Formal & Physical Sciences MathematicsENModular forms: IntroductionRichard E BorcherdsMarch 20, 2021 24 min★ ★ ★ ★ ★ 5/5Modular FormsNumber TheoryComplex Analysis
Formal & Physical Sciences MathematicsENComplex analysis: Classification of elliptic functionsRichard E BorcherdsMarch 19, 2021 24 min★ ★ ★ ★ ★ 5/5Elliptic FunctionsComplex AnalysisWeierstrass P-Function
Formal & Physical Sciences MathematicsENComplex analysis: Weierstrass elliptic functionsRichard E BorcherdsMarch 18, 2021 24 min★ ★ ★ ★ ★ 5/5Weierstrass Elliptic FunctionsComplex AnalysisElliptic Functions
Formal & Physical Sciences MathematicsENComplex analysis: Elliptic functionsRichard E BorcherdsMarch 17, 2021 26 min★ ★ ★ ★ ★ 5/5Complex AnalysisElliptic FunctionsMeromorphic Functions
Formal & Physical Sciences MathematicsENComplex analysis: Maximum modulus principleRichard E BorcherdsMarch 16, 2021 19 min★ ★ ★ ★ ★ 5/5Complex AnalysisMaximum Modulus PrincipleHolomorphic Functions
Formal & Physical Sciences MathematicsENComplex analysis: Gamma functionRichard E BorcherdsMarch 15, 2021 24 min★ ★ ★ ★ ★ 5/5Gamma FunctionComplex AnalysisFunctional Equation
Formal & Physical Sciences MathematicsENComplex analysis: SingularitiesRichard E BorcherdsMarch 14, 2021 27 min★ ★ ★ ★ ★ 5/5Complex AnalysisSingularitiesPoles
Formal & Physical Sciences MathematicsENComplex analysis: Zeta function functional equationRichard E BorcherdsMarch 13, 2021 14 min★ ★ ★ ★ ☆ 4/5Riemann Zeta FunctionFunctional EquationComplex Analysis
Formal & Physical Sciences MathematicsENComplex analysis: Summing seriesRichard E BorcherdsMarch 13, 2021 16 min★ ★ ★ ★ ★ 5/5Complex AnalysisResidue CalculusSeries
Formal & Physical Sciences MathematicsENComplex analysis: Residue calculusRichard E BorcherdsMarch 11, 2021 30 min★ ★ ★ ★ ★ 5/5Complex AnalysisResidue TheoremContour Integration
Formal & Physical Sciences MathematicsENComplex analysis: Locally uniform convergenceRichard E BorcherdsMarch 10, 2021 37 min★ ★ ★ ★ ☆ 4/5Complex AnalysisUniform ConvergenceHolomorphic Functions
Formal & Physical Sciences MathematicsENComplex analysis: Analytic continuationRichard E BorcherdsMarch 9, 2021 22 min★ ★ ★ ★ ☆ 4/5Analytic ContinuationComplex AnalysisGamma Function
Formal & Physical Sciences MathematicsENComplex analysis: Cauchy's integral formulaRichard E BorcherdsMarch 8, 2021 23 min★ ★ ★ ★ ★ 5/5Cauchy's Integral FormulaComplex AnalysisHolomorphic Functions
Formal & Physical Sciences MathematicsENComplex analysis: Cauchy's theoremRichard E BorcherdsMarch 7, 2021 20 min★ ★ ★ ★ ☆ 4/5Cauchy's TheoremComplex AnalysisGreen's Theorem
Formal & Physical Sciences MathematicsENComplex analysis: IntegrationRichard E BorcherdsMarch 6, 2021 22 min★ ★ ★ ★ ★ 5/5Complex AnalysisIntegrationPath Integral
Formal & Physical Sciences MathematicsENQuestions and Answers 1Richard E BorcherdsMarch 5, 2021 35 min★ ★ ★ ★ ★ 5/5MathematicsQ&AResearch Advice
Formal & Physical Sciences MathematicsENComplex analysis: Harmonic functionsRichard E BorcherdsMarch 4, 2021 30 min★ ★ ★ ★ ★ 5/5Complex AnalysisHarmonic FunctionsLaplace Equation
Formal & Physical Sciences MathematicsENComplex analysis: Holomorphic functionsRichard E BorcherdsMarch 3, 2021 26 min★ ★ ★ ★ ★ 5/5Complex AnalysisHolomorphic FunctionsCauchy-Riemann Equations
Formal & Physical Sciences MathematicsENComplex analysis: Exp, log, sin, cosRichard E BorcherdsMarch 2, 2021 32 min★ ★ ★ ★ ★ 5/5Complex AnalysisExponential FunctionLogarithm
Formal & Physical Sciences MathematicsENComplex analysis: RootsRichard E BorcherdsMarch 1, 2021 31 min★ ★ ★ ★ ★ 5/5Complex AnalysisRootsPolar Coordinates
