Fausto ACERNESE | MATHEMATICS AND STATISTICS

cod. 0712200001

MATHEMATICS AND STATISTICS

	0712200001
	DIPARTIMENTO DI FARMACIA
	EQF6
	GESTIONE E VALORIZZAZIONE DELLE RISORSE AGRARIE E DELLE AREE PROTETTE
	2018/2019

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2016
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
1	ELEMENTI DI MATEMATICA MODULO DI MATEMATICA E STATISTICA
	MAT/04	3	21	LESSONS	BASIC COMPULSORY SUBJECTS
2	STATISTICA MODULO DI MATEMATICA E STATISTICA
	SECS-S/01	6	42	LESSONS	BASIC COMPULSORY SUBJECTS

PROFESSORS

	MARCELLA NIGLIO2 T Curriculum
	FAUSTO ACERNESE1 Curriculum

	Objectives
	THE FIRST UNIT OF THE COURSE AIMS TO PROVIDE THE ACQUISITION OF BASIC TOOLS OF MATHEMATICS AND GEOMETRY WHICH ALLOW TO FACE MATHEMATICAL PROBLEMS AND TO STUDY THE APPLICATION OF MODELS BASED ON MATHEMATICAL STRUCTURES. THE SECOND PART OF THE COURSE AIMS TO PRESENT STATISTICAL TOOLS FOR DATA ANALYSIS, PROBABILITY AND STATISTICAL INFERENCE. KNOWLEDGE ACQUIRED: BASIC TOOLS OF MATHEMATICS BASIC TOOLS OF DATA ANALYSIS AND STATISTICAL INFERENCE THE MAIN SKILLS ACQUIRED ALLOW STUDENTS: TO FACE A MATHEMATICAL PROBLEM SELECTING PROPER TOOLS; TO PROPERLY SUMMARIZE A DATABASE; TO INTERPRET A STATISTICAL REPORT; TO PROPERLY USE PROBABILITY THEORY AND STATISTICAL INFERENCE TO FACE AGRICULTURAL PROBLEMS.

THE FIRST UNIT OF THE COURSE AIMS TO PROVIDE THE ACQUISITION OF BASIC TOOLS OF MATHEMATICS AND GEOMETRY WHICH ALLOW TO FACE MATHEMATICAL PROBLEMS AND TO STUDY THE APPLICATION OF MODELS BASED ON MATHEMATICAL STRUCTURES.

THE SECOND PART OF THE COURSE AIMS TO PRESENT STATISTICAL TOOLS FOR DATA ANALYSIS, PROBABILITY AND STATISTICAL INFERENCE.

KNOWLEDGE ACQUIRED:
BASIC TOOLS OF MATHEMATICS
BASIC TOOLS OF DATA ANALYSIS AND STATISTICAL INFERENCE

THE MAIN SKILLS ACQUIRED ALLOW STUDENTS:
TO FACE A MATHEMATICAL PROBLEM SELECTING PROPER TOOLS;
TO PROPERLY SUMMARIZE A DATABASE;
TO INTERPRET A STATISTICAL REPORT;
TO PROPERLY USE PROBABILITY THEORY AND STATISTICAL INFERENCE TO FACE AGRICULTURAL PROBLEMS.

	Prerequisites
	IT IS REQUIRED THE KNOWLEDGE OF BASIC CONCEPTS OF MATHEMATICS.

