Formal & Physical Sciences MathematicsENRings 18 Hilbert's theoremsRichard E BorcherdsOctober 23, 2021 30 min★ ★ ★ ★ ★ 5/5Hilbert's Basis TheoremNoetherian RingsInvariant Theory
Formal & Physical Sciences MathematicsENRings 17 Noetherian ringsRichard E BorcherdsOctober 22, 2021 27 min★ ★ ★ ★ ★ 5/5Noetherian RingsCommutative AlgebraRing Theory
Formal & Physical Sciences MathematicsENRings 16 Factorization of polynomialsRichard E BorcherdsOctober 21, 2021 25 min★ ★ ★ ★ ★ 5/5Polynomial FactorizationIrreducibilityEisenstein's Criterion
Formal & Physical Sciences MathematicsENRIngs 15 PolynomialsRichard E BorcherdsOctober 20, 2021 29 min★ ★ ★ ★ ★ 5/5PolynomialsUnique FactorizationRings
Formal & Physical Sciences MathematicsENRIngs 14 Limits and exactnessRichard E BorcherdsOctober 16, 2021 22 min★ ★ ★ ★ ★ 5/5RingsModulesLimits
Formal & Physical Sciences MathematicsENRings 13 Colimits and exactnessRichard E BorcherdsOctober 15, 2021 33 min★ ★ ★ ★ ★ 5/5Category TheoryColimitsExact Sequences
Formal & Physical Sciences MathematicsENRings 12 Duality and injective modulesRichard E BorcherdsOctober 13, 2021 50 min★ ★ ★ ★ ★ 5/5DualityInjective ModulesProjective Modules
Formal & Physical Sciences MathematicsENCategories 6 Monoidal categoriesRichard E BorcherdsOctober 10, 2021 23 min★ ★ ★ ★ ★ 5/5Monoidal CategoriesCategory TheorySymmetric Monoidal Categories
Formal & Physical Sciences MathematicsENRings 11 Tensor products of modulesRichard E BorcherdsOctober 9, 2021 26 min★ ★ ★ ★ ★ 5/5Tensor ProductModulesRings
Formal & Physical Sciences MathematicsENRings 10 Tensor products of abelian groupsRichard E BorcherdsOctober 8, 2021 27 min★ ★ ★ ★ ★ 5/5Tensor ProductsAbelian GroupsCategory Theory
Formal & Physical Sciences MathematicsENRings 9 Projective modulesRichard E BorcherdsOctober 7, 2021 34 min★ ★ ★ ★ ★ 5/5Projective ModulesHomological AlgebraVector Bundles
Formal & Physical Sciences MathematicsENRings 8 Free modulesRichard E BorcherdsOctober 6, 2021 21 min★ ★ ★ ★ ★ 5/5Free ModulesRing TheoryRank
Formal & Physical Sciences MathematicsENRIngs 7: LocalizationRichard E BorcherdsOctober 3, 2021 23 min★ ★ ★ ★ ★ 5/5LocalizationRing TheoryCommutative Algebra
Formal & Physical Sciences MathematicsENRings 6 Prime and maximal idealsRichard E BorcherdsOctober 2, 2021 29 min★ ★ ★ ★ ★ 5/5Prime IdealsMaximal IdealsSpectrum of a Ring
Formal & Physical Sciences MathematicsENRings and modules 5 Examples of unique factorizationsRichard E BorcherdsOctober 1, 2021 22 min★ ★ ★ ★ ★ 5/5Unique FactorizationGaussian IntegersQuadratic Fields
Formal & Physical Sciences MathematicsENRings and modules 4 Unique factorizationRichard E BorcherdsSeptember 30, 2021 38 min★ ★ ★ ★ ★ 5/5Unique FactorizationIntegral DomainsEuclidean Domains
Formal & Physical Sciences MathematicsENRings and midules 3: Burnside ring and rings of differential operatorsRichard E BorcherdsSeptember 29, 2021 18 min★ ★ ★ ★ ★ 5/5Burnside RingDifferential OperatorsRing Theory
Formal & Physical Sciences MathematicsENRings and modules 2: Group ringsRichard E BorcherdsSeptember 28, 2021 23 min★ ★ ★ ★ ★ 5/5Group RingsMonoid RingsIdempotents
Formal & Physical Sciences MathematicsENRings and modules 1 IntroductionRichard E BorcherdsSeptember 27, 2021 30 min★ ★ ★ ★ ★ 5/5Ring TheoryModulesAbstract Algebra
Formal & Physical Sciences MathematicsENCategories 5 Limits and colimitsRichard E BorcherdsSeptember 24, 2021 31 min★ ★ ★ ★ ★ 5/5Category TheoryLimitsColimits
