Partial Ordering: Relations, Sequences, Summation

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Equivalence Relations and Partial Orderings

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

Partial Ordering: Relations, Sequences, Summation

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Relations and Sequences

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

Möbius inversion: posets

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

Lattices for Abstract Interpretation

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

Relations, Sequences and Summations

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

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Introduction to Real Numbers

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.

Entropy: Examples and Properties

Explores examples of guessing letters, origins of entropy, and properties in information theory.

Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.