Covers sequences as ordered lists and functions, distinguishing from sets. Explores relations (binary and n-ary) with properties like reflexive, symmetric, transitive. Introduces graphs as visual representations of relations, with real-world applications in networks and optimization.
Explains fundamental discrete structures including sets (unordered collections), functions (mappings between sets), sequences (ordered lists), relations, and graphs. Uses set builder notation, natural numbers, and introduces closed versus recursive function definitions with examples.
Introduces discrete mathematics concepts through problem-solving approach. Covers handshake problems, sequences, logic puzzles, and graph theory basics. Emphasizes understanding discrete structures (individually separate and distinct mathematical objects) versus continuous mathematics.
Explores binary relations on sets, relation properties (reflexive, symmetric, transitive), equivalence relations, and partitions. Covers composition of relations, inverse relations, and how relations connect to graphs with directed edges and multigraphs.
Comprehensive chapter summary covering logical connectives, quantifiers, proof strategies, and mathematical reasoning. Includes review problems on truth tables, negations, contrapositives, pigeonhole principle, and graph coloring with knights and knaves puzzles.