Search results for “SAGE”

55th International Mathematical Olympiad. Cape Town, South Africa, 2014.

58th International Mathematical Olympiad. Rio de Janeiro, Brazil, 2017.

61st International Mathematical Olympiad, 2020.

Linear dependence and independence of the rows of a matrix, the criterion via a linear combination, and the connection to rank.

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.

Time series forecasting problems: the time series model, the forecasting horizon, the least squares method; econometrics as the main source of problems — trends, seasonalities, change points; examples of forecasting sales volumes and electricity prices; the linear autoregression model; a brief survey of forecasting methods; adaptive short-term forecasting methods: the exponential moving average and the smoothing parameter, the models of Holt, Theil–Wage, Winters with linear and exponential trend, adaptive autoregression; the tracking signal and a statistical test of model adequacy, the Trigg–Leach model; adaptive selection and adaptive composition of models, the LAVR method — local adaptation of weights with regularisation, the monotonicity constraint as a regulariser; experiments on the sales forecasting problem.

57th International Mathematical Olympiad. Hong Kong, 2016.