	Contents
	UNIT I: MATHEMATICS (3 CFU) COMBINATORIX. MATRIX AND DETERMINANTS. EQUATION SYSTEMS LINEAR, CRAMER AND ROUCHE-CAPELLI THEOREM. REAL NUMBERS. PRIMARY FUNCTIONS. FIELD OF EXISTENCE AND GRAPHICS OF REAL VARIABLE. THE FUNCTIONS POWER N-MA, ROOT N-MA, POWER WITH REAL EXPONENT, EXPONENTIAL, LOGARITHMIC, TRIGONOMETRIC (SINE, COSINE, TANGENT AND COTANGENT). OPERATIONS ON LIMITS AND THEIR PROPERTIES. PROPERTY ON CONTINUOUS FUNCTIONS. DISCONTINUITY. INCREASING AND DECREASING FUNCTIONS. DERIVATIVES AND DIFFERENTIALS OF THE FUNCTIONS OF A VARIABLE. DERIVATIVE OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOSITE FUNCTIONS. FORMULA AND RULES OF DERIVATION. THEOREMS : ROLLE, LAGRANGE AND OF DE L'HOSPITAL. ASYMOPOTES. MAXIMUM, MINIMUM AND INFLECTIONS. STUDY OF A FUNCTION GRAPH. THEOREMS, RULES AND PROPERTY OF INTEGRATION. INDEFINITE INTEGRAL IMMEDIATE. UNIT II: STATISTICS (6 CFU) DATA ANALYSIS (10 HOURES): STATISTICAL SURVEY,DATA ANALYSIS IN UNIVARIATE AND BIVARIATE DOMAIN; GRAPHICAL REPRESENTATIONS; LOCATION, VARIABILITY AND SHAPE STATISTICAL INDICES; DEPENDENCE BETWEEN TWO CHARACTERS. PROBABILITY (14 HOURES): INTRODUCTION TO ELEMENTARY PROBABILITY THEORY, RANDOM VARIABLES (CONTINUOUS AND DISCRETE), BASIC PROBABILITY MODELS. INFERENCE (14 HOURES): SAMPLING THEORY; PARAMETRIC ESTIMATION, HYPOTHESIS TESTING, CONFIDENCE INTERVALS, LINEAR REGRESSION MODEL (4 HOURES): DEFINITION, ESTIMATION AND TESTING;

Contents

UNIT I: MATHEMATICS (3 CFU)
COMBINATORIX. MATRIX AND DETERMINANTS. EQUATION SYSTEMS LINEAR, CRAMER AND ROUCHE-CAPELLI THEOREM. REAL NUMBERS. PRIMARY FUNCTIONS. FIELD OF EXISTENCE AND GRAPHICS OF REAL VARIABLE. THE FUNCTIONS POWER N-MA, ROOT N-MA, POWER WITH REAL EXPONENT, EXPONENTIAL, LOGARITHMIC, TRIGONOMETRIC (SINE, COSINE, TANGENT AND COTANGENT). OPERATIONS ON LIMITS AND THEIR PROPERTIES. PROPERTY ON CONTINUOUS FUNCTIONS. DISCONTINUITY. INCREASING AND DECREASING FUNCTIONS. DERIVATIVES AND DIFFERENTIALS OF THE FUNCTIONS OF A VARIABLE. DERIVATIVE OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOSITE FUNCTIONS. FORMULA AND RULES OF DERIVATION. THEOREMS : ROLLE, LAGRANGE AND OF DE L'HOSPITAL. ASYMOPOTES. MAXIMUM, MINIMUM AND INFLECTIONS. STUDY OF A FUNCTION GRAPH. THEOREMS, RULES AND PROPERTY OF INTEGRATION. INDEFINITE INTEGRAL IMMEDIATE.

UNIT II: STATISTICS (6 CFU)
DATA ANALYSIS (10 HOURES): STATISTICAL SURVEY,DATA ANALYSIS IN UNIVARIATE AND BIVARIATE DOMAIN; GRAPHICAL REPRESENTATIONS; LOCATION, VARIABILITY AND SHAPE STATISTICAL INDICES; DEPENDENCE BETWEEN TWO CHARACTERS.

PROBABILITY (14 HOURES): INTRODUCTION TO ELEMENTARY PROBABILITY THEORY, RANDOM VARIABLES (CONTINUOUS AND DISCRETE), BASIC PROBABILITY MODELS.

