∴Foundations
Basic concepts including arithmetic, fractions, ratios, and number systems
ArithmeticFractions & RatiosNumber Systems
xAlgebra
Variables, equations, polynomials, abstract algebra
Elementary AlgebraAdvanced AlgebraAbstract AlgebraBoolean AlgebraRepresentation TheoryHomological Algebra
△Geometry
Plane, solid, analytic, and differential geometry
Plane GeometrySolid GeometryAnalytic GeometryNon-Euclidean GeometryDifferential GeometryRiemannian GeometrySymplectic GeometryAlgebraic GeometryProjective Geometry
θTrigonometry
Trigonometric, inverse, and hyperbolic functions
Basic TrigonometryTrigonometric ApplicationsInverse TrigonometryHyperbolic Functions
∫Analysis
Limits, differentiation, integration, differential equations
Limits & ContinuityDifferentiationIntegrationDifferential EquationsReal AnalysisComplex AnalysisFunctional AnalysisHarmonic AnalysisCalculus of VariationsTensor Analysis
⊗Linear Algebra
Vectors, matrices, linear transformations, vector spaces
VectorsMatricesLinear TransformationsVector SpacesInner Product Spaces
⁝Probability & Statistics
Probability, statistics, stochastic processes, Bayesian statistics
ProbabilityStatisticsStochastic ProcessesBayesian StatisticsQueueing TheoryInformation Theory
⊂Discrete Math
Logic, set theory, combinatorics, graph theory
LogicSet TheoryCombinatoricsGraph TheoryOrder TheoryLattice Theory
ℕNumber Theory
Elementary, algebraic, analytic number theory, cryptography
Elementary Number TheoryAlgebraic Number TheoryAnalytic Number TheoryCombinatorial Number TheoryCryptographic Number Theory
○Topology
General, algebraic, differential topology, knot theory
General TopologyAlgebraic TopologyDifferential TopologyKnot Theory
⊢Mathematical Logic
Model theory, proof theory, computability, category theory
Model TheoryProof TheoryComputability TheoryCategory TheoryAxiomatic Set Theory
∞Dynamics & Chaos
Dynamical systems, chaos theory, fractals, ergodic theory
Dynamical SystemsChaos TheoryFractalsErgodic Theory
↗Optimization
Linear programming, nonlinear, convex optimization, dynamic programming
Linear ProgrammingNonlinear OptimizationConvex OptimizationInteger ProgrammingDynamic Programming
≈Numerical Analysis
Error analysis, interpolation, numerical integration, numerical DE
Error AnalysisInterpolationNumerical IntegrationNumerical Differential EquationsNumerical Linear Algebra
⊕Applied Math
Finance, physics, CS, engineering, biology applications
Financial MathematicsMathematics of MusicMathematical PhysicsCS MathematicsEngineering MathematicsBio/Medical MathematicsMathematical EconomicsArt & Architecture MathematicsNatural Sciences MathematicsEveryday Mathematics
πConstants
Major mathematical constants: π, e, φ, √2, γ, i, etc.
∑Symbols
Operation, set, logic, calculus symbols and Greek letters