Paola CAVALIERE | FUCNTION THEORY

cod. 0512300023

FUCNTION THEORY

	0512300023
	DEPARTMENT OF MATHEMATICS
	EQF6
	MATHEMATICS
	2024/2025

PERCORSO SHARED STUDY PATHWAY

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2018
	SPRING SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	Objectives
	THE UNIT AIMS TO PROVIDE STUDENTS WITH A FIRM GROUNDING IN THE THEORY AND TECHNIQUES OF MODERN ANALYSIS AND TO OFFER STUDENTS AMPLE OPPORTUNITY TO BUILD ON THEIR PROBLEM-SOLVING ABILITY IN THIS AREA. THE TECHNIQUES AND EXAMPLES TO BE DISCUSSED WILL ESSENTIALLY SUPPORT, IN A VARIETY OF WAYS, MANY LATER ADVANCED COURSES, PARTICULAR PURE AND APPLIED MATHEMATICS COURSE AS MEASURE THEORY AND INTEGRATION, FUNCTIONAL ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, GEOMETRY OF MANIFOLDS, MATHEMATICAL TOOLS FOR ECONOMIC ANALYSIS AND OTHER APPLIED SCIENCES. SPECIFICALLY, THIS MODULE SETS OUT TO EXPLORE SOME CORE NOTIONS IN THE GENERAL THEORY OF METRIC AND NORMED SPACES, SUCH AS CAUCHY SEQUENCES, CONVERGENCE, CONTINUITY AND UNIFORM CONTINUITY, COMPACTNESS AND COMPLETENESS, AND THEIR RELATIONS TO CONTINUITY. A FOCUS STUDY OF INFINITE-DIMENSIONAL NORMED LINEAR SPACES, INCLUDING FUNCTION SPACES IN WHICH A SINGLE POINT REPRESENTS A FUNCTION, WILL BE ALSO PROVIDED. AS IT WILL BE HIGHLIGHTED, THE GEOMETRICAL INTUITION DERIVED FROM FINITE-DIMENSIONAL EUCLIDEAN SPACES REMAINS ESSENTIAL, ALTHOUGH COMPLETELY NEW FEATURES ARISE IN THE CASE OF INFINITE-DIMENSIONAL SPACES. THIS COURSE WILL THUS BE THE BRIDGE FROM ANALYSIS ON THE REAL LINE AND ON FINITE DIMENSIONAL EUCLIDEAN SPACES, AS CONSIDERED IN FIRST TWO YEARS MATHEMATICAL ANALYSIS COURSES, TO A MUCH MORE FLEXIBLE AND GENERAL FRAMEWORK, WHERE THE ABSTRACTION NOT ONLY SIMPLIFIES AND ELUCIDATES MATHEMATICAL IDEAS THAT RECUR IN DIFFERENT GUISES, BUT ALSO HELPS ECONOMIZE THE INTELLECTUAL EFFORT INVOLVED IN LEARNING THEM. KNOWLEDGE AND UNDERSTANDING THE COURSE IS DESIGNED TO ENABLE STUDENTS TO: INTERPRET THE MAIN CONCEPTS IN METRIC AND NORMED SPACES THEORY, ANALYTICALLY, GRAPHICALLY AND VERBALLY; DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER; TO FORMULATE AND DEVELOP TREATED ARGUMENTS IN A LOGICAL MANNER; IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE IN MODERN ANALYSIS; ANALYZE MATHEMATICAL PROBLEMS IN THE FRAMEWORK OF FUNCTION SPACES AND SOLVE IT USING A WIDE ARRAY OF TOOLS. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: DEFINE AND STATE SOME OF THE BASIC DEFINITIONS OF CONCEPTS CONCERNING METRIC AND NORMED SPACES SUCH AS BOUNDEDNESS, SEPARABILITY, COMPACTNESS, AND COMPLETENESS; STATE SOME OF THE PRINCIPAL THEOREMS AS TREATED IN THE MODULE; USE SOME OF THE BASIC DEFINITIONS AND PRINCIPAL THEOREMS IN THE INVESTIGATION OF EXAMPLES; PROVE RESULTS (PROPOSITIONS AND THEOREMS) CONCERNING THOSE ASPECTS OF METRIC AND NORMED SPACES TREATED IN THE MODULE. AUTONOMY OF JUDGEMENT A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: APPLY COMPLEX IDEAS TO FAMILIAR AND TO NOVEL SITUATIONS; WORK WITH ABSTRACT CONCEPTS AND IN A CONTEXT OF GENERALITY; REASON LOGICALLY AND WORK ANALYTICALLY; PERFORM WITH HIGH LEVELS OF ACCURACY; TRANSFER EXPERTISE BETWEEN DIFFERENT TOPICS IN MATHEMATICS. COMMUNICATION SKILLS A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: COMMUNICATE WITH CLARITY; WORK EFFECTIVELY, INDEPENDENTLY AND UNDER DIRECTION; ANALYZE AND SOLVE COMPLEX PROBLEMS ACCURATELY; ADOPT EFFECTIVE STRATEGIES FOR STUDY. LEARNING ABILITY A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: SELECT AND APPLY APPROPRIATE METHODS AND TECHNIQUES TO SOLVE PROBLEMS; JUSTIFY CONCLUSIONS USING MATHEMATICAL ARGUMENTS WITH APPROPRIATE RIGOUR; COMMUNICATE RESULTS USING APPROPRIATE STYLES, CONVENTIONS AND TERMINOLOGY. HE/SHE ALSO SHOULD HAVE GAINED PROFICIENCY IN DEALING WITH ABSTRACT CONCEPTS, WITH EMPHASIS ON CLEAR EXPLANATIONS OF SUCH CONCEPTS TO OTHERS, IN THE ART OF WRITING PROOFS AND TO DEVELOP HIS/HER ANALYTIC SKILLS THROUGH THE STUDY OF COMPLEX AND ABSTRACT SYSTEMS.

