1. Linear Algebra Foundations
Vector space structure forms the foundation of all machine learning mathematics. A vector \(\mathbf{x} = [x_1, \ldots, x_n]^\top \in \mathbb{R}^n\) is an ordered list of \(n\) numb...
Read full chapter →The essential AI Math (500 Questions) cheat sheet: 8 concise chapters you can read in minutes, distilled from the full deck. When you're ready, drill the flashcards or test yourself under exam conditions.
Vector space structure forms the foundation of all machine learning mathematics. A vector \(\mathbf{x} = [x_1, \ldots, x_n]^\top \in \mathbb{R}^n\) is an ordered list of \(n\) numb...
Read full chapter →Subspace concepts reveal the structure of linear transformations. The span of vectors \(\{\mathbf{v}_1, \ldots, \mathbf{v}_k\}\) consists of all linear combinations \(\sum_i c_i \m...
Read full chapter →Derivatives measure instantaneous rates of change, forming the foundation of optimization in machine learning. The derivative \(f'(x) = \lim_{h \to 0}(f(x+h)-f(x))/h\) is the slope...
Read full chapter →Unconstrained optimization finds minima of \(f(\theta)\). Convex problems \(f(\lambda\mathbf{x} + (1-\lambda)\mathbf{y}) \leq \lambda f(\mathbf{x}) + (1-\lambda)f(\mathbf{y})\) hav...
Read full chapter →Probability axioms form the foundation. Kolmogorov axioms: \(P(\Omega) = 1\), \(P(A) \geq 0\), and \(P(A \cup B) = P(A) + P(B)\) for disjoint \(A, B\). The complement rule \(P(A^c)...
Read full chapter →Self-information (surprisal) \(I(x) = -\log_2 p(x)\) measures surprise: rare events carry more information. Doubling rarity adds exactly 1 bit, since log converts products to sums,...
Read full chapter →A single neuron computes \(a = \sigma(\mathbf{w}^\top\mathbf{x} + b)\) where \(\mathbf{w}\) are weights, \(b\) is bias, and \(\sigma\) is a nonlinear activation. A layer in matrix...
Read full chapter →The Transformer architecture relies on self-attention. For an input sequence \(X \in \mathbb{R}^{n \times d_{\text{model}}}\), three learned projections produce queries \(Q = XW_Q\...
Read full chapter →Done reading?
Test yourself with the AI Math (500 Questions) practice exam — timed questions, instant score, full review of wrong answers. Free.
🎯 Take the Practice Exam →