Data representation in computers and finite precision arithmetic. Formulation of solution methods via algorithms. Numerical methods for the solution of algebraic equations. Basic concepts in linear programming.
Lectures are supported and integrated by laboratory activities in Excel and Matlab environment, or in their open source counter parts.
Knowledge acquired:
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.
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 to be used as requirements (required and/or recommended)
Courses required: none
Courses recommended: first level courses of Mathematical Analysis and Numerical Analysis.
Teaching Methods
CFU: 9
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
Further information
Attendance of lectures, practice and lab:
Recommended
Teaching tools: textbooks, UniFi E-Learning: http://e-l.unifi.it
Office hours:
Monday 15:00-17:00 and by appointment
Contact:
Viale Morgagni, 40/44 - 50134 Firenze
Phone: 055 4796716
Fax: 055 4796744
E-mail: alessandra.papini@unifi.it
Altri recapiti
Web: http://www2.de.unifi.it/anum/Papini/
Type of Assessment
Oral exam
Course program
Fundamentals of floating point arithmetic: representation of integer and real numbers; unit roundoff; error propagation. Formulation of solution methods via algorithms.
Algebraic equations: conditioning and localization of the roots of a polynomial; the algorithm of Horner-Ruffini; Euclide’s algorithm for finding the gratest common divisor of two polynomials; Sturm’s theorem; real roots and Newton-Horner’s method; Newton’s method as a fixed-point iteration; deflation techniques.
Basic concepts on constrained and unconstrained optimization; optimality and feasibility; formulation of a linear program (LP) and model problems; geometrical interpretation and solution of a LP; basic solutions and extreme points; the fundamental theorem of linear programming; the simplex method. Introduction to the theory of duality: primal and dual problems; weak duality theorem and strong duality; economic meaning of dual variables.
Elements of Excel and Matlab (or of their open source counter parts).