Mathematics & Physics Knowledge System

Not everyone arrives at a concept from the same place. A child, a student, and a researcher all need the same truth — but told differently. Every concept in the system carries all three layers, and you decide where to start.

• Three Levels of Depth

  Every concept explained three ways

  Each concept opens with a child-friendly analogy (ages 5–8), builds into a student-level intuition, then delivers the full formal definition with proofs and properties. MSc and PhD-level explanations are available for research-depth topics. You choose your entry point — or read all three.

• Machine-Verified Math

  SymPy checks the answers, not a human stamp

  A 3,800-line Python symbolic engine checks worked examples and mathematical properties — differentiation, integration, limits, series, algebra, ODEs, linear systems, complex arithmetic, matrices, and modular arithmetic. Every claim either passes, fails, or is honestly marked SKIP — never counted as a pass.

• 87 Interactive Labs

  Explore by doing, not by watching

  2D function plotter, 3D surface plotter (Three.js), tangent-line explorer, formula explorer, matrix transforms, vector fields (Mafs), series convergence visualizer, graph traversal (D3-force), geometry construction, probability distribution explorer — all on a safe expression parser (no eval). 87 labs across mathematics and physics.

• 23-Section Template

  Every concept covered the same rigorous way

  Overview → history → intuition → formal definition → proofs → applications → worked examples → practice problems → quiz → flashcards → references. Enforced by Zod schema. The corpus forms a single connected graph with 0 orphans, checked in CI.

• Flagship Engineering Projects

  14 real-world science & engineering case studies

  From the Apollo Program and GPS Navigation to the Large Hadron Collider and LIGO — each project breaks down the governing mathematics and physics into multi-phase problem sets with historical telemetry data, derivations, and worked solutions.

• SM-2 Spaced Repetition

  SQLite-backed adaptive learning with 12 curated tracks

  Real progress tracking in a local SQLite database. Adaptive practice, 12 curated audience tracks (CS, civil engineering, pure math, applied math, physics core, theoretical physics, applied physics, and astrophysics — at undergraduate and graduate levels), placement quiz, and full-screen flashcard review.

• Knowledge Graph & Search

  Navigate mathematics as a connected graph

  Every concept is cross-linked with symmetric return paths — no dead ends. A D3-force visualization lets you see and traverse the entire corpus across 62 domains. Full-text BM25 search (field-weighted, typo-tolerant) runs server-side. A searchable formula index covers 35,400+ equations.

• Live Data Pipeline

  Extractors with mandatory human review

  Scrapers pull drafts from Wikipedia, ProofWiki, NIST DLMF, and OpenStax. Every draft lands in staging at confidence < 0.85 and is never auto-published — a human reviews and promotes by hand. A staleness checker flags concepts whose source has changed.

• Vector Lecture PDF Export

  University-standard lecture notes, generated on demand

  A pure-Node PDF engine converts any concept or domain course packet into typeset lecture notes with LaTeX equations rendered as vector SVG paths via MathJax — no headless Chrome needed. Download individual concepts or full domain packets.

• PWA + Embed API

  Installable, offline-capable, and embeddable

  Full PWA with real installability and offline support via a hand-rolled service worker. An embed API lets third parties drop any concept into their own pages. No AI chatbot — the platform teaches through structured reading and graded practice.

Mathematics and physics are not just abstract theories — they are the foundational languages that build civilizations, explore the cosmos, and power modern computing. Each project breaks down real engineering feats into multi-phase problem sets with step-by-step LaTeX derivations, historical telemetry data, and interactive simulators.

A placement quiz routes you into the right track. The system then adapts within the track using SM-2 spaced repetition — surfacing concepts you're weakest on, not the ones you already know.

Computer Science Math — Undergraduate

The mathematics a CS undergraduate needs to read algorithms papers, reason about correctness and complexity, and follow the standard core curriculum — discrete math, algorithms, theory of computation, and the linear algebra/probability every later course assumes.

Computer Science Math — Graduate (MS/PhD)

Beyond the undergraduate core: the rigor and depth a master's or PhD student needs for research in algorithms, theory, machine learning, or systems — real analysis for optimization/ML theory, abstract algebra for cryptography and coding theory, advanced complexity theory, and the mathematics of information.

Civil Engineering Math — Undergraduate

The mathematics a civil engineering undergraduate needs — the calculus, linear algebra, differential equations, and probability/statistics behind statics, structural analysis, fluid mechanics, surveying, geotechnics, and transportation engineering.

Civil Engineering Math — Graduate (MS/PhD)

Beyond the undergraduate core: the advanced mathematics for structural dynamics, finite element analysis, computational fluid dynamics, geotechnical modeling, and reliability-based design — partial differential equations, advanced linear algebra, numerical methods, and probabilistic risk analysis.

Pure Mathematics — Undergraduate

The standard pure mathematics undergraduate curriculum: rigorous analysis, algebra, geometry, topology, and number theory — the foundations for graduate study or research in any branch of mathematics.

Pure Mathematics — Graduate (MS/PhD)

Graduate pure mathematics: rigorous analysis, modern algebra, topology, geometry, and their interactions — the mathematical depth required for research in any contemporary pure mathematics field.

Applied Mathematics & Data Science — Undergraduate

The mathematical foundations for data science, machine learning, and applied statistics — linear algebra, probability, calculus, optimization, and the computational techniques that underpin modern data analysis.

Applied Mathematics & Data Science — Graduate (MS/PhD)

Graduate-level applied mathematics for data science and machine learning research — rigorous probability, measure theory, advanced optimization, stochastic processes, and the mathematical frameworks for modern ML theory.

Physics Core Curriculum — Undergraduate

The foundational physics sequence covering classical Newtonian mechanics, rotational dynamics, electromagnetism, wave phenomena, thermodynamics, and the origins of modern quantum physics and special relativity.

Theoretical Physics — Graduate

Advanced analytical mechanics, relativistic field theories, operator quantum mechanics, quantum statistical mechanics, general relativity, quantum electrodynamics, and the Standard Model.

Applied Physics & Engineering Physics

Physics applied to real-world engineering systems: fluid dynamics, circuit networks, optics and laser engineering, condensed matter semiconductor devices, and nuclear power reactors.

Astrophysics & Cosmology

The physics of celestial bodies and cosmic evolution: orbital mechanics, stellar evolution and fusion, relativistic black holes, gravitational radiation, and Big Bang cosmological dynamics.

The entire system runs locally. Progress tracking is a real SQLite database — not localStorage. Search is a server-side BM25 index, not a hosted service. The content pipeline pulls from live sources but requires human sign-off before anything ships.

Frontend

Angular

Math verifier

Python

Backend

.NET

The platform is live. Run the placement quiz, pick a concept at the level that fits you, and let spaced repetition track what sticks — then open a lab or a flagship project and derive it yourself.