Topics¶

This directory is the heart of leaps. Every subject worth learning lives here as its own topic directory — a self-contained knowledge base with structured modules, exercises, test questions, and resources.

Topics are organized into broad categories. Within each topic, modules are numbered and sequenced so that a learner (human or AI) can progress logically from fundamentals to advanced material. See CONTRIBUTING.md for instructions on adding a new topic or module.

[!NOTE] This page is also the landing page of the published leaps book. The book is built with Zensical from this TOPICS/ directory and deployed to GitHub Pages on every push to main. It exposes exactly this index of courses and the courses themselves — nothing else.

Available Courses¶

These courses are live today. Each links to its topic overview, which in turn links every module.

The catalog below maps the full landscape of planned topics.

Adding a New Topic¶

Open an issue using the New Topic Request template, or follow CONTRIBUTING.md to build it directly.

Topic Map¶

mindmap
  root((leaps))
    Programming Languages
      Python
      Rust
      C / C++
      Go
      JavaScript
      Haskell
    Systems & Low-Level
      Operating Systems
      Computer Architecture
      Compilers
      Networking
    Mathematics
      Calculus
      Linear Algebra
      Discrete Mathematics
      Probability & Statistics
      Abstract Algebra
    Data Science & AI/ML
      Machine Learning
      Deep Learning
      Data Engineering
      Statistics
    Web & Frontend
      HTML / CSS
      JavaScript Frameworks
      Browser APIs
      Web Performance
    DevOps & Infrastructure
      Linux
      Docker & Containers
      Kubernetes
      CI/CD
      Cloud Platforms
    Sciences
      Physics
      Chemistry
      Biology
      Neuroscience
    Design & Creative
      Graphic Design
      Typography
      Music Theory
      3D Modeling
    Humanities
      Philosophy
      History of Science
      Logic & Argumentation
      Economics
    Professional Skills
      Technical Writing
      System Design
      Leadership
      Communication

Topic Categories¶

Programming Languages¶

Languages as primary objects of study — syntax, semantics, idioms, and the mental models each language instills.

Systems & Low-Level¶

How computers actually work beneath the abstractions.

Mathematics¶

Rigorous mathematical foundations with an emphasis on intuition and application.

Data Science & AI/ML¶

The theory and practice of learning from data.

Web & Frontend¶

Building things for the browser — from fundamentals to modern toolchains.

DevOps & Infrastructure¶

The systems that build, ship, and run software reliably at scale.

Sciences¶

Formal sciences — grounded in real textbooks and primary sources.

Design & Creative¶

Visual thinking, aesthetics, and creative craft as learnable disciplines.

Humanities¶

Ideas, arguments, and the human record.

Professional Skills¶

Skills that amplify everything else — communication, design thinking, and technical leadership.

Getting Started Recommendations¶

Not sure where to begin? These curated paths are based on common starting points.

If you are a programmer wanting to go deeper into systems¶

Go (modules 0-9) → Computer Architecture → Operating Systems → C → Rust

Rationale: Establish a comfortable, statically-typed baseline in Go, understand what the hardware actually does, then learn how the OS mediates access to it, then write code without a safety net, then write code with safety guarantees.

If you are starting from scratch with no programming background¶

Go (modules 0-9) → Discrete Mathematics → Algorithms & Data Structures → Linear Algebra

Rationale: Go's small, readable syntax minimizes the barrier to entry while teaching you real static typing and concurrency. Discrete math builds the logical reasoning that makes advanced CS tractable. Algorithms teaches structured problem-solving. Linear algebra unlocks everything in data science.

If you want to explore mathematics as a programmer¶

Discrete Mathematics → Probability & Statistics → Linear Algebra → Calculus → Abstract Algebra

Rationale: Discrete math is where programming meets mathematics most naturally. Statistics builds intuition for uncertainty. Linear algebra connects to nearly every applied field. Calculus deepens the continuous-math intuition. Abstract algebra is the payoff — structure everywhere.

If you want to get into AI/ML seriously¶

A general-purpose language → Linear Algebra → Probability & Statistics → Machine Learning → Deep Learning

Rationale: You cannot understand gradient descent without linear algebra, you cannot reason about model uncertainty without statistics, and you cannot debug neural networks without understanding both.

Cross-topic Learning Paths¶

The diagram below shows how topics in leaps depend on and reinforce each other. Arrows indicate "is a useful prerequisite for". This is not exhaustive — use it as a map, not a mandate.

flowchart TD
    PY[Python] --> ML[Machine Learning]
    PY --> DE[Data Engineering]
    PY --> WEB[Web / TypeScript]

    DMATH[Discrete Mathematics] --> ALGO[Algorithms]
    DMATH --> PL[Programming Languages Theory]

    LINALG[Linear Algebra] --> ML
    LINALG[Linear Algebra] --> QM[Quantum Mechanics]
    PROB[Probability & Statistics] --> ML
    CALC[Calculus] --> LINALG
    CALC --> PROB

    ALGO --> OS[Operating Systems]
    ALGO --> COMP[Compilers]

    ARCH[Computer Architecture] --> OS
    OS --> NET[Networking]
    OS --> DOCKER[Docker & Containers]
    NET --> DOCKER
    DOCKER --> K8S[Kubernetes]

    C[C] --> RUST[Rust]
    C --> OS
    RUST --> COMP

    ML --> DL[Deep Learning]
    DL --> LLM[LLM / Foundation Models]

    LOGIC[Logic & Argumentation] --> DMATH
    LOGIC --> PHIL[Philosophy of Mind]
    DL --> PHIL

    style PY fill:#4B8BBE,color:#fff
    style DMATH fill:#306998,color:#fff
    style LINALG fill:#e36d26,color:#fff
    style ML fill:#2d8a4e,color:#fff
    style DL fill:#1a5c35,color:#fff