Assessments

A short readiness check spanning algebra, functions, graphs, basic programming, NumPy familiarity, and mathematical notation. It gauges where you are before Week 1 so you can study efficiently. Answer honestly — the goal is to surface gaps, not to score high. After submitting, review the flagged areas noted in each explanation before starting the course.

A short checkpoint on Week 1: number systems, operator precedence, exponents and logarithms, summation and product notation, argmax, and sets. Aim for 80% or better before moving to Week 2. Each explanation points to the chapter to revisit if you miss it.

A short checkpoint on Week 2: functions, domain and range, composition, the standard ML activation functions (sigmoid, tanh, ReLU, softplus), and NumPy arrays, shapes, and broadcasting. Aim for 80% or better before moving to Week 3. Each explanation names the chapter to revisit if you miss it.

A short checkpoint on Week 3: vectors, the dot product, linear combinations, the L1/L2/L∞ norms, Euclidean distance, cosine similarity, and orthogonality. Aim for 80% or better before moving to Week 4. Each explanation names the chapter to revisit if you miss it.

A short checkpoint on Week 4: matrix shapes, the inner-dimension rule for matrix multiplication, the transpose, matrix–vector products, writing systems as $A\mathbf{x} = \mathbf{b}$, and classifying solutions as unique, infinite, or none. Aim for 80% or better before moving to Week 5. Each explanation names the chapter to revisit if you miss it.

Span, independence, basis and rank; the null and column spaces; eigenvalues and eigenvectors ($Av=\lambda v$); covariance; and PCA intuition including explained variance.

Limits (including indeterminate $0/0$ forms), continuity, the derivative from first principles, the power/product/quotient rules, derivatives of $e^x$ and $\ln x$, and central-difference numerical differentiation.

The chain rule, computational graphs with forward/backward passes on $y=(wx+b)^2$, partial derivatives, the gradient vector, the direction of steepest ascent, and reading contour plots.

Critical points and the second-derivative test, the gradient-descent update and learning-rate regimes, MSE, the linear-regression gradient $\frac{\partial L}{\partial w}=\frac{2}{n}X^\top(\hat{y}-y)$, gradient checking, and the closed-form normal equations.

A cumulative assessment covering Weeks 1–4: algebra and notation, functions and activations, NumPy shapes and broadcasting, vectors and norms, matrices, and linear systems. It mixes direct calculation, shape reasoning, and short interpretation questions. Aim for 80% or better; each explanation points to the chapter to revisit if you miss it.

A cumulative multiple-choice final spanning weeks 1–8: algebra and notation, functions, linear algebra, calculus, optimization, and NumPy shape-reasoning. A mix of calculation, interpretation, and shape questions.

Implement the course's core numerical routines from scratch in pure NumPy: vector operations, matrix multiplication, a numerical derivative, gradient descent, and linear regression — each with a required signature and shape contract.

Decode four equations of the kind ML papers assume you can read at a glance — MSE, softmax, cosine similarity, and a linear/attention layer — by naming every symbol, its type, and its dimensions, then rewriting, exemplifying, and implementing each.