Numerical methods for the solution of algebraic equations; basic concepts in linear programming; data representation in computers and finite precision arithmetic; statistical treatment of numerical data; computer simulation of random events. Lectures are supported and integrated by laboratory activities in Excel and Matlab environment, or in their open source counter parts.
The course aims to present mathematical problems and methodologies which can be used to improve teaching of mathematics in secondary schools; special focus is on a numerical approach to the solution of mathematical problems, and on ways to use computers as effective aids for teaching and learning mathematics.
Competence acquired:
Knowledge of ad-hoc numerical methods for solving algebraic equations, and of fundamentals of optimization and linear programming, of data representation in computers, of statistical treatment of numerical data and computer simulation of random events.
Skills acquired (at the end of the course):
Ability to use and develop simple programs in Excel and Matlab environments, or in their open source versions, to illustrate the numerical solution of mathematical problems, and prepare lectures.
Prerequisites
Courses recommended: first level courses of Mathematical Analysis and Numerical Analysis
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other indivual formative activities: 153
Hours for lectures: 36
Hours for laboratory: 24
Hours for laboratory-field/practice: 0
Seminars (hours): 12
Stages (hours): 0
Intermediate examinations (hours): 0
Algebraic equations: real roots and Newton-Horner’s method; complex roots and Bairstow’s method; techniques of deflation. Basic concepts on constrained and unconstrained optimization; optimality and feasibility; formulation of a linear program; basic solutions and extreme points; the simplex method. Fundamentals of floating point arithmetic: representation of integer and real numbers; unit roundoff; error propagation. Statistical treatment of numerical data; computer simulation of random events. Elements of Excel and Matlab (or of their open source counter parts).