Introduction
Maths, Statistics & Probability
Introduction
Graphs
Field Theory
- Differential equations
  Visualisation
  First order ODEs
  Separable ODEs
  Linear ODEs
  Homogeneous functions & ODEs
  Exact & Inexact ODEs
  Existence & Uniqueness of Solutions
  Autonomous Equations & Stability
  Second order ODEs
  Standard form linear ODEs
  Homogeneous LODEs with constant coefficients
  Nonhomogeneous LODEs with constant coefficients
  Series solutions
  Harmonic motion
  Nonlinear second order ODEs
  Introduction
  2D linear systems
  Classification of fixed points
  Nonlinear systems in the phase plane
- Partial differential equations
  Introduction
  First order PDEs
  Second order linear PDEs
  Method of separation of variables
  Laplace's equation
  The 1D wave equation: d'Alembert's solution
  The wave equation in higher dimensions: Huygens' principle
  General second order linear PDE
  Reaction - diffusion equations
Probability & Statistics
Machine Learning
Introduction
Feature Engineering
Feature Selection
Feature Extraction (Dimensionality Reduction)
Time Series Analysis
- K-means clustering
- Measuring Entropy
- Ensemble learning
Recommender Systems
The Confusion Matrix
Data Management
- Data warehousing - ETL vs ELT
Deep Learning
Introduction
Logistic Regression
- Gradient Descent
- Vectorization
Machine Learning Strategies
Generative AI
Introduction
Prompting and Prompt Engineering
- Pre-training Large Language Models
- Efficient Multi-GPU Compute Strategies
Instruction Fine-Tuning
Model Evaluation: Metrics & Benchmarks
Parameter Efficient Fine-Tuning (PEFT)
Reinforcement Learning From Human Feedback (RLHF)
Model Optimization for Deployment
Stable Diffusion

Artificial Intelligence 🤖

Graphs

In this section, we focus on applications of derivatives and in particular how to use them in order to extract information about graphs. The material offers building blocks to optimisation problems in general.

Applications Stationary points