Engineering Mathematics
AI/ML-facing engineering mathematics — linear algebra, probability, calculus for gradients, and optimization — on ExamMaster.
Undergraduate depth: concept notes and, where they help, in-browser labs. Reading is free.
Lessons
- Chain RuleIn Engineering Mathematics because layered models are compositions of functions, and their training signal moves backward through those layers by the chain rule.
- Conditional Probability and Bayes RuleIn Engineering Mathematics because engineering decisions update when new evidence arrives, and conditional probability is the formal language for that update.
- Derivatives as Rates of ChangeIn Engineering Mathematics because learning curves, sensitivity, and optimization all begin with how one quantity changes as another changes.
- Eigenvalue IntuitionIn Engineering Mathematics because repeated matrix actions are easier to read when you know the special directions that only stretch or flip.
- Expectation, Variance and CovarianceIn Engineering Mathematics because mean behavior, spread, and co-movement are the first summaries used to reason about data and risk.
- Gradient DescentIn Engineering Mathematics because the standard first optimizer follows the negative gradient as the local direction of steepest decrease.
- Linear Algebra in MLIn Engineering Mathematics because datasets, embeddings, and weight matrices are all linear-algebra objects before they become code.
- Learning RateIn Engineering Mathematics because even the right direction can fail if the step size is too timid or too aggressive.
- LikelihoodIn Engineering Mathematics because model fitting asks which parameter choice makes the observed data look most plausible under the assumed mechanism.
- Linear SystemsIn Engineering Mathematics because solving A x = b is the shared backbone behind calibration, regression, and many numerical engineering workflows.
- Local and Global MinimaIn Engineering Mathematics because optimization quality depends on whether a low point is merely nearby-best or truly best overall.
- Loss LandscapesIn Engineering Mathematics because training a model is literally moving through a loss surface whose slopes, flats, and valleys decide optimization behavior.
- Matrices as TransformationsIn Engineering Mathematics because model layers, projections, and feature mixing are matrix actions on vectors, not just rectangular tables to memorize.
- Multivariable SurfacesIn Engineering Mathematics because once a function has many inputs, its behavior is better imagined as a surface or landscape than as a single curve.
- Norms and ProjectionsIn Engineering Mathematics because distance, error, and best-fit ideas in ML all depend on how you measure length and what it means to project onto a simpler subspace.
- Objectives and ParametersIn Engineering Mathematics because optimization begins by naming what can change and what success means numerically.
- Partial Derivatives and GradientsIn Engineering Mathematics because real models depend on many variables, and optimization needs one derivative per coordinate plus a combined direction signal.
- Probability Inside Evaluation MetricsIn Engineering Mathematics because accuracy, precision, recall, and calibration all summarize uncertain outcomes through probability language.
- Random Variables and DistributionsIn Engineering Mathematics because uncertainty only becomes analyzable after outcomes are packaged into variables and distributions.
- Regularization TradeoffIn Engineering Mathematics because the best fit to training data is not always the best model once complexity and generalization are accounted for.
- Sampling, Bias and VarianceIn Engineering Mathematics because data quality and estimator stability matter before any sophisticated model choice does.
- Vectors in R^nIn Engineering Mathematics because features, embeddings, and parameter updates are all easier to reason about once a point is seen as a vector in a coordinate space.
Practise Engineering Mathematics
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