Partial Ordering: Relations, Sequences, Summation

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Lattices for Abstract Interpretation

Covers lattices, abstract interpretation, fixpoint analysis, Hoare logic, and partial orders with extreme elements.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Equivalence Relations and Partial Orderings

Introduces equivalence relations, partitions, partial orderings, and total ordering concepts with examples and definitions.

Partial Ordering: Relations, Sequences, Summation

Explores partial orderings, divisibility relations, lattices, lexicographic ordering, comparability, and total orderings.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Relations, Sequences and Summations

Covers topics on relations, sequences, and summations, including lattices, recurrence relations, and sigma notation.

Real Numbers: Sets and Operations

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

Integers: Elementary Concepts

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Relations and Sequences: Well-ordered Sets and Geometric Series

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.

Möbius inversion: posets

Covers the Möbius inversion for posets, defining partially ordered sets and explaining the incidence algebra.