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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/00%3A_Front_Matter
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.05%3A_Combinatorics-_Inclusion_ExclusionThis page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses il...This page explains the inclusion-exclusion principle for counting distinct elements in overlapping sets, detailing how to adjust for over-counting overlaps. An example with students in math courses illustrates this principle. It also defines a derangement as a permutation where no element retains its original position, and concludes with practice checkpoints on related counting problems.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations/4.04%3A_Partially_Ordered_SetsThis page defines partially ordered sets (posets) and their properties like reflexivity, anti-symmetry, and transitivity. It explains representation through Hasse diagrams and illustrates examples suc...This page defines partially ordered sets (posets) and their properties like reflexivity, anti-symmetry, and transitivity. It explains representation through Hasse diagrams and illustrates examples such as numeric divisibility and subset relations. Key terms related to posets, including comparable elements, total ordering, and lattices, are defined, alongside practical checkpoints for assessing poset properties and constructing Hasse diagrams.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.03%3A_Predicate_LogicThis page covers the use of predicates and quantifiers in logic for effective communication, including negation and application through exercises. It provides examples involving bees, flowers, trees, ...This page covers the use of predicates and quantifiers in logic for effective communication, including negation and application through exercises. It provides examples involving bees, flowers, trees, and moose, highlighting logical equivalences and implications related to these subjects. The text encourages readers to translate natural language statements into logical notation and practice negation and interpretation, reinforcing their understanding of predicate logic in various scenarios.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.04%3A_PathsThis page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Euler...This page discusses key concepts in graph theory, including definitions of walks, trails, and paths, highlighting their distinct characteristics regarding vertex and edge repetition. It explains Eulerian trails and Hamiltonian paths and addresses graph connectivity, stating that a graph is connected if any vertex pair has a connecting path. Additionally, it introduces \(n\)-connected graphs and includes practice checkpoints to reinforce understanding of these concepts.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/05%3A_Graph_Theory/5.05%3A_CyclesThis page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, ...This page defines important graph theory terms such as circuit, cycle, Eulerian circuit, and Hamiltonian circuit. It explains that a circuit is a closed walk with the same starting and ending vertex, while a cycle does not repeat vertices. An Eulerian circuit covers every edge once, and a Hamiltonian circuit visits each vertex once. Additionally, it offers practice checkpoints for readers to engage with the concepts, including drawing cycles and identifying specific types of circuits.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/00%3A_Front_Matter/01%3A_TitlePageDiscrete Mathematics for Computer Science (Fitch)
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.04%3A_Sets_in_Relational_DatabaseThis page explains how databases organize structured data in tables and the role of SQL in accessing this data. It describes the various types of SQL joins, such as inner, left, right, and outer joins...This page explains how databases organize structured data in tables and the role of SQL in accessing this data. It describes the various types of SQL joins, such as inner, left, right, and outer joins, and illustrates these concepts with examples. Additionally, it covers how SQL statements enable data retrieval and manipulation based on specific conditions.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.01%3A_Formal_LogicThis page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's ...This page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's Laws. It highlights conditions for compound statements to be false and includes practice checklists for truth tables and equivalence inquiries from previous exercises.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.01%3A_TerminologyThis page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent inf...This page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent infinite definitions, while defined terms rely on these and established definitions. Axioms are unproven statements serving as a foundation for deriving new statements. Mastering these concepts is essential for solving mathematical problems.
