Vector properties, magnitudes, and algebraic operations including addition and scalar multiplication. Introduces matrix representations, arithmetic, and computational techniques for solving linear systems.
A graduate-level sequence exploring the gradient vector as the foundational tool for modern optimization. Students move from the geometric interpretation of multivariate derivatives to the implementation of stochastic algorithms used in machine learning.
A graduate-level exploration of vector quantities as high-dimensional data points. This sequence bridges linear algebra and data science, examining how geometric intuitions like magnitude, direction, and distance evolve and paradoxically degrade in high-dimensional spaces.
An advanced exploration of vector fields and tensor calculus for graduate students, bridging the gap between vector analysis and general relativity through curvilinear coordinates, transformation rules, and continuum mechanics.
A rigorous graduate-level sequence exploring the algebraic and topological foundations of vector quantities, transitioning from Euclidean geometry to abstract Banach and Hilbert spaces.
