All Notes
Every topic recorded so far, grouped by field — each seen through the six modes of knowing.
Mathematics
Formal Sciences12 notes
Abstract Algebra
Groups, rings, fields, and algebraic structures — the study of structure itself, abstracted from any particular domain.
Algebra
Variables, expressions, equations, and the art of manipulating abstract symbolic structures.
Arithmetic
Numbers, operations, and the fundamental processes of computation — the bedrock of mathematical reasoning.
Calculus
Limits, derivatives, integrals — the mathematics of continuous change and accumulation.
Category Theory
Objects, morphisms, and universal constructions — the mathematics of mathematical structure.
Geometry
Points, shapes, space, and spatial reasoning — from Euclid's constructions to differential manifolds.
Information Theory
Entropy, coding, and the fundamental limits of communication — the mathematics of uncertainty, compression, and reliable transmission over noisy channels.
Linear Algebra
Vectors, matrices, and linear transformations
Probability
Chance, randomness, and stochastic reasoning
Set Theory
Collections, membership, and the foundational language of mathematics.
Statistics
The science of learning from data — inference, estimation, hypothesis testing, and modeling under uncertainty, powering evidence-based reasoning across all empirical domains.
Topology
Continuity, connectedness, and topological spaces
Computer Science
Formal Sciences12 notes
Algorithms & Data Structures
The design, analysis, and implementation of efficient algorithms and the data structures that support them — the mathematical and engineering foundation of all non-trivial computation.
Compilers
The translation of high-level programming languages into efficient machine code — lexing, parsing, semantic analysis, optimization, and code generation as a pipeline of effective procedures.
Computer Graphics
The synthesis of images from geometric and appearance models — rendering pipelines, shaders, textures, lighting, and the algorithms that turn 3D scenes into 2D pixels at interactive rates.
CPU Design
Architecture, microarchitecture, instruction sets, pipelining, memory hierarchy, and the engineering of high-performance, correct, and efficient processors.
Databases
The design, implementation, and optimization of systems for storing, querying, and managing large volumes of structured data under concurrency, failures, and performance constraints.
Distributed Systems
The design and implementation of systems that run on multiple computers that do not share memory or a common clock — consensus, replication, fault tolerance, and the fundamental limits imposed by asynchrony and partial failure.
Machine Learning
Algorithms that learn patterns from data to make predictions, classify, generate, or act — the science and engineering of building systems that improve from experience.
Networking
The design and implementation of protocols, abstractions, and systems that enable communication between computers — layering, packetization, addressing, routing, reliability, and the end-to-end principle.
Operating Systems
The software layer that manages hardware resources, provides abstractions, enforces protection, and schedules computation — the foundational runtime environment for all higher-level software.
Programming
Data, algorithms, and the construction of software — transforming human intent into executable computation.
Security
The principles, mechanisms, and engineering practices for protecting systems, data, and communications against threats — confidentiality, integrity, availability, authentication, and authorization in the presence of adversaries.
Web Development
The engineering of interactive, performant, and accessible applications on the web platform — spanning DOM, components, HTTP, state, caching, build pipelines, and deployment under real-world constraints.
Logic
Formal Sciences2 notes
Systems Theory
Formal Sciences1 note
Physics
Natural Sciences8 notes
Electromagnetism
Electric and magnetic fields, charges, currents, induction, and electromagnetic waves
Fluid Mechanics
Pressure, density, viscosity, flow regimes, Bernoulli's principle, and the Navier-Stokes equations governing fluid motion
General Relativity
Spacetime curvature as the origin of gravity; geodesics, black holes, gravitational waves, and the large-scale structure of the universe.
Newtonian Mechanics
Classical mechanics of particles and rigid bodies: forces, motion, energy, momentum, frames, and the deterministic laws governing macroscopic dynamics.
Optics
Light as rays and waves: reflection, refraction, interference, diffraction, polarization, and the design of optical instruments and systems
Quantum Mechanics
Wave functions, superposition, uncertainty, quantization, and the probabilistic description of particles and fields at the smallest scales
Thermodynamics
Heat, energy, entropy, work, and the fundamental limits on transformations of matter and energy
Wave Mechanics
Oscillations, traveling and standing waves, superposition, resonance, Fourier analysis, and the wave equation across mechanical, acoustic, electromagnetic, and quantum domains
Chemistry
Natural Sciences1 note
Biology
Natural Sciences2 notes
Cell Biology
Cells as fundamental units of life: membranes, organelles, information flow, metabolism, and the compartmentalized chemistry that enables growth, replication, and response
Evolution
Natural selection, adaptation, speciation, and the historical development of life
Geology
Natural Sciences1 note
Electrical Engineering
Applied Sciences2 notes
Circuits & Electronics
Passive and active components, Kirchhoff laws, circuit analysis techniques, RLC dynamics, and frequency-domain design — the practical realization of electromagnetic fields in engineered networks.
Signal Processing
Transforms, filtering, sampling, and frequency-domain analysis of signals — the mathematics and algorithms of extracting information from waveforms.
Robotics
Applied Sciences1 note
Embedded Systems
Applied Sciences1 note
Economics
Social Sciences1 note
Sociology
Social Sciences1 note
Psychology
Social Sciences1 note
Linguistics
Social Sciences1 note
Jurisprudence
Social Sciences1 note
Finance
Social Sciences1 note
Political Science
Social Sciences1 note
Philosophy
Humanities7 notes
Aesthetics
Beauty, form, and artistic judgment
Epistemology
Knowledge, belief, justification, and truth
Ethics
Good, value, moral principles, and how one ought to live
Metaphysics
The inquiry into existence, essence, being, substance, categories, and the ultimate structure of reality
Philosophy of Mind
Consciousness, selfhood, qualia, and the nature of mental experience — the mind as a self-organizing system.
Philosophy of Science
Empiricism, falsification, modeling, and the scientific method
Political Philosophy
Order, justice, governance, power, and the legitimate use of authority