9: General Recursive Definitions and Structural Induction (5)

  • Chapter 6: Set Theory
    • 6.1: Set Theory: Definitions and the Element Method of Proof (9)
    • 6.2: Properties of Sets (9)
    • 6.3: Disproofs and Algebraic Proofs (10)
    • 6.4: Boolean Algebras, Russell's Paradox, and the Halting Problem (6)

  • Chapter 7: Properties of Functions
    • 7.1: Functions Defined on General Sets (9)
    • 7.2: One-to-One, Onto, and Inverse Functions (9)
    • 7.3: Composition of Functions (8)
    • 7.4: Cardinality with Applications to Computability (5)

  • Chapter 8: Properties of Relations
    • 8.1: Relations on Sets (7)
    • 8.2: Reflexivity, Symmetry, and Transitivity (11)
    • 8.3: Equivalence Relations (9)
    • 8.4: Modular Arithmetic with Applications to Cryptography (13)
    • 8.5: Partial Order Relations (9)

  • Chapter 9: Counting and Probability
    • 9.1: Introduction (13)
    • 9.2: Possibility Trees and the Multiplication Rule (15)
    • 9.3: Counting Elements of Disjoint Sets: The Addition Rule (15)
    • 9.4: The Pigeonhole Principle (14)
    • 9.5: Counting Subsets of a Set: Combinations (11)
    • 9.6: r-Combinations with Repetition Allowed (7)
    • 9.7: Pascal's Formula and the Binomial Theorem (16)
    • 9.8: Probability Axioms and Expected Value (8)
    • 9.9: Conditional Probability, Bayes' Formula, and Independent Events (10)

  • Chapter 10: Theory of Graphs and Trees
    • 10.1: Trails, Paths, and Circuits (12)
    • 10.2: Matrix Representation of Graphs (4)
    • 10.3: Isomorphisms of Graphs (4)
    • 10.4: Trees: Examples and Basic Properties (6)
    • 10.5: Rooted Trees (5)
    • 10.6: Spanning Trees and a Shortest Path Algorithm (4)

  • Chapter 11: Analysis of Algorithm Efficiency
    • 11.1: Real-Valued Functions of a Real Variable and Their Graphs
    • 11.2: O-, Ω-, and Θ-Notations
    • 11.3: Application: Analysis of Algorithm Efficiency I
    • 11.4: Exponential and Logarithmic Functions: Graphs and Orders
    • 11.5: Application: Analysis of Algorithm Efficiency II

  • Chapter 12: Regular Expressions and Finite-State Automata
    • 12.1: Formal Languages and Regular Expressions
    • 12.2: Finite-State Automata
    • 12.3: Simplifying Finite-State Automata


Known for its accessible, precise approach, Susanna Epp's Discrete Mathematics With Applications, 5th Edition, introduces discrete mathematics with clarity and precision. Coverage emphasizes the major themes of discrete mathematics as well as the reasoning that underlies mathematical thought. Students learn to think abstractly as they study the ideas of logic and proof. While learning about logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that ideas of discrete mathematics are essential to and underlie today's science and technology. The author's emphasis on reasoning provides a foundation for computer science and upper-level mathematics courses.

