gc625 / notes

My Notes

These are my notes for some of my University courses. Currently include:

• Fundamentals of Pure Mathematics (Y2, SEM2)
• Introduction to Algorithms and Data Structures (Y2, SEM1)
• Introduction to Algorithms and Data Structures (Y2, SEM2)
• Introductory Applied Machine Learning (Y3, SEM1)
  • Chapter 1: Basic Math and Naive Bayes
  • Chapter 2: Decision Trees
  • Chapter 3: Linear and Logistic Regression
  • Chapter 4: Optimisation, Regularisation and SVMs
  • Chapter 5: K Nearest Neighbours
  • Chapter 6: Gaussian Mixture Models and K Means
  • Chapter 7: PCA and Hierarchical Clustering
  • Chapter 8: Introduction to Artificial Neural Networks
• Honours Differential Equations (Y3, SEM1)
  • Chapter 1: Solving Linear Systems
  • Chapter 2: Fundamental Matrices
  • Chapter 3: Solving Nonhomogeneous Systems
  • Chapter 4: Phase Portraits and System Stability
  • Chapter 5: Lyapunov Functions
  • Chapter 6: Introduction to Fourier Series
  • Chapter 7: Solving PDEs
  • Chapter 8: Introduction to Sturm Liouville Theory
  • Chapter 9: The Laplace Transform (Incomplete)
• Honours Analysis (Y3, SEM1)
  • Chapter 1: Real Numbers and Sequences
  • Chapter 2: Bolzano-Weierstrass Theorem, Cauchy Sequences and Series
  • Chapter 3: Continuity and Uniform Convergence of Sequences
  • Chapter 4: Uniform Convergence of Series
  • Chapter 5: Power Series
  • Chapter 6: Lebesgue Integrable Functions
  • Chapter 7: Lebesgue Integrability of Series and the Riemann Integral
  • Chapter 8: Lebesgue Integrability Over Intervals and the Fundamental Theorem of Calculus
  • Chapter 9: Fatoux Lemma and the Dominated Convergence Theorem
  • Chapter 10: The Space of L^2 Functions
  • Chapter 11: Fourier Series
• Foundations of Natural Language Processing (Y3, SEM2)
  • Chapter 1: Intro to NLP, Ambiguity and Working with Corpora
  • Chapter 2: N-Gram Models and Smoothing Techniques
  • Chapter 3: Further Smoothing, Noisy Channel Model and Naive Bayes for Text Classification
  • Chapter 4: Logistic Regression for Text Classification, Morphological Parsing and POS Tagging
  • Chapter 5: Syntactic Parsing, CKY and PCFGs
  • Chapter 6: Evaluating Parsing, Improving Vanilla PCFGs, Dependency Parsing and Semantics from Syntax
  • Chapter 7: Semantic Role Labelling, Word Sense Disambiguation and Distributional Semantics
  • Chapter 8: Word2Vec, ANNs for NLP and Discourse Coherence
• Honours Algebra (Y3, SEM2)
  • Chapter 1: Fields and Vector Spaces
  • Chapter 2: The "Morphisms" and Representing Matrices
  • Chapter 3: Abstract Linear Mappings and Change of Basis Matrices
  • Chapter 4: Rings, Ideals and Subrings
  • Chapter 5: Factor Rings, The First Isomorphism Theorem and Modules
  • Chapter 6: Determinants and Multilinear Forms
  • Chapter 7: Eigenvalues, Triangularisation and Diagonalisation
  • Chapter 8: Inner Product Spaces and Orthogonal Projections
  • Chapter 9: Adjoint Endomorphisms and The Spectral Theorem
  • Chapter 10: The Jordan Normal Form