Mathematics

Learn how to prove interval-arithmetic code works and test climate emulator precision with a reduced energy-balance model.

Build a change-point detector for streaming sensor data, then test how well it finds real shifts while controlling false discoveries.

Build a U-statistics project that tests finite-sample error bounds, then compare theory with bootstrap results on wage inequality data.

Build number theory skills by studying elliptic curves, rational points, and search methods for new solutions to a^3 + b^3 + c^3 = d.

Build proof skills and Python simulations to study how torus rotations spread out, and connect equidistribution rates to continued fractions.

Model geodesics on 3D-printed translation surfaces, track a rolling ball, and test saddle-connection statistics with real data.

Use Z3, combinatorics, and induction to classify small finite semirings, count special idempotent cases, and test algebraic patterns.

Compare Cayley graph spectra for small groups, test expansion, and build proof skills with eigenvalues, symmetry, and group structure.

Test patterns in Iwasawa lambda values for quadratic fields with SageMath and LMFDB data, then analyze trends with careful statistics.

Study how fast shuffles mix a deck, then build simulations and bounds to connect Markov chains, probability, and real card order data.