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Möbius inversion: posets

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

Functional Analysis I: November 18, 2021

Covers partially ordered sets, maximal elements, upper bounds, and the Zorn lemma in functional analysis.

Type Classes: Basics and Implementation

Covers the basics of type classes in Scala, implementation examples, and advantages over class extension.

Permutations and Combinations

Covers the concepts of permutations and combinations, explaining how to calculate them with examples.

Maximal Solutions in Advanced Analysis II

Explores the concept of maximal solutions in advanced analysis.

Relations and Sequences: Well-ordered Sets and Geometric Series

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

Introduction to Real Numbers

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.

Quantum Field Theory II: Cross Section & Lifetime

Covers cross section, lifetime, quantum fluid, asymptotic states, discrete symmetries, and normal ordering in quantum field theory.

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Posets and Equivalence Relations

Introduces posets, Hasse diagrams, and equivalence relations on sets.