HeyJaredML & AI: Foundations & Methods
Learn Machine Learning and AI for free: from the foundations to modern approaches and analysis. This is a free resource based on various courses I have taught over 20 years.
- Indexed videos, last 90 days
- 15
- Latest publication
- Jul 24, 2026
- Audience
- ~2.2K subscribers
- Earliest in this view
- Jul 5, 2026
Latest videos
One Particle = An Entire Universe: Ergodic Theory (opens the original)
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Can the long-term behaviour of a **single trajectory** reveal the statistical properties of an entire dynamical system? This question lies at the heart of **ergodic theory**, one of the deepest and most beautiful areas of modern mathematics. In this video, we develop the intuition behind **Birkhoff's Ergodic Theorem** from first principles. Starting with deterministic dynamical systems, we introduce observables, time averages, invariant measures, equilibrium distributions and space averages befo
The Real Meaning of the Tensor Product ⊗ (opens the original)
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Where do tensors actually come from? Rather than starting with arrays of numbers, this video builds tensors from first principles. Beginning with multilinear maps, we construct the tensor product, explain its universal property, show why tensor products are needed, and reveal how choosing a basis turns abstract tensors into the multidimensional arrays used throughout physics, engineering and machine learning. By the end of the video you'll understand why tensors are fundamentally abstract mathem
Why Linear Maps Aren't Enough: Multilinear Maps Explained (opens the original)
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Linear maps are one of the central ideas in linear algebra—but what happens when a function depends linearly on two, three or even more vectors at the same time? In this video we introduce **multilinear maps**, the natural generalisation of linear maps and one of the key mathematical ideas behind tensors, differential geometry, continuum mechanics, quantum mechanics and modern machine learning. Starting from familiar linear maps, we develop the concept of separate linearity, study bilinear and t
What Exactly are Embeddings? From Topology to Geometry (opens the original)
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When we embed one mathematical space inside another, what exactly is being preserved? Sometimes we preserve only the points. Sometimes we preserve the topology. Sometimes we even preserve every distance. In this video we build a hierarchy of increasingly stronger maps: • Topological embeddings • Isometric embeddings • Isometric isomorphisms Along the way we explain why these notions are fundamental throughout modern mathematics, from geometry and topology to differential geometry, machine learni
Why Every Finite-Dimensional Space Is Really Just Rn: The Most Beautiful Theorem in Linear Algebra (opens the original)
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At first glance, finite-dimensional vector spaces can look completely different. They may have different vectors, different norms, or even different inner products. Remarkably, they are all essentially the same. In this video we prove one of the most important results in finite-dimensional analysis: every finite-dimensional normed space is linearly homeomorphic to Euclidean space, and every finite-dimensional inner product space is isometrically isomorphic to (\mathbb{R}^n) when expressed in an
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~2.2K subscribers
Measured Sep 19, 2026
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