Peter Kempthorne continues MIT's 18.642, Topics in Mathematics with Applications in Finance, with a session spanning linear algebra and probability theory. He covers eigenvalues, eigenvectors, matrix diagonalization, and singular value decomposition, framing each as a tool for modeling dynamic systems and analyzing data. The lecture then turns to probability foundations, including distributions, moments, and covariance, before connecting them to principal component analysis and its use in portfolio management and stochastic modeling. Throughout, Kempthorne ties abstract mathematical machinery back to financial applications, showing how matrix decompositions and statistical moments underpin the quantitative methods used in modern finance. The pacing assumes familiarity with undergraduate linear algebra and statistics, building toward the stochastic models that structure the rest of the course. It is a working session of derivations and examples rather than a polished overview, consistent with MIT OpenCourseWare's standard lecture recordings.