Learning path · 6 steps
Geometry Foundations to the Pythagorean Theorem
Move from the language of points, lines, and planes through triangles, angles, length, and right triangles to the Pythagorean theorem.
OCME · Bilingual mathematics & derivations
Learning paths
Compare goals and step counts, then open a path to read one step at a time. Learning order is not a formal proof.
Learning path · 3 steps
From Sets and Functions to the Tends-To Relation
Establish a foundational chain from set membership through total functions to convergence semantics.
Learning path · 6 steps
Modern General Mathematics Literacy
Use six current objects to demonstrate a branching entry path into general mathematical literacy.
Learning path · 4 steps
Entry Path to Formalized Mathematics
Move from set and function semantics into precise Lean and Mathlib statements and content-addressed evidence objects.
Learning path · 4 steps
Proof and Evidence Literacy
Identify proof obligations before distinguishing human proof, finite computational evidence, and exact formal proof.
Learning path · 5 steps
Foundational Mathematical Language
Move from the concrete language of counting to sets, propositions, and logical connectives, establishing the vocabulary needed to read later mathematical objects.
Learning path · 11 steps
Wave-One Domain Foundations
Branch from natural numbers, sets, and propositions into arithmetic, equations, probability, induction, factorials, and elementary combinatorial counting.
Learning path · 4 steps
Set Language toward Topology
Build the set-language prerequisites needed to read the definition of a topological space, progressing through sets, membership, subsets, and basic set operations.
Learning path · 5 steps
From Sample Spaces to Events
Use set language and sample spaces to establish the precise boundary of an event as a set of outcomes.
Learning path · 5 steps
From Natural Numbers to Absolute Value on the Real Line
Move from natural numbers used for counting to integers and rational numbers, enter the real-number system through completion language, and then express number-line distance with absolute value.
Learning path · 16 steps
Seven-Round Foundation Expansion: Numbers, Functions, Counting, and Coordinates
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 17 steps
Seven-Round Algebra and Probability Foundations: Powers, Identities, Functions, and Finite Models
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 17 steps
Daily Seven-Round Cycle I: Quantifiers, Discrete Structures, Linear Systems, and Conditional Models
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 15 steps
Function Invertibility and Finite Probability Moments: Seven-Round Workflow
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 20 steps
Real Order, Average Rates, Coordinate Geometry, and Data Summaries: Seven-Round Workflow
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 17 steps
Matrices, Real 2×2 Linear Algebra, Labeled Triangles, and Coordinate Transformations: Seven-Round Workflow
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 18 steps
Real Limits, Continuity, Derivatives, and Polynomial Integration: Seven-Round Workflow
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 21 steps
Final Core80 Seeds and Five Rounds of Existing-Family Depth
Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations.
Learning path · 17 steps
Cross-Domain Depth: Algebra, Sets, Distances, Finite Probability, and Quantifiers
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.
Learning path · 9 steps
Foundation Gaps: Natural Numbers, Expressions, Sets, and Finite Limit Models
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.
Learning path · 9 steps
Foundational Reasoning and Geometry: Induction, Counting, Typing, and Length
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.
Learning path · 14 steps
Finite Structures: Pythagoras, Number Systems, Inference, Events, and Labeled Triangles
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.
Learning path · 14 steps
Foundation Transforms: Angles, Number Lines, Equations, Factorials, and Circle Boundaries
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.
Learning path · 16 steps
Typed Data and Selection: Fractions, Ratios, Maps, Compositions, and Coordinates
Deepen cross-domain question families on seven existing knowledge objects and their prerequisites, keeping mathematical sources unchanged and checking boundaries in exact finite slices.