MATH.2060 Mathematics for Data Science
This course provides students with the additional mathematical background (beyond the prerequisite courses) needed for data science or machine learning. This course will cover the following areas: . Statistics and Probability: Probability distribution functions: uniform, normal, binomial, chi-square, Student's t-distribution, central limit theorem; Sampling, measurement, error, random number generation; Hypothesis testing for multivariables, A/B testing, confidence intervals, p-values; ANOVA, t-test; Linear regression, regularization . Linear Algebra: Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant; Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse; Special matrices: square matrix, identity matrix, triangular matrix, idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices; Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation; Vector space, basis, span, orthogonality, orthonormality, linear least square; Eigenvalues, eigenvectors, diagonalization, singular value decomposition . Calculus: Basics of Taylor's series, infinite series summation/integration concepts; Beta and gamma functions; Functions of multiple variables, limit, continuity, partial derivatives; Basics of ordinary and partial differential equations . Optimization: Basics of optimization, how to formulate the problem; Maxima, minima, convex function, global solution?; Linear programming, simplex algorithm; Integer programming; Constraint programming, knapsack problem; Randomized optimization techniques: hill climbing, simulated annealing, genetic algorithms
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Prerequisite
Prerequisite: MATH.1110