Learning Outcome 1: Demonstrate systematic knowledge and critical understanding in topics in linear algebra, probability, and statistical models relevant to data science.

Task: Individual Coursework Overview

This individual coursework requires in-depth investigation and understanding of topics in linear algebra, probability, and statistical models applied to data science. The tasks involve exploring properties and operations related to vectors, matrices, and probability concepts such as Markov chains and Eigenfaces. Use your initiative and demonstrate originality within the given time frame.

Task Breakdown:

Task 1: Markov Chains

• Investigate a Markov chain scenario involving flower mutations and maze navigation by mice.
• Construct and manipulate transition matrices to model these scenarios.
• Use Python and numpy to calculate and visualize outcomes over multiple time steps.

Task 2: Eigenfaces

• Utilize the Olivetti Faces dataset to explore eigenfaces and facial image analysis.
• Calculate mean faces, covariance matrices, and eigenvalues/vectors using numpy.
• Visualize and interpret results, including eigenface transformations and reconstruction of facial images.

Assessment:

• Each task will be assessed based on your ability to demonstrate systematic knowledge, critical understanding, and practical application of linear algebra, probability, and statistical models within data science contexts.