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Mathematics & Quantitative Subjects

• Algebra & Functions Equations, inequalities, polynomial and exponential functions, logarithms and algebraic manipulation.
• Calculus & Multivariable Calculus Limits, derivatives, integration, partial derivatives, gradients, multiple integrals, Jacobians and change of variables.
• Linear Algebra Vectors, matrices, systems of linear equations, eigenvalues, eigenvectors and matrix similarity.
• Optimization Single-variable and multivariable optimization, constrained and unconstrained optimization, objective functions and Lagrange multipliers.
• Advanced Analysis & Differential Equations Sequences and series, Taylor series, Fourier series, differential equations, Laplace transforms, nonlinear dynamical systems and chaos theory.
• Statistics & Probability Descriptive statistics, probability theory, probability distributions, sampling, confidence intervals, hypothesis testing, chi-square tests and nonparametric tests.
• Econometrics Simple and multiple linear regression (OLS), estimation methods, model assumptions, diagnostic testing, heteroskedasticity, model selection, instrumental variables (IV), time series and panel data.
• Data Science Python, data preprocessing, feature engineering, regression and classification, decision trees, k-nearest neighbors (k-NN), neural networks, model training and evaluation.
• Advanced Data Science Causal inference, potential outcomes, Directed Acyclic Graphs (DAGs), confounding, colliders, backdoor criterion, treatment effect estimation (ATE/CATE), propensity scores, causal meta-learners (S-, T- and X-learners), Difference-in-Differences, time-series forecasting, Large Language Models (LLMs), RAG, tool calling and Agentic AI.