Course Content
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Mathematics for ML 0/5
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Motivation for Linear AlgebraLecture1.1
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Motivation for ProbabilityLecture1.2
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Motivation for StatisticsLecture1.3
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Motivation for CalculusLecture1.4
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Application of Mathematics and real world case studiesLecture1.5
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Linear Algebra - Vectors 0/5
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Introduction to VectorsLecture2.1
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Operations with Vectors and their meaningLecture2.2
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Cosine and dor product, inner product of vectorsLecture2.3
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Basis, vector space and linear independenceLecture2.4
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Applications of changing basis vectorsLecture2.5
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Linear Algebra - Matrices 0/7
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How matrices transform spaceLecture3.1
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Composition or combination of matrix transformationsLecture3.2
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Gaussian elimination – solving apples and bananas problemLecture3.3
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From Gaussian elimination to inverse matrixLecture3.4
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Solving equations using inverse matrixLecture3.5
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Determinants of matricesLecture3.6
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Identify special matricesLecture3.7
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Eigenvalues and Eigenvectors 0/7
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Introduction to eigenvalues and eigenvectorsLecture4.1
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Special eigen-casesLecture4.2
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Calculating eigenvectorsLecture4.3
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Changing to the eigenbasisLecture4.4
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Eigenbasis exampleLecture4.5
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Diagonalisation and applications PracticeLecture4.6
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Introduction to PageRankLecture4.7
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Multivariate Calculus 0/1
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Multivariate Calculus 0/8
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Definition of a derivativeLecture6.1
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Differentiation examples & special casesLecture6.2
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Product ruleLecture6.3
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Chain ruleLecture6.4
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Variables, constants & contextLecture6.5
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Differentiate with respect to anythingLecture6.6
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The JacobianLecture6.7
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The HessianLecture6.8
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Intro to optimisation 0/5
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Newton-Raphson in one dimensionLecture7.1
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Gradient DescentLecture7.2
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Gradient descent in a sandpitLecture7.3
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Steepest strategiesLecture7.4
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Constrained optimisationLecture7.5
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Regression 0/4
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Simple linear regressionLecture8.1
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General non linear least squaresLecture8.2
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Least squares regression analysis in practiceLecture8.3
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Fitting the distribution of heights dataLecture8.4
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Statistics of Datasets 0/5
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Mean of a datasetLecture9.1
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Variance of one-dimensional datasetsLecture9.2
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Variance of higher-dimensional datasetsLecture9.3
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Effect on the meanLecture9.4
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Effect on the (co)varianceLecture9.5
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Principal Component Analysis 0/6
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Problem setting and PCA objectiveLecture10.1
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Finding the coordinates of the projected dataLecture10.2
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Reformulation of the objectiveLecture10.3
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Finding the basis vectors that span the principal subspaceLecture10.4
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Steps of PCALecture10.5
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PCA in high dimensionsLecture10.6
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Introduction to Probability 0/8
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Disjoint Events + General Addition RuleLecture11.1
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IndependenceLecture11.2
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Probability ExamplesLecture11.3
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Disjoint vs. IndependentLecture11.4
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Conditional ProbabilityLecture11.5
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Probability TreesLecture11.6
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Bayesian InferenceLecture11.7
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Examples of Bayesian InferenceLecture11.8
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Probability Distributions 0/5
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Normal DistributionLecture12.1
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Binomial DistributionLecture12.2
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Normal Approximation to BinomialLecture12.3
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Working with the Binomial DistributionLecture12.4
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Poison DistributionLecture12.5
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Special eigen-cases