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Sets1. Introduction to Sets2. Relations on SetsMiscMagic1. 1 = 0.999...Oddities1. Russel's Paradox2. The Orwell GroupTheoriesAlgebrasGroup Theory1. Groups in GeneralMonoid Theory1. Monoids in GeneralSemigroup1. Semigroups in GeneralCategory TheoryIn General1. Definition2. Dual Category3. Mono-, Epi- and Isomorphisms4. Initial and Terminal Objects5. Products and Coproducts6. Exponentation and Cartesian Closed CategoriesFunctors1. Definition2. Full, Faithful and Embeddings3. Preserves and Reflects4. Contra-, Co- and Bivariant5. Co- and Contravariant Hom FunctorsNatural Transformations1. Definition and ExamplesAdjoints1. Definition and ExamplesApplications1. Transition Systems, Hoare Languages and AdjointsLinear AlgebraMisc1. Cosine SimilarityRelations1. Intro2. Properties and Special Relations3. Functions as relationsFunctionsElementary1. Logarithmic2. Absoulte Value3. The Square Root