Rosalba ZIZZA | MATHEMATICAL METHODS FOR COMPUTER SCIENCE

cod. 0512100041

MATHEMATICAL METHODS FOR COMPUTER SCIENCE

	0512100041
	COMPUTER SCIENCE
	EQF6
	COMPUTER SCIENCE
	2024/2025

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2017
	SPRING SEMESTER

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

PROFESSORS

	CLELIA DE FELICE T Curriculum
	ROSALBA ZIZZA Curriculum

	Objectives
	GENERAL OBJECTIVE THE COURSE PROVIDES THE FUNDAMENTAL NOTIONS AND MATHEMATICAL TOOLS USEFUL IN THE COMPUTER SCIENCE CONTEXT. KNOWLEDGE AND UNDERSTANDING THE STUDENT GETS: - SIMPLE LOGIC TOOLS, PARTICULARLY KNOWLEDGE OF PROPOSITIONAL LOGIC AND PREDICATE CALCULUS - THE MATHEMATICAL REASONING THAT IS THE BASIS OF THE MOST COMMON PROOF METHODS AND STRATEGIES, NAMELY PROOFS BY CONTRADICTION, PROOFS BY CONTRAPOSITION, EXHAUSTIVE PROOFS, AND PROOFS BY CASES - BASIC STRUCTURES - THE CONCEPTS OF INDUCTION, RECURSION, AND STRUCTURAL INDUCTION ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE STUDENT WILL BE ABLE TO: - GIVE PRECISE AND FORMAL STATEMENTS OF SIMPLE PROBLEMS DESCRIBED IN NATURAL LANGUAGE ON SETS, STRINGS, NUMBERS, TREES (AND GRAPHS), BY USING CONCEPTS AND TECHNIQUES OF THE MATHEMATICAL AND LOGIC REASONING - DEMONSTRATE SIMPLE STATEMENTS ON SETS AND NUMBERS, BY APPLYING THE MOST COMMON PROOF METHODS AND STRATEGIES, LISTED IN THE PREVIOUS PARAGRAPH USE INDUCTION, RECURSION, AND STRUCTURAL INDUCTION TO SOLVE SET, STRING, NUMBER, TREE (AND GRAPH) PROBLEMS. AUTONOMY OF JUDGMENT THE STUDENT WILL BE ABLE TO: - FORMALIZE AND ANALYZE CONCEPTS AND PROBLEMS. - UNDERSTAND WHEN RECURSIVE REASONING CAN BE USED. - JUDGE THE FORMAL CORRECTNESS OF THE SOLUTION PROVIDED TO PROPOSED PROBLEMS. COMMUNICATIVE SKILLS THE STUDENT WILL BE ABLE TO: - KNOW HOW TO DESCRIBE A GIVEN PROBLEM IN A FORMAL WAY, USING LOGICAL MATHEMATICAL LANGUAGE. - PRESENT A SOLUTION TO A PROBLEM IN A FORMALLY CORRECT WAY. LEARNING ABILITY THE STUDENT WILL BE ABLE TO: - - USE THE LOGICAL MATHEMATICAL TOOLS PROVIDED TO FORMALIZE PROBLEMS THAT ARISE IN VARIOUS TYPES OF CONTEXTS. - UNDERSTAND FORMAL MODELS AND MATHEMATICAL REASONING TO SOLVE COMPUTER PROBLEMS.

GENERAL OBJECTIVE
THE COURSE PROVIDES THE FUNDAMENTAL NOTIONS AND MATHEMATICAL TOOLS USEFUL IN THE COMPUTER SCIENCE CONTEXT.

KNOWLEDGE AND UNDERSTANDING
THE STUDENT GETS:
- SIMPLE LOGIC TOOLS, PARTICULARLY KNOWLEDGE OF PROPOSITIONAL LOGIC AND PREDICATE CALCULUS
- THE MATHEMATICAL REASONING THAT IS THE BASIS OF THE MOST COMMON PROOF METHODS AND STRATEGIES, NAMELY PROOFS BY CONTRADICTION, PROOFS BY CONTRAPOSITION, EXHAUSTIVE PROOFS, AND PROOFS BY CASES
- BASIC STRUCTURES
- THE CONCEPTS OF INDUCTION, RECURSION, AND STRUCTURAL INDUCTION

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE STUDENT WILL BE ABLE TO:
- GIVE PRECISE AND FORMAL STATEMENTS OF SIMPLE PROBLEMS DESCRIBED IN NATURAL LANGUAGE ON SETS, STRINGS, NUMBERS, TREES (AND GRAPHS), BY USING CONCEPTS AND TECHNIQUES OF THE MATHEMATICAL AND LOGIC REASONING
- DEMONSTRATE SIMPLE STATEMENTS ON SETS AND NUMBERS, BY APPLYING THE MOST COMMON PROOF METHODS AND STRATEGIES, LISTED IN THE PREVIOUS PARAGRAPH
USE INDUCTION, RECURSION, AND STRUCTURAL INDUCTION TO SOLVE SET, STRING, NUMBER, TREE (AND GRAPH) PROBLEMS.

AUTONOMY OF JUDGMENT
THE STUDENT WILL BE ABLE TO:
- FORMALIZE AND ANALYZE CONCEPTS AND PROBLEMS.
- UNDERSTAND WHEN RECURSIVE REASONING CAN BE USED.
- JUDGE THE FORMAL CORRECTNESS OF THE SOLUTION PROVIDED TO PROPOSED PROBLEMS.

COMMUNICATIVE SKILLS
THE STUDENT WILL BE ABLE TO:
- KNOW HOW TO DESCRIBE A GIVEN PROBLEM IN A FORMAL WAY, USING LOGICAL MATHEMATICAL LANGUAGE.
- PRESENT A SOLUTION TO A PROBLEM IN A FORMALLY CORRECT WAY.