INFERENCE (14 HOURES): SAMPLING THEORY; PARAMETRIC ESTIMATION, HYPOTHESIS TESTING, CONFIDENCE INTERVALS,

LINEAR REGRESSION MODEL (4 HOURES): DEFINITION, ESTIMATION AND TESTING;

	Teaching Methods
	THE TWO UNITS ARE BASED ON 63 HOURS OF CLASS LECTURES: 21 HOURS OF MATHEMATICS AND 42 OF STATISTICS. THE TWO UNITS INCLUDE THEORETICAL LECTURES AND PRACTICAL LECTURES (MAINLY BASED ON EXERCISES AND CASE STUDIES).

	Verification of learning
	THE ACQUIRED KNOWLEDGE IS EVALUATED WITH A FINAL EXAM WHOSE SCORE IS GIVEN BY THE WEIGHTED MEAN OF THE SCORES OBTAINED IN THE TWO UNITS (SCORE RANGE: MIN 18, MAX 30). THE UNIT MATHEMATICS IS CHARACTERIZED BY TWO INTER-COURSE TESTS. 1) FIRST TEST: FROM THE LINEAR ALGEBRA TO THE STUDY OF FUNCTIONS, LIMITS AND THEIR PROPERTIES (MAXIMUM SCORE 16 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED) 2) SECOND TEST: DERIVATIVES AND INTEGRALS (MAXIMUM SCORE 10 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED) THE STATISTICAL UNIT IS CHARACTERIZED BY TWO INTER-COURSE TESTS. 1) FIRST TEST: DATA ANALYSIS (MAX SCORE: 7) AND PROBABILITY (MAX SCORE 9). THE TEST IS PASSED IF THE TOTAL SCORE IS AT LEAST 10. 2)SECOND TEST: STATISTICAL INFERENCE (MAXIMUM SCORE 10 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED) FINAL EXAM: WRITTEN EXAM (MAX SCORE 30) FOR EACH OF THE TWO UNITS. MATHEMATICS: STUDY OF FUNCTIONS (MAX SCORE 10), INTEGRALS (MAX SCORE 7), LIMITS (MAX SCORE 8), LINEAR ALGEBRA (MAX SCORE 5); STATISTICS: DATA ANALYSIS (MAX SCORE 7), PROBABILITY (MAX SCORE 9), INFERENCE (MAX SCORE 10), LINEAR MODELS (MAX SCORE 4). ALL STUDENTS THAT HAVE PASSED THE INTER-COURSE TESTS DO NOT HAVE TO CARRY OUT THE EXERCISES ON THE CORRESPONDING TOPICS (FOR EXAMPLE: IF THEY HAVE PASSED THE SECOND INTER-COURSE STATISTICAL TEST THEY DO NOT HAVE TO CARRY OUT THE EXEECISES OF STATISTICAL INFERENCE). THE FINAL SCORE OF THE WRITTEN EXAM IS GIVEN BY THE WEIGTHED MEAN OF THE SCORES OF THE TWO UNITS (AND THE MINIMUM SCORE FOR EACH OF THEM IS 18). THE ORAL INTEVIEW (MAX SCORE 30) IS BASED ON THREE QUESTIONS SUBMITTED TO THE STUDENTS IN MATHEMATICS AND FURTHER THREE QUESTIONS IN STATISTICS. THE FINAL SCORE FOR EACH UNIT IS GIVEN BY THE MEAN OF THE SCORES OF THE WRITTEN AND ORAL EXAM. THE FINAL SCORE OF THE EXAM IS GIVEN BY THE WEIGHTED MEAN OF THE SCORE OBAINED IN THE TWO UNITS. AN ADDITIONAL “CUM LADE” MAY BE ATTRIBUTED TO STUDENTS WITH THE MAXIMUM SCORE (30/30) WHO HAVE DEMONSTRATED AUTONOMY AND ABILITY TO FACE MATHEMATICAL AND STATISTICAL PROBLEMS.

