95642 - Mathematics for Computer Science

Learning outcomes

At the end of the course, the student knows the mathematical concepts, methods and techniques relevant to computer science - including elements of calculus, algebra, geometry and probability. He knows the practical application of these concepts in computer science, and knows computer tools to use these concepts.

Course contents

The program is divided into 3 main parts : Basic Concepts (diactic unit 0 ) Linear algebra and study of functions ( diactic units 1-3 ) units and elements of probability (diactic unit 4) . Some topics, included in round brackets, have secondary priority and therefore they will be developed, even partially, according to the time available.

Prerequisites basic mathematic.

Teaching units 0.

Elements of mathematic

0.1 Equations and inequalities of the second degree

0.2 Exponentials

0.3 Logarithms

Knowledge acquired in the unit teaching 0: The purpose of this unit is to review with the student some basic mathematical ingredients necessary to learn the concepts and techniques that will be developed in detail during the course.

Didactic units

1. Elements of linear algebra ( Total 13 hours teaching units )

1.1 Vector spaces

Vector spaces , vectors and operations with vectors ,

1.2 Matrices

Transformation matrices , operations with matrices , (determinants, eigenvalues and eigenvectors)

1.3 System of  equations

An inconsistent system, a consistent system, a dependent systemand an independent system.

Knowledge acquired in the didactic unit 1:

It introduces the student to vector calculus and matrices.

2 Functions 

2.1 Functions of one variable

The graph of a function, increasing functions and descrescent functions, maximum and minimum

2.2 Polynomial functions

Linear, quadratic and polynomial functions.

2.3 Exponential functions, the logarithmic laws

Knowledge acquired in the didactic unit 2:

At the end of this unit the student is able to understand the concept of function. Furthermore it becomes able to recognize the main differences between various types of elementary functions. This teaching unit and corroborated by several examples and exercises.

3 Limits and differential and integral calculus

3.1 Limits

3.2 Differential calculus

Derived rate of change, rules for computing the derivatvie, (higher order derivatives and Taylor formula)

3.3 Integral calculus

From derivatives to integrals.

3.4 Elements of Numerical integration

The purpose of this unit is to teach the student different numerical techniques to calculate an approximate value of a definite integral.

4 Elements of Propability

4.1. Probability thoery:

- Probability spaces and random variables

- Conditional probability and independence

- Discrete (and continuous) distributions

 

Teaching methods

Frontal lessons.

Weekly exercises complete the preparation.

Assessment methods

A written test , and possibly an individual oral test : both primarily dedicated to the resolution of exercises.

Teaching tools

Blackboard lectures mainly. Overhead projector, personal computer and projector will be used for some lectures.

Office hours

See the website of Cristiano Frattagli