THE UNIT AIMS TO PROVIDE STUDENTS WITH A FIRM GROUNDING IN THE THEORY AND TECHNIQUES OF MODERN ANALYSIS AND TO OFFER STUDENTS AMPLE OPPORTUNITY TO BUILD ON THEIR PROBLEM-SOLVING ABILITY IN THIS AREA. THE TECHNIQUES AND EXAMPLES TO BE DISCUSSED WILL ESSENTIALLY SUPPORT, IN A VARIETY OF WAYS, MANY LATER ADVANCED COURSES, PARTICULAR PURE AND APPLIED MATHEMATICS COURSE AS MEASURE THEORY AND INTEGRATION, FUNCTIONAL ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, GEOMETRY OF MANIFOLDS, MATHEMATICAL TOOLS FOR ECONOMIC ANALYSIS AND OTHER APPLIED SCIENCES.
SPECIFICALLY, THIS MODULE SETS OUT TO EXPLORE SOME CORE NOTIONS IN THE GENERAL THEORY OF METRIC AND NORMED SPACES, SUCH AS CAUCHY SEQUENCES, CONVERGENCE, CONTINUITY AND UNIFORM CONTINUITY, COMPACTNESS AND COMPLETENESS, AND THEIR RELATIONS TO CONTINUITY. A FOCUS STUDY OF INFINITE-DIMENSIONAL NORMED LINEAR SPACES, INCLUDING FUNCTION SPACES IN WHICH A SINGLE POINT REPRESENTS A FUNCTION, WILL BE ALSO PROVIDED. AS IT WILL BE HIGHLIGHTED, THE GEOMETRICAL INTUITION DERIVED FROM FINITE-DIMENSIONAL EUCLIDEAN SPACES REMAINS ESSENTIAL, ALTHOUGH COMPLETELY NEW FEATURES ARISE IN THE CASE OF INFINITE-DIMENSIONAL SPACES.
THIS COURSE WILL THUS BE THE BRIDGE FROM ANALYSIS ON THE REAL LINE AND ON FINITE DIMENSIONAL EUCLIDEAN SPACES, AS CONSIDERED IN FIRST TWO YEARS MATHEMATICAL ANALYSIS COURSES, TO A MUCH MORE FLEXIBLE AND GENERAL FRAMEWORK, WHERE THE ABSTRACTION NOT ONLY SIMPLIFIES AND ELUCIDATES MATHEMATICAL IDEAS THAT RECUR IN DIFFERENT GUISES, BUT ALSO HELPS ECONOMIZE THE INTELLECTUAL EFFORT INVOLVED IN LEARNING THEM.

KNOWLEDGE AND UNDERSTANDING

THE COURSE IS DESIGNED TO ENABLE STUDENTS TO: INTERPRET THE MAIN CONCEPTS IN METRIC AND NORMED SPACES THEORY, ANALYTICALLY, GRAPHICALLY AND VERBALLY; DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER; TO FORMULATE AND DEVELOP TREATED ARGUMENTS IN A LOGICAL MANNER; IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE IN MODERN ANALYSIS; ANALYZE MATHEMATICAL PROBLEMS IN THE FRAMEWORK OF FUNCTION SPACES AND SOLVE IT USING A WIDE ARRAY OF TOOLS.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING

A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: DEFINE AND STATE SOME OF THE BASIC DEFINITIONS OF CONCEPTS CONCERNING METRIC AND NORMED SPACES SUCH AS BOUNDEDNESS, SEPARABILITY, COMPACTNESS, AND COMPLETENESS; STATE SOME OF THE PRINCIPAL THEOREMS AS TREATED IN THE MODULE; USE SOME OF THE BASIC DEFINITIONS AND PRINCIPAL THEOREMS IN THE INVESTIGATION OF EXAMPLES; PROVE RESULTS (PROPOSITIONS AND THEOREMS) CONCERNING THOSE ASPECTS OF METRIC AND NORMED SPACES TREATED IN THE MODULE.

