Overview
I am a data scientist and software developer residing in Sydney, Australia. I am currently the Chief Data Officer at the NSW Cancer Institute.

This is my personal website, which holds links to my research notes, and any related projects I happen to be working on, that mostly tend to be in the area of mathematics and computer science.

Currently my main areas of interest are: formal proof construction, group theory, algebraic graph theory and networks, coding and information theory, and the application of symmetry and invariance in developing models to speed up machine learning tasks. I am also interested in using ML techniques to automate data engineering problems.

Jamie Gabriel
 

General Notebooks


Setup
I mostly use JupyterLab running through Docker to manage most things related to research. Full details and set up instructions here. Occasionally I like to work with the HTM Machine Intelligence algorithms which can be tricky to get going so I have included that in these notes. This set up is really nice across lots of different math research and works well across different operating systems.

If I am not using JupyterLab, it's usually RStudio & R these days and I tend to build anything web related in Shiny with Django as the backend.


Python for Math
I tend not to use Sage these days but here is a really nice way to install and config the Sage JupyterLab environment running on Docker. For full details of the Docker Image see https://hub.docker.com/r/cemulate/sagemath-jupyterlab/.


Latest
  • 16th January 22: Ascertaining the criteria needed for graph populations to be bounded or unbounded (ES2)

  • 15th January 22: Exploring the fundamental properties of graphs and graph populations(ES1_2)

  • 10th January 22: A new series of notes on Exceptional Structures in mathematics(ES1_1)

  • 15th December 21: Ascertaining the uniqueness of algebraic solutions to the geometric quintic equation (SPE26)

  • 19th December 21: Deriving an algebraic solution of the general quintic polynomial equation (SPE25)

  • 3rd December 21: An overview of the fundamental structures of Algebraic Calculus and area on a parabola (AC1_2)

  • 1st December 21: Outlining the foundations of Affine geometry to underpin the construction of dCB curves(DCB3)

  • 13th November 21: Using De Casteljau's algorithm and splitting dCB curves (DCB2)

  • 2nd November 21: Transforming the general quintic to geometric form (SPE24)

  • 27th October 21: Incorporating the patterns found in signs of coefficient to generate a general solution to polynomial equations (SPE23)

  • 23rd October 21: Introduction to DeCastelau Bezier Curves and the DCB Parametrization theorem (DCB1)

  • 10th October 21: Continuing to explore the bridge between BiTri numbers and polygonal subdivisions (SPE22)

  • 6th October 21: Exploring ternary operations on Fuss polygonal subdivisions and thier associated ternary trees (SPE21)

  • 2nd October 21: Exploring the link between polygon subdivisions and polynomial equations (SPE20)

  • 22nd September 21: Understanding the formal object that is a sum of all polygons with all of their subdivisions into triangles (SPE18)

  • 20th September 21: Understanding how Catalan and Fuss numbers relate to binary and ternary trees and how these trees can be created from n-gons (SPE16)

  • 2nd September 21: Exploring the structure of the quartic equation in relation to BiTriQuad numbers (SPE15)

  • 15th August 21: Exploring the relationship between solutions to polynomial equations, sides of polygons and BiTri numbers (SPE13_14)

  • 10th August 21: Continuing to explore patterns of matrices created by the solutions of polynomial equations, referencing Knuth, Stanley and Dickau (SPE11)

  • 4th August 21: Exploring different pattterns in the matrices created by the solutions of polynomial equations (SPE10)

  • 29th July 21: Extending the conjecture beyond Catalan numbers using matrices and examining resulting patterns using OEIS to find Catalan and Fuss numbers (SPE9)

  • 26th July 21: Comparing the conjecture for a solution to the general cubic using Catalan Numbers to traditional formulas (SPE8)

  • 15th July 21: Testing a conjecture for a solution to the general cubic using Catalan Numbers (SPE7)

  • 10th July 21: Extending the power series approach to the quartic case (SPE6)

  • 28th June 21: Unpacking the structure of coefficients in the solutions of general polynomials (SPE5)

  • 20th June 21: Finding patterns in solutions of general polynomials (SPE4)

  • 18th June 21: Extending the power series approach to the cubic case (SPE3)

  • 7th June 21: Discovering Catalan numbers in the solutions of general quadratics when using power series subsitution (SPE2)

  • 2nd June 21: The inherent difficulties that arise when solving higher degree polynomials using radicals (SPE1)