Course Code: DSM101
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Synopsis

Mathematical Foundations for Data Science will introduce students to the essential matrix algebra, optimisation, probability and statistics required for pursuing Data Science. Students will be exposed to computational techniques to perform row operations on matrices, compute partial derivatives and gradients of multivariable functions. Basic concepts on minimisation of cost functions and linear regression will also be taught so that students will have sound mathematical foundations to proceed and understand standard algorithms in Data Science and Machine Learning.
Level: 1
Credit Units: 5
Presentation Pattern: EVERY JAN

Topics

  • Introduction and Linear Algebra for Data Preparation I
  • Introduction and Python programming
  • Vectors, matrices and operations
  • System of linear equations
  • Linear transformation and matrix inversion
  • Linear Algebra for Data Preparation II
  • Eigenvalues and eigenvectors
  • Dimensionality reduction
  • Orthogonality and projection
  • Principal Component Analysis (PCA) basics
  • Differential Calculus and Rate of Change
  • Common functions
  • Derivatives
  • Chain rule
  • Partial derivatives
  • Optimisation Basics
  • Gradient vectors
  • Introduction to optimisation
  • Critical points
  • Optimisation and PCA
  • Gradient descent
  • PCA
  • Descriptive Statistics and Linear Regression
  • Descriptive statistics
  • Linear regression

Learning Outcome

  • Interpret eigenvalues and eigenvectors.
  • Explain gradient-based optimisation methods to solve basic minimisation problems.
  • Show descriptive statistics to extract insights from datasets.
  • Apply basic linear algebra concepts to manipulate data in Python for data science tasks.
  • Use differential calculus to analyse and interpret rates of change in data-related functions.
  • Implement a linear regression.
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