Computer science | MATHEMATICAL METHODS FOR COMPUTER SCIENCE

cod. 0512100041

MATHEMATICAL METHODS FOR COMPUTER SCIENCE

	0512100041
	DIPARTIMENTO DI INFORMATICA
	EQF6
	COMPUTER SCIENCE
	2017/2018

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2017
	SECONDO SEMESTRE

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
INF/01	4	32	LESSONS	BASIC COMPULSORY SUBJECTS
INF/01	2	16	EXERCISES	BASIC COMPULSORY SUBJECTS

	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

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

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 FURTHER READING: KEITH DEVLIN, INTRODUCTION TO MATHEMATICAL THINKING, 2012