Formal & Physical Sciences MathematicsENComplex analysis: ArithmeticRichard E BorcherdsFebruary 28, 2021 25 min★ ★ ★ ★ ★ 5/5Complex NumbersArithmeticQuaternions
Formal & Physical Sciences MathematicsENComplex analysis: IntroductionRichard E BorcherdsFebruary 27, 2021 18 min★ ★ ★ ★ ☆ 4/5Complex AnalysisCauchy's TheoremAnalytic Continuation
Formal & Physical Sciences MathematicsENSphere packings in 8 dimensions (after Maryna Viazovska)Richard E BorcherdsFebruary 26, 2021 31 min★ ★ ★ ★ ★ 5/5Sphere PackingE8 LatticeModular Forms
Formal & Physical Sciences MathematicsENLie groups: Modular functionRichard E BorcherdsFebruary 25, 2021 28 min★ ★ ★ ★ ★ 5/5Lie GroupsModular FunctionInvariant Measure
Formal & Physical Sciences MathematicsENLie groups: Haar measureRichard E BorcherdsFebruary 24, 2021 24 min★ ★ ★ ★ ★ 5/5Haar MeasureLie GroupsIntegration
Formal & Physical Sciences MathematicsENLie groups: Lie's theoremRichard E BorcherdsFebruary 23, 2021 23 min★ ★ ★ ★ ★ 5/5Lie AlgebrasSolvable Lie AlgebrasLie's Theorem
Formal & Physical Sciences MathematicsENLie groups: Engel's theoremRichard E BorcherdsFebruary 22, 2021 24 min★ ★ ★ ★ ☆ 4/5Lie AlgebrasEngel's TheoremNilpotent
Formal & Physical Sciences MathematicsENLie groups: Bianchi classificationRichard E BorcherdsFebruary 21, 2021 24 min★ ★ ★ ★ ★ 5/5Lie GroupsBianchi ClassificationThurston Geometries
Formal & Physical Sciences MathematicsENLie groups: Positive characteristic is weirdRichard E BorcherdsFebruary 20, 2021 21 min★ ★ ★ ★ ★ 5/5Lie GroupsLie AlgebrasPositive Characteristic
Formal & Physical Sciences MathematicsENLie groups: Poincare-Birkhoff-Witt theoremRichard E BorcherdsFebruary 19, 2021 30 min★ ★ ★ ★ ★ 5/5Lie GroupsPoincaré-Birkhoff-Witt TheoremUniversal Enveloping Algebra
Formal & Physical Sciences MathematicsENLie groups: Baker Campbell Hausdorff formulaRichard E BorcherdsFebruary 18, 2021 25 min★ ★ ★ ★ ★ 5/5Lie GroupsLie AlgebrasBaker-Campbell-Hausdorff
Formal & Physical Sciences MathematicsENLie groups: Exponential mapRichard E BorcherdsFebruary 17, 2021 25 min★ ★ ★ ★ ★ 5/5Lie GroupsExponential MapMatrix Groups
Formal & Physical Sciences MathematicsENLie groups: Lie groups and Lie algebrasRichard E BorcherdsFebruary 16, 2021 36 min★ ★ ★ ★ ★ 5/5Lie GroupsLie AlgebrasSimply Connected
Formal & Physical Sciences MathematicsENLie groups: Lie algebrasRichard E BorcherdsFebruary 15, 2021 30 min★ ★ ★ ★ ★ 5/5Lie GroupsLie AlgebrasJacobi Identity
Formal & Physical Sciences MathematicsENLie groups: IntroductionRichard E BorcherdsFebruary 14, 2021 36 min★ ★ ★ ★ ☆ 4/5Lie GroupsMathematicsGroup Theory
Formal & Physical Sciences MathematicsENTheory of numbers: Quadratic reciprocityRichard E BorcherdsFebruary 12, 2021 28 min★ ★ ★ ★ ★ 5/5Quadratic ReciprocityNumber TheoryGauss Sums
Formal & Physical Sciences MathematicsENTheory of numbers: Gauss's lemmaRichard E BorcherdsFebruary 11, 2021 28 min★ ★ ★ ★ ★ 5/5Number TheoryGauss's LemmaQuadratic Residues
Formal & Physical Sciences MathematicsENTheory of numbers: Quadratic residuesRichard E BorcherdsFebruary 10, 2021 29 min★ ★ ★ ★ ★ 5/5Quadratic ResiduesNumber TheoryLegendre Symbol
Formal & Physical Sciences MathematicsENTheory of numbers: Jacobi symbolRichard E BorcherdsFebruary 10, 2021 25 min★ ★ ★ ★ ★ 5/5Jacobi SymbolLegendre SymbolQuadratic Reciprocity
Formal & Physical Sciences MathematicsENTheory of numbers: Chevalley-Warning theoremRichard E BorcherdsFebruary 9, 2021 19 min★ ★ ★ ★ ★ 5/5Number TheoryChevalley-WarningFinite Fields