Linear Algebra is not just about solving systems of equations; it is the mathematical backbone of modern Computer Science, specifically in Artificial Intelligence and Machine Learning. We emphasize structures that power algorithms.
Why this course matters: You cannot build or understand advanced ML models without a solid grasp of vector spaces and matrix operations. Once you master this geometry in flat spaces, you’ll be ready for the fun that happens on curved surfaces (Manifold Learning).
This foundational course provides the essential mathematical toolkit for understanding classic and modern ML algorithms. We focus on the geometric and optimization principles that drive predictive modeling.
Dimensionality Reduction: Principal Component Analysis (PCA) and Singular Value Decomposition (SVD).
Classification & Regression: Applications of QR decomposition and Support Vector Machines (SVM).
Optimization Theory: Introduction to convex optimization, penalty methods (L1/L2 regularization), and the Karush-Kuhn-Tucker (KKT) conditions.
The course highlights how these mathematical fundamentals underpin advanced research. We explore applications in:
Artificial Vision (Image Processing) and the architecture of Large Language Models (LLMs).
Analysis of complex biological data (e.g., Omics), which is my area of research in applied math.
Furthermore, we discuss the evolution of these concepts into emerging geometric methods, such as Manifold Learning, Network Science and Topological Data Science (TDS), offering a clear perspective on possible subjects for dissertations or doctoral studies.
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