Quantitative reasoning and logical structures across arithmetic, geometry, and advanced analysis. Builds problem-solving skills through pattern recognition and modeling.
Analyzes the shape, center, and spread of numerical datasets using histograms, box plots, and dot plots. Examines measures of central tendency and variability to interpret data consistency and skewness.
Analysis of data spread using range, interquartile range, and mean absolute deviation. Examines how individual data points differ from the center and from each other within a distribution.
Random, stratified, and cluster sampling methods for data collection and analysis. Addresses sample size determination, bias reduction, and the principles of making valid inferences about larger populations.
Analysis of relationships between two variables using scatter plots and lines of best fit. Identifies patterns of association, correlation coefficients, and potential outliers in quantitative datasets.
Discrete and continuous-time stochastic models, including Markov chains and Poisson processes. Examines stationarity, autocorrelation, and transition probabilities to analyze systems evolving over time.
Mathematical foundations for calculating the long-term average of random variables across multiple trials. Addresses discrete probability distributions and applications in game theory and financial forecasting.
Expected value calculations and risk assessment techniques for making informed choices under uncertainty. Equips students with decision trees and Bayesian reasoning to evaluate potential outcomes in real-world scenarios.
Hypothesis testing, confidence intervals, and p-values used to draw population conclusions. Evaluates statistical significance and error types within experimental and observational data.
Application of derivatives to identify absolute extrema within constrained systems. Addresses problems in surface area maximization, cost minimization, and physical efficiency.
Examines first-order and higher-order linear equations using techniques like separation of variables, Laplace transforms, and power series. Connects mathematical models to physical systems such as population growth, fluid dynamics, and electrical circuits.