Projects
ArtificialEconomist.com Economoose.com YetiPredict.com
Notes
Logic, the natural numbers and computability Algebra Real and complex analysis
Geometry Non-relativistic field theory Rigid body physics
Computer science and integer RISC instructions (ARM)Floating point algorithms Freestanding C Data structures and algorithms
Univariate probability Multivariate probability Univariate time series Multivariate time series Probabilistic Turing machines and algorithms, and encryption
Neural networks Computer vision Statistics for audio and text, and multi-modal models
Statistical mechanics Relativistic field theory Quantum mechanics and quantum computing Chemistry and geology Biology Engineering Electronics
Manufacturing CPUs and peripherals Floating Point Units (FPUs), cache, other Reduced Instruction Set Computers (RISC) and Complex Instruction Set Computers (CISC)Audio 2D graphics 3D graphics Multithreading, multi-core CPUs, Graphics Processing Units, and Single Instruction, Multiple Data (SIMD)
Microsoft Disk Operating System (MS-DOS)Memory Mapping Units (MMUs), protection rings, GNU/Linux and hosted C Advanced Linux: Including encrypting systems, Logical Volume Management (LVM) and Systemd Networks Single-node databases and Structured Query Language (SQL)Audio and video output in Linux, and sandboxing applications system virtual machines and hardware emulation Advanced CPU architecture, including hardware-assisted virtualisation, trusted execution environment, secure enclave and dynamic frequency scaling
Other imperative languages: Fortran, Algol, Pascal Functional languages: Meta Language (ML), Caml and Haskell C++, objects and generic programming Java, garbage collection, process virtual machines and Kotlin Other C-family languages: Rust, Nim, Zig and Objective-C Communicating sequential processes (CSP) and actor model concurrent languages: Erlang, Elixer, Swift, Go Other compiled languages: Forth, Smalltalk and Simula Scheme Other Lisp-family languages: Racket, Common Lisp, Clojure and Scala Reverse engineering
JavaScript, HyperText Markup Language (HTML), Cascading Style Sheets (CSS) and the World Wide Web (WWW), and WebAssembly (Wasm)Python R Other interpreted languages: STATA, Lua, Perl, Ruby, Julia, PHP and FreeBASIC
Specific Linux distributions and OS-level virtualisation with Docker Distributed computing Integrated Development Environments (IDEs)Android
FreeBSD and OpenBSD Windows 3.x, Windows 9x and Windows NT Classic Mac OS, macOS and iOS
Decision and game theory General equilibrium Industrial organisation Money, banking and finance Microeconomics Macroeconomics Public choice History Epistemology and ontology Political science and philosophy

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Real and complex analysis

Pre-calculus

Ordering of infinite sets

Limits of infinite sequences

Properties of functions

Limits and continuous functions

Transcendental and real numbers

Univariate real analysis

Univariate differentiation

Identifying and evaluating \(e\)

Univariate integration

The sine and cosine functions, and identifying \(\pi\)

The tangent function, and evaluating \(\pi\)

Polar coordinates

Other trigonometric functions

Taylor and Fourier analysis

The gamma and beta functions

Ordinary Differential Equations (ODEs)

Univariate optimisation

Multivariate real analysis: Scalar fields

Multivariate functions

Multivariate differentiation of scalar fields

Multivariate integration of scalar fields

Multivariate real analysis

Multivariate differentiation of vector fields

Multivariate integration of vector fields

Partial Differential Equations (PDEs)

Multivariate optimisation

Complex analysis

Complex calculus

Laplace transforms

Quadratic maps, the logistic map, the Mandlebrot set and the Julia set

Riemann surfaces

Please select a chapter from the left.

Preface

This is a live document, and is full of gaps, mistakes, typos etc.