Formal & Physical Sciences MathematicsENCategories 4 Adjoint functorsRichard E BorcherdsSeptember 23, 2021 15 min★ ★ ★ ★ ★ 5/5Category TheoryAdjoint FunctorsFree Functor
Formal & Physical Sciences MathematicsENCategories 3 Natural transformationsRichard E BorcherdsSeptember 22, 2021 15 min★ ★ ★ ★ ★ 5/5Category TheoryNatural TransformationsNatural Isomorphisms
Formal & Physical Sciences MathematicsENCategories 2: FunctorsRichard E BorcherdsSeptember 21, 2021 20 min★ ★ ★ ★ ★ 5/5Category TheoryFunctorsMathematics
Formal & Physical Sciences MathematicsENCategories 1 IntroductionRichard E BorcherdsSeptember 20, 2021 24 min★ ★ ★ ★ ★ 5/5Category TheoryMathematicsAlgebra
Formal & Physical Sciences MathematicsENAlgebraic topology: Fundamental group of a knotRichard E BorcherdsMay 2, 2021 22 min★ ★ ★ ★ ★ 5/5Algebraic TopologyFundamental GroupKnot Theory
Formal & Physical Sciences MathematicsENAlgebraic topology: Calculating the fundamental groupRichard E BorcherdsApril 23, 2021 29 min★ ★ ★ ★ ★ 5/5Algebraic TopologyFundamental GroupVan Kampen's Theorem
Formal & Physical Sciences MathematicsENAlgebraic topology: Fundamental groupRichard E BorcherdsApril 17, 2021 29 min★ ★ ★ ★ ★ 5/5Algebraic TopologyFundamental GroupHomotopy
Formal & Physical Sciences MathematicsENAlgebraic topology: IntroductionRichard E BorcherdsApril 13, 2021 29 min★ ★ ★ ★ ★ 5/5Algebraic TopologyHomotopyHomology
Formal & Physical Sciences MathematicsENModular forms: Petersson inner productRichard E BorcherdsApril 1, 2021 15 min★ ★ ★ ★ ★ 5/5Modular FormsPetersson Inner ProductHecke Operators
Formal & Physical Sciences MathematicsENModular forms: Hecke operators for formsRichard E BorcherdsMarch 31, 2021 20 min★ ★ ★ ★ ★ 5/5Modular FormsHecke OperatorsRamanujan Tau Function
Formal & Physical Sciences MathematicsENModular forms: Product formula for jRichard E. BorcherdsMarch 30, 2021 13 min★ ★ ★ ★ ★ 5/5Modular FormsElliptic Modular FunctionHecke Operators
Formal & Physical Sciences MathematicsENModular forms: Hecke operatorsRichard E BorcherdsMarch 29, 2021 16 min★ ★ ★ ★ ★ 5/5Modular FormsHecke OperatorsNumber Theory
Formal & Physical Sciences MathematicsENModular forms: Theta functions in higher dimensionsRichard E BorcherdsMarch 28, 2021 22 min★ ★ ★ ★ ★ 5/5Modular FormsTheta FunctionsLattices
Formal & Physical Sciences MathematicsENModular forms: Theta functionsRichard E BorcherdsMarch 27, 2021 18 min★ ★ ★ ★ ★ 5/5Modular FormsTheta FunctionsRiemann Zeta Function
Formal & Physical Sciences MathematicsENModular forms: Discriminant and E2Richard E BorcherdsMarch 26, 2021 18 min★ ★ ★ ★ ★ 5/5Modular FormsDiscriminantEisenstein Series
Formal & Physical Sciences MathematicsENModular forms: Modular functionsRichard E BorcherdsMarch 25, 2021 17 min★ ★ ★ ★ ★ 5/5Modular FormsModular FunctionsElliptic Modular Function
Formal & Physical Sciences MathematicsENModular forms: ClassificationRichard E BorcherdsMarch 24, 2021 23 min★ ★ ★ ★ ★ 5/5Modular FormsClassificationEisenstein Series
Formal & Physical Sciences MathematicsENModular forms: Fundamental domainRichard E BorcherdsMarch 23, 2021 15 min★ ★ ★ ★ ★ 5/5Modular FormsFundamental DomainSL2(Z)
Formal & Physical Sciences MathematicsENModular forms: Fourier coefficients of Eisenstein seriesRichard E BorcherdsMarch 22, 2021 24 min★ ★ ★ ★ ★ 5/5Modular FormsEisenstein SeriesFourier Coefficients
Formal & Physical Sciences MathematicsENModular forms: Eisenstein seriesRichard E BorcherdsMarch 21, 2021 24 min★ ★ ★ ★ ★ 5/5Modular FormsEisenstein SeriesElliptic Curves