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
CFUHOURSACTIVITY
432LESSONS
216EXERCISES


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

FURTHER READING:
KEITH DEVLIN, INTRODUCTION TO MATHEMATICAL THINKING, 2012
More Information
A DETAILED PROGRAM AND FURTHER INFORMATION MAY BE FOUND AT THE PERSONAL WEB PAGE OR THE ELEARNING PLATFORM
HTTP://ELEARNING.INFORMATICA.UNISA.IT
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