Applied Math Micro-Challenges — Month 1

Complete a 10–15 line NumPy exercise that constructs one- and two-dimensional arrays and inspects their shapes, axes, and data types.

Complete a 10–15 line NumPy exercise that applies vector addition, scalar multiplication, and Euclidean norms.

Complete a 10–15 line NumPy exercise that distinguishes element-wise multiplication from matrix multiplication.

Compute vector dot products in NumPy and interpret each result as a weighted sum or similarity score.

Approximate the partial derivatives of a two-variable function with finite differences, assemble its gradient vector, and identify a local descent direction.

Complete a 10–15 line exercise that calculates conditional probabilities and applies Bayes’ rule to a small diagnostic example.

Compute and interpret mean, variance, standard deviation, and covariance for a small dataset using NumPy.

Complete a 10–15 line Matplotlib and Seaborn exercise that creates correctly labelled univariate and bivariate plots.