This is an open, unconventional textbook covering mathematics, computing, and artificial intelligence from foundational principles. It's designed for practitioners seeking a deep understanding, moving beyond exam preparation and focusing on real-world application. The author, drawing from years of experience in AI/ML, has compiled notes that prioritize intuition, context, and clear explanations, avoiding dense notation and outdated material.
The compendium covers a broad range of topics, from vectors and matrices to machine learning, computer vision, and multimodal learning, with future chapters planned for areas like data structures and AI inference.
The compendium covers a broad range of topics, from vectors and matrices to machine learning, computer vision, and multimodal learning, with future chapters planned for areas like data structures and AI inference.
For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
A new mathematical proof resolves a 35-year-old bet between Noga Alon and Peter Sarnak regarding the prevalence of optimal expander graphs, demonstrating that both mathematicians were partially incorrect. The proof, building on work in random matrix theory, reveals that approximately 69% of regular graphs are Ramanujan graphs.
analogue I-K of the Laplacian in potential theory
