ΛAXIOM
⚡00/69

THE MAP_

All of mathematics as one dependency tree — 69 nodes from counting to the spectral theorem. Master the prerequisites, unlock the frontier, climb.

▶ BEGIN AT NODE ZERO0/69 mastered
▞ BEDROCKNumbers, rebuilt from raw counting. You think you know this. You don't.▞ LOGIC & PROOFThe machinery of certainty. Learn to argue so well reality has to agree.▞ SET THEORYEverything is a set. EVERYTHING. The periodic table of mathematics.▞ ALGEBRA COREArithmetic with the masks on. Solve for the unknown, every time.▞ FUNCTIONS & GROWTHMachines that eat numbers. Curves, growth, and the art of the inverse.▞ GEOMETRY & TRIGTriangles and circles — the load-bearing shapes of the universe.▞ VECTORS & MATRICESArrows and grids of numbers that move entire planes around.▞ VECTOR SPACESLinear algebra with proofs. The cathedral. The spectral theorem lives at the t…What Is a Number?●The Laws of Arithmetic●Zero & the Negatives●Fractions & the Rationals●Exponents & Roots●Order & Inequality●Irrationals & the Real Li…●Absolute Value & Distance●Propositions & Connectives●Implication●Quantifiers●Direct Proof●Contrapositive & Iff Proo…●Proof by Contradiction●Induction●Strong Induction & Well-O…●Sets & Membership●Set Operations●Set Identities & Element …●Ordered Pairs & Cartesian…●Relations & Equivalence●Functions as Mappings●Injections, Surjections, …●Composition & Inverse Fun…●Cardinality & Infinity●Variables & Expressions●Linear Equations●Linear Inequalities●The Coordinate Plane●Lines & Slope●Systems of Linear Equatio…●Polynomial Arithmetic●Factoring●Quadratic Equations●Rational Expressions & Eq…●Functions & Their Graphs●Quadratic Functions & Par…●Polynomial Functions●Exponential Functions●Logarithms●Inverse Functions●Sequences & Series●Counting & the Binomial T…●Angles, Triangles & Simil…●The Pythagorean Theorem●Trig Ratios●The Unit Circle & Radians●Trig Identities●Circles in the Plane●Vectors●The Dot Product●Matrices & Their Arithmet…●Matrix Multiplication●Linear Transformations of…●Determinants●Matrix Inverses●Gaussian Elimination●Vector Spaces●Subspaces●Span & Linear Combinations●Linear Independence●Basis & Dimension●Linear Maps●Rank–Nullity●Change of Basis●Eigenvalues & Eigenvectors●Diagonalization●Orthogonality & Gram–Schm…●The Spectral Theorem