Verification of learning

THE ACQUIRED KNOWLEDGE IS EVALUATED WITH A FINAL EXAM WHOSE SCORE IS GIVEN BY THE WEIGHTED MEAN OF THE SCORES OBTAINED IN THE TWO UNITS (SCORE RANGE: MIN 18, MAX 30).

THE UNIT MATHEMATICS IS CHARACTERIZED BY TWO INTER-COURSE TESTS.
1) FIRST TEST: FROM THE LINEAR ALGEBRA TO THE STUDY OF FUNCTIONS, LIMITS AND THEIR PROPERTIES (MAXIMUM SCORE 16 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED)
2) SECOND TEST: DERIVATIVES AND INTEGRALS (MAXIMUM SCORE 10 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED)

THE STATISTICAL UNIT IS CHARACTERIZED BY TWO INTER-COURSE TESTS.
1) FIRST TEST: DATA ANALYSIS (MAX SCORE: 7) AND PROBABILITY (MAX SCORE 9). THE TEST IS PASSED IF THE TOTAL SCORE IS AT LEAST 10.
2)SECOND TEST: STATISTICAL INFERENCE (MAXIMUM SCORE 10 POINTS, MINIMUM SCORE 6 POINTS TO BE PASSED)

FINAL EXAM:
WRITTEN EXAM (MAX SCORE 30) FOR EACH OF THE TWO UNITS.
MATHEMATICS: STUDY OF FUNCTIONS (MAX SCORE 10), INTEGRALS (MAX SCORE 7), LIMITS (MAX SCORE 8), LINEAR ALGEBRA (MAX SCORE 5);
STATISTICS: DATA ANALYSIS (MAX SCORE 7), PROBABILITY (MAX SCORE 9), INFERENCE (MAX SCORE 10), LINEAR MODELS (MAX SCORE 4).
ALL STUDENTS THAT HAVE PASSED THE INTER-COURSE TESTS DO NOT HAVE TO CARRY OUT THE EXERCISES ON THE CORRESPONDING TOPICS (FOR EXAMPLE: IF THEY HAVE PASSED THE SECOND INTER-COURSE STATISTICAL TEST THEY DO NOT HAVE TO CARRY OUT THE EXEECISES OF STATISTICAL INFERENCE).
THE FINAL SCORE OF THE WRITTEN EXAM IS GIVEN BY THE WEIGTHED MEAN OF THE SCORES OF THE TWO UNITS (AND THE MINIMUM SCORE FOR EACH OF THEM IS 18).
THE ORAL INTEVIEW (MAX SCORE 30) IS BASED ON THREE QUESTIONS SUBMITTED TO THE STUDENTS IN MATHEMATICS AND FURTHER THREE QUESTIONS IN STATISTICS.

THE FINAL SCORE FOR EACH UNIT IS GIVEN BY THE MEAN OF THE SCORES OF THE WRITTEN AND ORAL EXAM.

THE FINAL SCORE OF THE EXAM IS GIVEN BY THE WEIGHTED MEAN OF THE SCORE OBAINED IN THE TWO UNITS.

AN ADDITIONAL “CUM LADE” MAY BE ATTRIBUTED TO STUDENTS WITH THE MAXIMUM SCORE (30/30) WHO HAVE DEMONSTRATED AUTONOMY AND ABILITY TO FACE MATHEMATICAL AND STATISTICAL PROBLEMS.

	Texts
	UNIT I: TOM M.APOSTOL, CALCULUS I,1975 JOHN WILEY & SONS, INC. UNIT II: CASELLA G. AND BERGER R.L., STATISTICAL INFERENCE, DUXBURY ADVANCED SERIES.

	More Information
	FAUSTO ACERNESE (PART 1) HTTPS://DOCENTI.UNISA.IT/FAUSTO.ACERNESE MARCELLA NIGLIO (PART 2) DOCENTI.UNISA.IT/MARCELLA.NIGLIO

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Fausto ACERNESE | MATHEMATICS AND STATISTICS