Mathematics Lessons | HM Math Studio

Browse mathematics lessons in algebra, geometry, trigonometry, statistics and mathematical foundations.

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Matrix Operations — Read and combine matrices, trace row-by-column products, and model practical problems with an editable matrix explorer and worked solutions.
Data Management — Explore data, compare distributions, calculate normal probabilities, and fit regression lines, with worked examples and practice.
Functions and Their Graphs — A complete learning module with worked examples, interactive graphs, domain practice, collapsible solutions, and selected review problems.
Angles & Coterminal Angles — Describe rotations, locate terminal sides, and recognize angles that share the same direction.
Trigonometric Ratios & Right Triangles — Connect side ratios to angles, solve right triangles, and model heights, shadows, ladders, and supporting wires.
Probability — Describe chance with sample spaces, event rules, conditional probability, independence, and expected value.
Exponential & Logarithmic Functions — Build from inverse functions to exponential and logarithmic graphs, equations, and models of growth and decay.
Laws of Sines & Cosines — Solve oblique triangles, investigate the ambiguous case, and choose a law from the information given.
Vectors — Describe directed motion with components and combine vectors geometrically and algebraically.
Graphs of Trigonometric Functions — Read and sketch periodic graphs using amplitude, period, phase shift, and midline.
Fundamental Trigonometric Identities — Use reciprocal, quotient, and Pythagorean identities to simplify and verify expressions.
Mathematical Language & Sets — Translate ideas precisely, distinguish expressions from sentences, and work with sets.
Elementary Logic — Build and check truth tables, translate compound propositions, and test logical equivalence.
Problem Solving & Reasoning — Develop conjectures, test them, and explain solutions using patterns, deduction, and Polya’s model.
Analytic Geometry — Connect coordinates with distances, circles, slopes, and equations of lines.
Symmetries & Tilings — Identify isometries, finite symmetry groups, and the structure of repeating plane patterns.
Complex Numbers and the Plane — Use complex arithmetic to describe points, distances, rotations, roots, and geometric loci.
Transformations and the Riemann Sphere — Connect complex formulas with translations, rotations, reciprocal inversion, and stereographic projection.
The Erlangen Program — Understand geometry through transformation groups, congruence, invariants, and changes of model.
Möbius Transformations and Steiner Circles — Explore fractional linear maps, cross ratios, circle symmetry, and the geometry of fixed points.
Hyperbolic Models and Cycles — See geodesics, ideal points, parallelism, and cycles in the disk and upper half-plane.
Hyperbolic Distance and Area — Derive hyperbolic length, distance, circle measurements, and triangle area from the disk and half-plane metrics.
Elliptic Geometry — Compare the sphere and antipodal quotient, then measure great-circle distance and spherical excess.
Curvature and Absolute Geometry — Compare three curvature signs, common geometric properties, and the Euclidean behavior of small regions.
Quaternions and Spatial Rotations — Extend complex-number ideas to quaternion products, inverses, and rotations in three dimensions.