Giovanna BIMONTE | MATHEMATICS
Giovanna BIMONTE MATHEMATICS
cod. 0212800001
MATHEMATICS
| 0212800001 | |
| DEPARTMENT OF ECONOMICS AND STATISTICS | |
| EQF6 | |
| STATISTICS FOR BIG DATA | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| SECS-S/06 | 10 | 60 | LESSONS |
| Exam | Date | Session | |
|---|---|---|---|
| BIMONTE | 14/01/2025 - 09:00 | SESSIONE ORDINARIA | |
| BIMONTE | 14/01/2025 - 09:00 | SESSIONE DI RECUPERO | |
| BIMONTE | 22/01/2025 - 09:00 | SESSIONE ORDINARIA | |
| BIMONTE | 22/01/2025 - 09:00 | SESSIONE DI RECUPERO | |
| BIMONTE | 05/02/2025 - 09:00 | SESSIONE ORDINARIA | |
| BIMONTE | 05/02/2025 - 09:00 | SESSIONE DI RECUPERO | |
| BIMONTE | 15/04/2025 - 09:00 | SESSIONE ORDINARIA |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE OF GENERAL MATHEMATICS IS TO PROVIDE STUDENTS WITH THE FUNDAMENTAL NOTIONS OF MATHEMATICAL ANALYSIS AND OPTIMIZATION. KNOWLEDGE AND LEARNING SKILLS: THE STUDENTS WILL ACQUIRE THE FUNDAMENTAL NOTIONS OF LINEAR ALGEBRA, THE DIFFERENTIAL AND INTEGRAL CALCULUS AS WELL AS THE BASIC ELEMENTS OF THE OPTIMIZATION. THIS TOOLS ARE INDISPENSABLE FOR THE UNDERSTANDING OF THE QUANTITATIVE THEMES DEALT IN THE OTHER DISCIPLINES. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENTS, ON THE BASE OF THE ACQUIRED TECHNIQUES, WILL HAVE TO BE ABLE TO FACE PROBLEMS OF OPTIMIZATIONS AND INTEGRATIONS, AT THE BASIS OF SEVERAL INSTRUMENTS PUT FORWARD IN THE OTHER DISCIPLINES. |
| Prerequisites | |
|---|---|
| PREREQUISITES: IT IS RECOMMENDED THE KNOWLEDGE OF BASIC MATHEMATICAL ELEMENTS: REMARKABLE IDENTITIES, OPERATIONS WITH POLYNOMIALS, EQUATIONS AND INEQUALITIES OF I AND II DEGREE. EUCLIDEAN GEOMETRY: BASIC CONCEPTS AND GEOMETRIC LOCUS IN THE PLANE. |
| Contents | |
|---|---|
| -STRUCTURES. THE SET R: REAL NUMBERS, OPERATIONS, PROPERTIES. THE SET R^N: VECTORS, OPERATIONS, PROPERTIES. -FUNCTIONS. COMPOSITE FUNCTION, INVERSE FUNCTION. REAL FUNCTIONS OF ONE REAL VARIABLE: DOMAIN, MAXIMA/MINIMA, CONVEXITY, OTHER PROPERTIES. REAL FUNCTIONS OF N REAL VARIABLES:DOMAIN, MAXIMA/MINIMA, CONVEXITY, OTHER PROPERTIES. -SEQUENCES OF REAL NUMBERS: DEFINITION AND PROPERTIES. LIMITS OF SEQUENCES AND THEIR COMPUTATION. -LIMITS AND CONTINUITY FOR FUNCTIONS. -ONE-VARIABLE DIFFERENTIAL CALCULUS. DIFFERENCE QUOTIENT, DERIVATIVE. DIFFERENTIABILITY. DIFFERENTIATION RULES. HIGHER-ORDER DERIVATIVES. TAYLOR FORMULA. CONVEXITY AND OPTIMIZATION CONDITIONS. -LINEAR ALGEBRA. SUBSPACES. LINEAR DEPENDENCE AND INDEPENDENCE. MATRICES AND THEIR OPERATIONS. LINEAR FUNCTIONS AND APPLICATIONS: DEFINITION, PROPERTIES, REPRESENTATION. DETERMINANT, RANK AND INVERSE MATRIX. LINEAR SYSTEMS: DISCUSSION AND STRUCTURE OF THE SOLUTIONS, SOLUTION. -N-VARIABLE DIFFERENTIAL CALCULUS. PARTIAL DERIVATIVES AND GRADIENT. DIFFERENTIABILITY. UNCONSTRAINED EXTREMA: OPTIMIZATION CONDITIONS. CONSTRAINED EXTREMA, LAGRANGEAN FUNCTION. -INTEGRATION. RIEMANN INTEGRAL. |
| Teaching Methods | |
|---|---|
| LESSONS, INDIVIDUAL WORK, WORKING TEAMS, EXERCISES,DISCUSSIONS IN CLASSROOM, INTERACTION WITH TEACHING BY EMAIL. |
| Verification of learning | |
|---|---|
| BY THE END OF THE MODULE THE STUDENT NEEDS TO DO A FORMAL EXAMINATION. THE EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL TEST, POSSIBLY TAKEN IN DIFFERENT DAYS AS WELL. WRITTEN TEST MUST TAKE PLACE PREVIOUSLY THAN THE ORAL TEST. THE MINIMUM SCORE IN BOTH TESTS IS 18/30. THE FINAL VALUATION IS GIVEN BY THE MEAN OF THE TWO SCORES. IN THE WRITTEN TEST STUDENTS SHOULD BE ABLE TO SOLVE SOME EXERCISES AND OBTAIN A SCORE AT LEAST OF 18/30. STUDENT SHOULD BE ABLE TO DEMONSTRATE AN UNDERSTANDING OF BASIC PROPERTIES, AND TO DEVELOP ANALYTICAL AND CRITICAL ABILITY WITH REGARD TO THE TOOLS AND THE DEVELOPED RULES. APPROVED POCKET CALCULATORS ARE ALLOWED. IT IS NOT POSSIBLE TO USE BOOKS, PAPERS, PC OR SMARTPHONE. THE TIME REQUIRED FOR THE WRITTEN TEST DEPENDS ON THE DIFFICULTY OF THE EXERCISES PROPOSED AND RANGES FROM A MINIMUM OF 1 HOUR TO A MAXIMUM OF 2 HOURS. IN THE ORAL TEST THE STUDENTS HAVE TO BE ABLE TO ENUNCIATE AND DEMONSTRATE THEOREMS AND TO HOLD UP, IN CLEAR AND EFFECTIVE WAY, AN ORAL DISCUSSION WITH OPPORTUNE REFERENCES TO THE CONTENTS OF THE COURSE. |
| Texts | |
|---|---|
| E. CASTAGNOLI, M. MARINACCI, E. VIGNA, PRINCIPLES OF MATHEMATICS AND ECONOMICS, MILANO, DISPENSE EGEA, 2013, ISBN 978-88-6407-192-3 INTEGRATIVE TEACHING MATERIALS. |
| More Information | |
|---|---|
| FREQUENCY OF THE COURSE IS HIGHLY RECOMMENDED, BUT NON-OBLIGATORY. IN THE COURSE STUDENT CAN ACT TOGETHER WITH THE PROFESSOR IN ORDER TO CLARIFY BOTH THEORETICAL AND PRACTICAL TOOLS AND PROBLEMS. STUDENTS CAN MADE SOME TEST SIMULATIONS FOR THE FINAL EXAM. |
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