LEARNING ABILITY
THE STUDENT WILL BE ABLE TO:
- - USE THE LOGICAL MATHEMATICAL TOOLS PROVIDED TO FORMALIZE PROBLEMS THAT ARISE IN VARIOUS TYPES OF CONTEXTS.
- UNDERSTAND FORMAL MODELS AND MATHEMATICAL REASONING TO SOLVE COMPUTER PROBLEMS.

	Prerequisites
	THE STUDENT SHOULD HAVE KNOWLEDGE OF MATHEMATICS AND LANGUAGE PROFICIENCY AT HIGH SCHOOL LEVEL.

	Contents
	• BASICS ON LOGIC (10 HOURS): PROPOSITIONAL LOGIC AND ITS APPLICATIONS, PROPOSITIONAL EQUIVALENCES. • BASIC ON LOGIC (12 ORE): PREDICATES AND QUANTIFIERS. • METHODS AND STRATEGY OF DIRECT AND INDIRECT PROOFS (6 HOURS) . • BASICS ON SETS, SET OPERATIONS, FUNCTIONS, CARDINALITY OF SETS (4 HOURS). •INDUCTION AND RECURSION (16 HOURS): INDUCTION, RECURSIVE DEFINITIONS, STRUCTURAL INDUCTION, RECURSIVE ALGORITHMS.

Contents

• BASICS ON LOGIC (10 HOURS): PROPOSITIONAL LOGIC AND ITS APPLICATIONS, PROPOSITIONAL EQUIVALENCES.
• BASIC ON LOGIC (12 ORE): PREDICATES AND QUANTIFIERS.
• METHODS AND STRATEGY OF DIRECT AND INDIRECT PROOFS (6 HOURS) .
• BASICS ON SETS, SET OPERATIONS, FUNCTIONS, CARDINALITY OF SETS (4 HOURS).
•INDUCTION AND RECURSION (16 HOURS): 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 A WRITTEN EXAM. THE WRITTEN EXAM CAN BE SUBSTITUTED BY A MIDTERM PLUS A FINAL WRITTEN TEST. THE EVALUATION CRITERIA INCLUDE THE COMPLETENESS AND CORRECTNESS OF THE LEARNING AND THE CLARITY OF THE PRESENTATION. THE MINIMUM GRADE (18) IS ASSIGNED WHEN THE STUDENT HAS A LIMITED KNOWLEDGE OF THE STUDIED LOGIC TOOLS, OF THE CONCEPTS OF INDUCTION, RECURSION, STRUCTURAL INDUCTION AND SHOWS UNCERTAINTIES IN THE APPLICATION OF THE STUDIED METHODS. THE MAXIMUM GRADE (30) IS ASSIGNED WHEN THE STUDENT SHOWS A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE ABOVE MENTIONED CONCEPTS AND OF THE STUDIED METHODS. IT IS ALSO ABLE TO SOLVE THE PROPOSED PROBLEMS GIVING EFFICIENT AND ACCURATE SOLUTIONS AND SHOWS THE ABILITY TO LINK DIFFERENT CONCEPTS TOGETHER. ''LODE'' IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS THAT SHE/HE IS ABLE TO PRESENT THE TOPICS WITH OWNERSHIP OF LANGUAGE AND AUTONOMOUS PROCESSING SKILLS.

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 A WRITTEN EXAM. THE WRITTEN EXAM CAN BE SUBSTITUTED BY A MIDTERM PLUS A FINAL WRITTEN TEST.

THE EVALUATION CRITERIA INCLUDE THE COMPLETENESS AND CORRECTNESS OF THE LEARNING AND THE CLARITY OF THE PRESENTATION.
THE MINIMUM GRADE (18) IS ASSIGNED WHEN THE STUDENT HAS A LIMITED KNOWLEDGE OF THE STUDIED LOGIC TOOLS, OF THE CONCEPTS OF INDUCTION, RECURSION, STRUCTURAL INDUCTION AND SHOWS UNCERTAINTIES IN THE APPLICATION OF THE STUDIED METHODS.
THE MAXIMUM GRADE (30) IS ASSIGNED WHEN THE STUDENT SHOWS A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE ABOVE MENTIONED CONCEPTS AND OF THE STUDIED METHODS. IT IS ALSO ABLE TO SOLVE THE PROPOSED PROBLEMS GIVING EFFICIENT AND ACCURATE SOLUTIONS AND SHOWS THE ABILITY TO LINK DIFFERENT CONCEPTS TOGETHER.
''LODE'' IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS THAT SHE/HE IS ABLE TO PRESENT THE TOPICS WITH OWNERSHIP OF LANGUAGE AND AUTONOMOUS PROCESSING SKILLS.

	Texts
	KENNETH D. ROSEN, DISCRETE MATHEMATICS AND ITS APPLICATIONS, EIGHTH EDITION, MCGRAW-HILL, 2018. FURTHER READING: KEITH DEVLIN, INTRODUCTION TO MATHEMATICAL THINKING, 2012.

	More Information
	E-LEARNING PLATFORM WEB SITE: HTTP://ELEARNING.INFORMATICA.UNISA.IT/EL-PLATFORM/ CONTACT INFORMATION: CDEFELICE@UNISA.IT RZIZZA@UNISA.IT HTTPS://DOCENTI.UNISA.IT/001119/HOME HTTPS://DOCENTI.UNISA.IT/020880/HOME

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Rosalba ZIZZA | MATHEMATICAL METHODS FOR COMPUTER SCIENCE