# Computer science | MATHEMATICAL METHODS FOR COMPUTER SCIENCE

## Computer science MATHEMATICAL METHODS FOR COMPUTER SCIENCE

 0512100041 DIPARTIMENTO DI INFORMATICA EQF6 COMPUTER SCIENCE 2016/2017

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2015 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY INF/01 4 32 LESSONS BASIC COMPULSORY SUBJECTS INF/01 2 16 EXERCISES BASIC COMPULSORY SUBJECTS

 CLELIA DE FELICE T
Objectives
KNOWLEDGE.

THE STUDENT MUST HAVE KNOWLEDGE:

A)OF SIMPLE LOGIC TOOLS, PARTICULARLY KNOWLEDGE OF PROPOSITIONAL LOGIC AND PREDICATE CALCULUS.
B)OF THE MATHEMATICAL REASONING THAT IS THE BASIS OF THE MOST COMMON PROOF METHODS AND STRATEGY, NAMELY PROOFS BY CONTRADICTION, PROOFS BY CONTRAPOSITION, EXHAUSTIVE PROOFS AND PROOFS BY CASES.
C)OF THE CONCEPTS OF INDUCTION, RECURSION, AND STRUCTURAL INDUCTION.

ABILIY TO APPLY KNOWLEDGE.

THE STUDENT MUST BE ABLE:

1)TO GIVE PRECISE AND FORMAL STATEMENTS OF SIMPLE PROBLEMS DESCRIBED IN NATURAL LANGUAGE ON SETS, STRINGS, NUMBERS, TREES, GRAPHS, BY USING CONCEPTS AND TECHNIQUES OF THE MATHEMATICAL AND LOGIC REASONING.
2)TO DEMONSTRATE SIMPLE STATEMENTS ON SETS AND NUMBERS, BY APPLYING THE MOST COMMON PROOF METHODS AND STRATEGY, LISTED IN THE PREVIOUS PARAGRAPH.
3) TO USE INDUCTION, RECURSION, AND STRUCTURAL INDUCTION.
Prerequisites
THE STUDENT SHOULD HAVE KNOWLEDGE OF MATHEMATICS AND LANGUAGE PROFICIENCY AT HIGH SCHOOL LEVEL.
Contents
•BASICS ON SETS, SET OPERATIONS, FUNCTIONS, CARDINALITY OF SETS.
•BASICS ON LOGIC: PROPOSITIONAL LOGIC AND ITS APPLICATIONS, PROPOSITIONAL EQUIVALENCES, PREDICATES AND QUANTIFIERS, PROOF METHODS AND STRATEGY DIRECT PROOFS, NAMELY PROOFS BY CONTRADICTION, PROOFS BY CONTRAPOSITION, EXHAUSTIVE PROOFS AND PROOFS BY CASES.
•INDUCTION AND RECURSION: INDUCTION, RECURSIVE DEFINITIONS, STRUCTURAL INDUCTION, RECURSIVE ALGORITHMS.
Teaching Methods
CLASS LECTURES INCLUDING EXERCISES. THE LECTURE WILL USE EXAMPLES TO ILLUSTRATE THE CONCEPTS, RELATE DIFFERENT TOPICS TO EACH OTHER, AND INTRODUCE THEIR APPLICATIONS.
Verification of learning
THE ASSESSMENT OF THE ACQUISITION OF THE BASIC CONCEPTS OF THE MODULE, LISTED IN THE “CONTENTS” SECTION, AND OF THE ABILITY TO APPLY THESE CONCEPTS AS DESCRIBED IN THE “OBJECTIVES” SECTION, WILL TAKE THE FORM OF BOTH A WRITTEN AND AN ORAL EXAM.
Texts
KENNETH D. ROSEN, DISCRETE MATHEMATICS AND ITS APPLICATIONS, SEVENTH EDITION, MCGRAW-HILL, 2012.