Projects
Notes
Logic, the natural numbers and computability Algebra including linear algebra Real analysis, variational calculus and functionals Complex analysis Abstract algebra Analytic geometry and Euclidian space Topology
Non-relativistic field theory Rigid body physics Relativistic field theory
Computer science, integer RISC instructions (RV64I) and building a hex and macro assembler Simple algorithms with integer addition and subtraction and arrays, decision problems, other problems, lossless compression Algorithms for integer multiplication and division, and floating point arithmetic Freestanding C, and building C compiler in assembly then C Data structures and algorithms
Univariate probability Multivariate probability Multivariate probability discriminative including machine learning Fully-connected neural networks Univariate time series Multivariate time series Multivariate probability inference Probabilistic Turing machines and algorithms, and encryption Statistical mechanics Quantum mechanics and quantum computing
Chemistry and geology Biology Engineering Electronics
Manufacturing RV64I CPUs, boot ROMS/firmware (mask ROM/diode matrix), punch cards, memory mapped IO for LEDs, volatile RAM (SRAM and DRAM) and micro-architecture including cache, prefetching, instruction pipelines, branch prediction, out-of-order execution and speculative execution Control additions (RV64I\_Zicsr\_Zifencei) Integer multiplication and division (RV64IM\_Zicsr\_Zifencei) Floating Point Units (FPUs) (RV64IMFDQ\_Zicsr\_Zifencei), Single Instruction, Multiple Data (SIMD) (RV64IMFDQV\_Zicsr\_Zifencei) and BLAS Other Reduced Instruction Set Computers (RISC) and Complex Instruction Set Computers (CISC), including Intel Management Engine (ME) and amd Platform Security Processor (PSP)2D graphics, keyboards, terminals, printers and controllers Non-volatile editable memory: bootloaders and computer storage including magnetic memory (magnetic core memory, magnetic tape, floppy disks, hard drives), Semiconductor memory incuding SSD (EPROM/EEPROM/flash memory), optical memory (CD/DVD etc)Networks Audio 3D graphics Multithreading and multi-core CPUs (RV64IMFDQVA\_Zicsr\_Zifencei aka RV64GQV)Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs)
RV64GQV\_S, Memory Mapping Units (MMUs), Address Generation Units (AGUs), protection rings CPU interrupts and GNU/Linux/Systemd Hosted C and compiling C code with Linux Securing the system and boot process: Including encrypting systems, Logical Volume Management (LVM), trusted execution environment, secure enclave, Supervisor Mode Access Prevention Networks on Linux Audio and video output in Linux, and sandboxing applications Serialisation, single-node databases, Structured Query Language (SQL) and Extract-Transform-Load/Extract-Load-Transform
Other imperative languages: Fortran, Algol, Pascal C++, objects, generic programming functional programming and clang/LLVM, and transpilers Other C-family languages: Rust, Zig
Scheme and Common Lisp (compiled natively), and dynamic typing Functional languages: Meta Language (ML), Caml, OCaml and Haskell Other compiled languages: Objective-C, Nim, Forth, COBOL, Smalltalk and Simula Communicating sequential processes (CSP) and actor model concurrent languages: Swift, Go C\#, F\#, VB.NET and mono
Java, garbage collection, process virtual machines and Kotlin Other Lisp-family languages, and compiling them to VM: Racket, Clojure and Scala Communicating sequential processes (CSP) and actor model concurrent languages with virual machines: The BEAM VM and Erlang, Elixer, Dart (other concurrency model?)
Other interpreted languages: Lua, Perl, Ruby, Julia, Octave, PHP and FreeBASIC
HyperText Markup Language (HTML), Cascading Style Sheets (CSS) and the World Wide Web (WWW)JavaScript, Just-In-Time compilation (JIT) and WebAssembly (Wasm)Server-side javascript and javascript frameworks and libraries
Python Python: Data Python: Internet packages
R Specific packages for R Validating code and compilers: Coq (ocaml), compcert, hol (ocaml), isabelle, agda (haskell)Logical programming languages including ada and prolog
Reverse engineering hardware, backing up ROMs, hardware emulation including use of JIT and dynamic recompilers, and emulation of retro video game systems Reverse engineering software
Statistics text, including large language models Statistics for audio with text, and multi-modal models Computer vision Working with specific datasets, and models including Llama and Stable Diffusion
Specific Linux distributions, system virtual machines, RV64GQVH\_S, hardware-assisted virtualisation and OS-level virtualisation with Docker Distributed computing Integrated Development Environments (IDEs)Android
Microsoft Disk Operating System (MS-DOS) and other non-multitasking operating systems including ZX BASIC, Classic MacOS, PC88, PC98, MSX, Machine Operating System for BBC Micro, Commadore 64 FreeBSD and OpenBSD Windows 3.x, Windows 9x and Windows NT macOS and iOS
Decision and game theory General equilibrium Industrial organisation Money, banking and finance Microeconomics Macroeconomics Public choice Languages and packages for economics: Dynare for Octave, QuantEcon for Python/Julia; NetLogo; Mesa for Python
History Epistemology and ontology Political science and philosophy

GitHub
LinkedIn

Real analysis, variational calculus and functionals

Download PDF

Univariate optimisation

Multivariate real analysis: Scalar fields

Multivariate functions

Multivariate differentiation of scalar fields

Multivariate integration of scalar fields

Generalising the binomial coefficient formula: The beta function

Multivariate real analysis: Vector fields

Multivariate differentiation of vector fields

Multivariate integration of vector fields

Partial Differential Equations (PDEs)

Multivariate optimisation of scalar fields

Variational calculus / calculus of variations / functionals

Variational calculus/functionals

Second-order Ordinary Differential Equations (ODEs)