Checking date: 25/04/2024

Course: 2024/2025

Advanced Mathematics
Bachelor in Statistics and Business (Plan: 400 - Estudio: 203)


Department assigned to the subject: Mathematics Department

Type: Compulsory
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
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
Skills and learning outcomes
Description of contents: programme
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
Learning activities and methodology
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
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

Extraordinary call: regulations
Basic Bibliography
  • D. Pestana, M. Rodríguez y F. Marcellán. Curso Práctico de variable compleja y teoría de transformadas. Pearson. 2014
  • B.N. Datta. Numerical Linear Algebra and Applications. Brooks & Cole. 1995
  • D. Zill. Ecuaciones diferenciales con aplicaciones de modelado. Thomson. 1997
  • James E. Gentle. Matrix Algebra: Theory, Computation, and Applications in Statistics. Springer. 2007
  • K. Sydsaeter and P. Hammond. Essential Mathematics for economics Analysis. Pearson. 2012
  • L.N. Trefethen & D. Bau. Numerical Linear Algebra. SIAM. 1997
  • Salas, Hille y Etgen. Calculus (I y II). Reverté. 2002

The course syllabus may change due academic events or other reasons.