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Lecture notes for the module 'MAT1032 Real Analysis I' in the Mathematics course. Topics covered in the notes include: - Bounds, Supremum, Infimum - Axiom of Completeness - Cauchy Sequences and Series - Inequalities - Limits and Covergence - Logic and Quantifiers - Sets and Notations - Types of Functions - Types of Numbers Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT1033 Probability and Statistics' in the Mathematics course. Topics covered in the notes include: - Probability - Hypothesis Testing - Discrete Random Variables - Continuous Random Variables - More Than One Random Variable - Bayes - Normal and Poisson Distribution Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module ''MAT2009 Operations Research and Optimization' in the Mathematics course. Topics covered in the notes include: - Linear Programming - The Simplex Method - Sensitivity Analysis - Dual Simplex Method - Complementary Slackness - Asymmetric Duality - Transportation Problem - Assignment Problem Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT2001 Numerical and Computational Methods' in the Mathematics course. Topics covered in the notes include: - Vectors and Matrices - Singular Value Decomposition (SVD) - Systems of Linear Equations - LU decomposition - Forward and Backward Substitution - Interpolation and Approximation - Lagrange, Newton and Hermite Interpolation - Numerical Integration Definitions in pink, formulae and equations in green, examples in blue.

Some lecture notes for the module 'MAT1034 Linear Algebra' in the Mathematics course. Topics covered in the notes include: - Systems of Linear Equations - Gaussian Elimination - Vector Spaces - Linear Operators - Inner Product Space Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT2048 Groups and Rings' in the Mathematics course. Topics covered in the notes include: - Binary Operations, Magmas, Semi Group, Monoid - Finite Groups and Cayley Tables - Permutations and Symmetries - Subgroups - Cosets and Lagrange Theorem - Group Homomorphisms - Normal Subgroups and Quotient Group - Rings and Fields - Homomorphisms, Ideals and Quotient Rings Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT 3043 Graphs and Networks' in the Mathematics course. Topics covered in the notes include: - Graphs - Connectedness - Eulerian and Hamiltonian Graphs - Trees - Planar Graphs and Geometric Dual - Graph Colourings - Matchings and Networks Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT3004 Introduction to Function Spaces' in the Mathematics course. Topics covered in the notes include: - Metric Spaces - Normed Spaces - Continuity and Convergence - Open and Closed Sets Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT3040 Mathematical Ecology and Epidemiology' in the Mathematics course. Topics covered in the notes include: - Single Species Ecology - Harvesting and Fishing - Interacting Species Populations - Predator-Prey Models - Competition and Mutualism Modelling - SIR and SEI Models - Quarantining - Spatial Ecology Definitions in pink, formulae and equations in green, examples in blue.

Lecture notes for the module 'MAT2047 Curves and Surfaces' in the Mathematics course. Topics covered in the notes include: - Vectors and Matrices - Isometric Transformation - Exponentiation - Plane Curves - Frenet-Serret Frame - Curvature - Rotation Number - Fundamental Forms Definitions in pink, formulae and equations in green, examples in blue.