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Mathematics Behind AI & ML — Deep Dive
The essential math that powers every neural network, recommendation engine, and language model — explained through real-world analogies
Co-Created by Kiran Shirol and Claude
Pillars
Linear Algebra
Calculus
Probability & Stats
Information Theory
Advanced Topics
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14 chapters
· 5 pillars
Pillar 1
Linear Algebra
Vectors, matrices, and decompositions — the language of neural networks.
1
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Vectors & Spaces
GPS coordinates for meaning — dot products, similarity, and why Spotify finds similar songs.
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2
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Matrices & Transformations
Instagram filters for data — why y = Wx + b is the most important equation in AI.
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3
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Eigenvalues, SVD & Decompositions
Finding natural axes — how PCA and LoRA compress billions of parameters.
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Pillar 2
Calculus
Derivatives, gradients, and optimization — how networks learn from errors.
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Derivatives & Gradients
The slope of the hill you’re standing on — flip it and walk downhill to find lowest error.
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5
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Chain Rule & Backpropagation
The blame chain — tracing errors backward through a neural network.
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6
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Optimization & Gradient Descent
Blindfolded on a mountain — learning rate, momentum, and Adam optimizer.
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Pillar 3
Probability & Statistics
Distributions, inference, and the math of uncertainty.
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Probability Foundations
Umbrella decisions — Bayes’ theorem updates beliefs when new evidence arrives.
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8
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Distributions & Expectations
The bell curve shows up everywhere — why weights start as Gaussians.
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9
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Maximum Likelihood & Bayesian Inference
Detective work — training a model is literally maximizing likelihood.
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10
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Hypothesis Testing & Statistical Learning
Court trial logic — the bias-variance tradeoff every ML engineer faces daily.
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Pillar 4
Information Theory
Entropy, surprise, and cross-entropy — measuring how good your model is.
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Information Theory for ML
Entropy is surprise — a good model is rarely surprised by reality.
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Pillar 5
Advanced Topics
Tensors, numerical stability, and the grand tour of modern AI math.
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Tensors & High-Dimensional Geometry
Scalar → vector → matrix → tensor — AI works in thousands of dimensions.
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13
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Numerical Methods & Stability
Floating point on a tiny notepad — tricks that keep neural networks stable.
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14
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The Math of Modern AI (Capstone)
Every formula in a transformer, diffusion model, and RL agent — it all connects.
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