# Computer science | MATHEMATICAL METHODS FOR COMPUTER SCIENCE

## Computer science MATHEMATICAL METHODS FOR COMPUTER SCIENCE

 0512100041 DIPARTIMENTO DI INFORMATICA EQF6 COMPUTER SCIENCE 2017/2018

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2017 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

 MARGHERITA NAPOLI T
Objectives
KNOWLEDGE AND UNDERSTANDING
THE STUDENT MUST HAVE KNOWLEDGE OF:
1.SIMPLE LOGIC TOOLS, AND IN PARTICULAR OF PROPOSITIONAL LOGIC AND PREDICATE CALCULUS, AND OF THE LOGIC REASONING THAT IS THE BASIS OF THE PROOF METHODS AND STRATEGY.
2.THE CONCEPTS OF INDUCTION, RECURSION, AND STRUCTURAL INDUCTION

APPLYING KNOWLEDGE AND UNDERSTANDING
THE STUDENT MUST BE ABLE TO:
1.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, PROVE SIMPLE STATEMENTS ON SETS AND NUMBERS.
2.USE INDUCTION, RECURSION, AND STRUCTURAL INDUCTION
Prerequisites
KNOWLEDGE OF MATHEMATICS AND LANGUAGE PROFICIENCY AT HIGH SCHOOL LEVEL.
Contents
•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. BASICS ON SETS, SET OPERATIONS, FUNCTIONS, CARDINALITY OF SETS
•INDUCTION AND RECURSION: INDUCTION, RECURSIVE DEFINITIONS, STRUCTURAL INDUCTION, RECURSIVE ALGORITHMS
Teaching Methods
CLASS LECTURES INCLUDING EXERCISES. EXAMPLES ARE USED TO ILLUSTRATE THE CONCEPTS, RELATE DIFFERENT TOPICS TO EACH OTHER, AND INTRODUCE APPLICATIONS.
Verification of learning
ACQUISITION OF BOTH THE BASIC CONCEPTS, LISTED IN THE “CONTENTS” SECTION, AND THE ABILITY TO APPLY THESE CONCEPTS, AS DESCRIBED IN THE “OBJECTIVES” SECTION, WILL BE CHECKED BY EITHER TWO MID-TERM TESTS OR A FINAL EXAMINATION. FINAL EXAMINATION CONSISTS OF WRITTEN AND ORAL EXAMINATION.
Texts

KENNETH D. ROSEN, DISCRETE MATHEMATICS AND ITS APPLICATIONS, SEVENTH EDITION, MCGRAW-HILL, 2012