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We begin with one number, then build toward feature vectors, row and column vectors, transposes, dataset matrices, and the first mathematical form of a machine-learning model.
We extend vectors into matrices and tensors, starting from real-world data tables, images, videos, and neural-network batches, then building toward formal matrix algebra, tensor …
We build the probability language needed for modern generative AI: random variables, probability distributions, Gaussian noise, white noise, colored noise, Markov chains, …
We build the mathematics behind modern large language models from scratch: text as probability, tokenization, embeddings, transformers, attention, loss functions, backpropagation, …
We build the mathematics of time-series learning from scratch: sequences, forecasting, stationarity, autocorrelation, ARIMA, state-space models, Kalman filtering, recurrent …