Calculus I Calculus II Linear Algebra

The goal of this course is to acquaint the student with mathematical tools necessary for an adequate compression of some advanced techniques of statistical analysis: - Complex numbers - Series of functions - Integral transforms - Matrix calculus - Singular value decomposition - Introduction to numerical calculus

T0. PRELIMINARIES - Complex numbers: Graphical representation, arithmetic, complex exponential. - Summation, products, indexed sums. T1. NUMERICAL ISSUES: CALCULUS - Errors, Floating-point arithmetic - Computer: Newton's method; Trapezoidal Rule. T2. MATRIX CALCULUS - Exponential matrix - Derivatives with scalars, vectors and matrices. - Multidimensional integration. Integration with scalars, vectors and matrices. T3. SINGULAR VALUES DESCOMPOSITION - Singular value decomposition - Moore-Penrose pseudoinverse. - Principal component analysis T4. NUMERICAL ISSUES: LINEAR ALGEBRA - Computer: LU factorization; Power method for approximating eigenvalues. T5. SERIES OF FUNCTIONS - Numerical series, convergence criteria. - Series of functions: powers, Taylor, Maclaurin. - Series of functions: Fourier. T6. INTEGRAL TRANSFORMS - Improper integrals. - Fourier transform. Characteristic function - Laplace transform. Moment-generating function

The course will primarily be taught using the blackboard, with supplementary materials accessible on the course webpage. Two written tests will be scheduled to be completed during class hours throughout the semester. Additionally, there will be two computer homework assignments to be submitted