# Computer science | MATHEMATICAL METHODS FOR COMPUTER SCIENCE

## Computer science MATHEMATICAL METHODS FOR COMPUTER SCIENCE

 0512100041 DIPARTIMENTO DI INFORMATICA EQF6 COMPUTER SCIENCE 2020/2021

 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

Objectives
KNOWLEDGE AND UNDERSTANDING
THE STUDENT MUST HAVE KNOWLEDGE OF:
1.SIMPLE LOGIC TOOLS, PARTICULARLY KNOWLEDGE OF PROPOSITIONAL LOGIC AND PREDICATE CALCULUS
2.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
3.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
2.DEMONSTRATE SIMPLE STATEMENTS ON SETS AND NUMBERS, BY APPLYING THE MOST COMMON PROOF METHODS AND STRATEGY, LISTED IN THE PREVIOUS PARAGRAPH
3.USE INDUCTION, RECURSION, AND STRUCTURAL INDUCTION
Prerequisites
THE STUDENT SHOULD HAVE 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/INDIRECT PROOFS. BASICS ON SETS, SET OPERATIONS, FUNCTIONS, CARDINALITY OF SETS. (16 HOURS OF LECTURES + 8 HOURS OF EXERCISES)
• INDUCTION AND RECURSION: INDUCTION, RECURSIVE DEFINITIONS, STRUCTURAL INDUCTION, RECURSIVE ALGORITHMS. (16 HOURS OF LECTURES + 8 HOURS OF EXERCISES)
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. IT 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, SEVENTH EDITION, MCGRAW-HILL, 2012