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EP - Expanded Problem


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Group Quantity Questions
Chapter 1: Speaking Mathematically
1.1 4 002 004 006 011 013
1.2 4 004 005 008 009 012 015
1.3 5 002 004 005 006 008 013 014 017
1.4 3 002 004 009
Chapter 2: The Logic of Compound Statements
2.1 12 002 005 007 008 009 013 015 017 019 022 026 028 029 033 034 035 037 042 043 045 045.EP 048 049 052
2.2 13 004 008 013 015 017 018 020_022_023b 020_022_023c 020_022_023e 020_022_023g 021 021.EP 025 030 033 035 038 039 040 041 043 045 046 048 050
2.3 9 002 009 011 015 019 023 028 029 030 031 032 038 040.MI 042
2.4 6 002 004 006 008 010 012 014 015 019 021 024 027 031
2.5 9 002 003 005 006 008 008.EP 009 012 013 014 016 018 020 024 025 026 028 030 031 034 035 036 039 040 042 043 044 045 045.EP
Chapter 3: The Logic of Quantified Statements
3.1 7 004 005 010 016 018 022 029
3.2 9 002 003 004 007 008 010 012 015 017 019 021 023 025 027 038 040 042 044 046 048
3.3 9 002 003 004 006 010 012 016 017 019 020 021 023 026 030 035 036 038 047 050 056 058 061
3.4 6 004 006 011 012 013 014 015 017 018 020 022 026 029 032 034
Chapter 4: Elementary Number Theory and Methods of Proof
4.1 8 002 004 007 011 015 016 024 030
4.2 6 005 013 018 027 029 035
4.3 12 001 002 003 005 007 008 014 017 022 025 030 038
4.4 20 001 002 003 005.EP 006 007 008 009 011 012 013 017 021 025 028 035 037 039 041 042
4.5 16 001 002 003 004 006 007 008 009 010 013 014 014.EP 021 027 041 044
4.6 11 001 002 003 004 005 006 007 011 016 021 027
4.7 10 004 006 011 018 024 027 030 032 032.EP 034
4.8 4 007 013 025 032
4.9 13 002 003 003.EP 004 004.EP 007 008 010 011 013 015 016 017
4.10 15 002 003 004 005 007 008 011 012 013 014 018 019 020 030 031
Chapter 5: Sequences, Mathematical Induction, and Recursion
5.1 15 001 002 004 006 007 013 015 016 017 019 020 021 022 024 025 026 028 028.EP 030 032 034 036 038 041 042 044 045 048 050 052 054 057 058 060 062 063 064 067 070 071 072 074 076 082 083 085 086
5.2 7 007 012 014 020 023 026 027 031 035
5.3 7 005 009 012 020 030 039 046
5.4 4 003 006 018 025
5.5 2 002 007
5.6 9 002 004 006 008 010 016 021 022 024 032 036 037 040
5.7 7 007 008 011 012 013 015 016 017 022 023 025 027 033 037
5.8 6 002 003 004 006 008 009 010 011 014 015 023 023.EP
5.9 5 008 013 017 019 020 025
Chapter 6: Set Theory
6.1 9 001 004 009 010 012 013 016 020 023 025 027 029 030 035
6.2 9 002 004 006 013 018 024 026 031 035
6.3 10 002 004 008 013 020 024 029 032 042 046 046.EP
6.4 6 002 009 014 018 019 021
Chapter 7: Properties of Functions
7.1 9 002 005 006 007 008 009 011 012 014 018 024 025 026 028 032 039 042
7.2 9 002 005 007 008 012 017 025 041 043 048 049 051 054
7.3 8 002 004 005 006 007 008 009 009.EP 014 020 027
7.4 5 004 009 015 020 028
Chapter 8: Properties of Relations
8.1 7 004 006 007 009 011 014 017 020 022
8.2 11 002 005 010 013 014 016 017 019 021 022 024 026 029 030 032 033 035 044 046 047 049 052
8.3 9 004 005 006 009 010 012 014 015 015.EP 022 030 039
8.4 13 002 005 011 014 015 017 018 020 021 023 024 024.EP 026 027 032 037 038 040
8.5 9 006 011 016 022 023 025 027 028 029 030 032 036 037
Chapter 9: Counting and Probability
9.1 13 004 005 006 007 008 010 011 012 013 014 017 017.EP 019 022 023 026 027 029 030
9.2 15 002 005 007 008 010 011 014 015 015.EP 017 022 023 025 026 027 028 032 037 038 040
9.3 15 002 005 007 008 009 012 013 017 019 021 021.EP 022 023 024 032 034 036
9.4 14 002 004 006 008 009 011 013 014 015 016 017 018 019 021 023 027 028 030 036
9.5 11 005 006 007 008 010 012 014 016 017 018 020 021 024 025
9.6 7 004 006 009 011 012 014 017 018
9.7 16 002 004 007 011 022 024 026 027 030 030.EP 032 032.EP 034 039 044 046 048 049 050 052
9.8 8 003 005 006 009 010 012 014 015 017 017.EP 018 020
9.9 10 001 002 003 007 008 009 012 012.EP 014 015 024 025 029 030 032
Chapter 10: Theory of Graphs and Trees
10.1 12 002 003 005 008 009 013 015 017 017.EP 020 024 028 030 035 036 042
10.2 4 001 002 005 006 008 009 013
10.3 4 003 004 007 024
10.4 6 001 006 007 015 023 028
10.5 5 002 012 014 017 019 021 024
10.6 4 004 006 008 022
Chapter 11: Analysis of Algorithm Efficiency
11.1 002 004 007 009 011 013 023
11.2 007 008
11.3 001 003 005 007 010 013 016 018 021 029 034 039 043
11.4 002 005 008 019 026 039
11.5 003 004 006 012 015 017
Chapter 12: Regular Expressions and Finite-State Automata
12.1 008 009 011 012 014 015 017 018 023 025 026 029 032 033 035 038
12.2 001 004 009 010 019 022 024 030 034 035
12.3 002 003 005
Total 531 (300)