AUTONOMY OF JUDGEMENT

A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: APPLY COMPLEX IDEAS TO FAMILIAR AND TO NOVEL SITUATIONS; WORK WITH ABSTRACT CONCEPTS AND IN A CONTEXT OF GENERALITY; REASON LOGICALLY AND WORK ANALYTICALLY; PERFORM WITH HIGH LEVELS OF ACCURACY; TRANSFER EXPERTISE BETWEEN DIFFERENT TOPICS IN MATHEMATICS.

COMMUNICATION SKILLS

A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: COMMUNICATE WITH CLARITY; WORK EFFECTIVELY, INDEPENDENTLY AND UNDER DIRECTION; ANALYZE AND SOLVE COMPLEX PROBLEMS ACCURATELY; ADOPT EFFECTIVE STRATEGIES FOR STUDY.

LEARNING ABILITY

A STUDENT WHO COMPLETES THIS MODULE SUCCESSFULLY SHOULD BE ABLE TO: SELECT AND APPLY APPROPRIATE METHODS AND TECHNIQUES TO SOLVE PROBLEMS; JUSTIFY CONCLUSIONS USING MATHEMATICAL ARGUMENTS WITH APPROPRIATE RIGOUR; COMMUNICATE RESULTS USING APPROPRIATE STYLES, CONVENTIONS AND TERMINOLOGY.
HE/SHE ALSO SHOULD HAVE GAINED PROFICIENCY IN DEALING WITH ABSTRACT CONCEPTS, WITH EMPHASIS ON CLEAR EXPLANATIONS OF SUCH CONCEPTS TO OTHERS, IN THE ART OF WRITING PROOFS AND TO DEVELOP HIS/HER ANALYTIC SKILLS THROUGH THE STUDY OF COMPLEX AND ABSTRACT SYSTEMS.

	Prerequisites
	THE PREREQUISITES ARE ONE AND SEVERAL VARIABLES CALCULUS, AND LINEAR ALGEBRA.

	Contents
	METRIC AND NORMED SPACES (14 HOURS): DEFINITION OF METRIC SPACE AND EXAMPLES. NORMS AND INNER PRODUCTS ON VECTOR SPACES. SOME FUNDAMENTAL INEQUALITIES. BASIC NOTIONS IN METRIC SETTING: DISTANCE FROM A SET, BALLS, DIAMETER OF A SET, BOUNDED AND TOTALLY BOUNDED SET, CAUCHY AND CONVERGENT SEQUENCES; OPEN AND CLOSED SETS, INTERIOR, CLOSURE AND BOUNDARY OF A SET, DENSE SETS. SEPARABLE SPACES. FINITE DIMENSIONAL SPACES. CONTINUOUS MAPPINGS (10 HOURS): CONTINUOUS MAPPINGS. TOPOLOGICALLY EQUIVALENT METRICS. ISOMETRIES. BOUNDED LINEAR OPERATOR AND THEIR CHARACTERIZATIONS. UNIFORMLY CONTINUOUS FUNCTIONS. LIPSCHITZ FUNCTIONS AND CONTRACTIVE MAPS. HÖLDER FUNCTIONS. LIPSCHITZ EQUIVALENT METRICS. INFINITE DIMENSIONAL SPACES AND RELEVANT ISTANCES. COMPLETE METRIC SPACES AND BANACH SPACE (12 HOURS): COMPLETNESS AND CHARACTERIZATIONS. COMPLETATION OF A METRIC SPACE AND OF A NORM SPACE. RELEVANT ISTANCES OF COMPLETE AND UNCOMPLETE SPACES. EQUIVALENT NORMS. BANACH-CACCIOPPOLI FIXED POINT THEOREM AND SEVERAL APPLICATIONS. COMPACTNESS IN METRIC SPACES (12 HOURS): COMPACT AND SEQUENTIALLY COMPACT SETS. COMPACTNESS IN FINITE DIMENSIONAL SPACES. CRITERIA FOR COMPACTNESS IN METRIC SPACES AND IN NORMED SPACES. CONTINUITY AND COMPACTNESS. WEIESTRASS AND CANTOR THEOREMS. EXTENSION OF CONTINUOUS AND UNIFORMLY CONTINUOUS FUNCTIONS. APPLICATIONS.

Contents

METRIC AND NORMED SPACES (14 HOURS): DEFINITION OF METRIC SPACE AND EXAMPLES. NORMS AND INNER PRODUCTS ON VECTOR SPACES. SOME FUNDAMENTAL INEQUALITIES. BASIC NOTIONS IN METRIC SETTING: DISTANCE FROM A SET, BALLS, DIAMETER OF A SET, BOUNDED AND TOTALLY BOUNDED SET, CAUCHY AND CONVERGENT SEQUENCES; OPEN AND CLOSED SETS, INTERIOR, CLOSURE AND BOUNDARY OF A SET, DENSE SETS. SEPARABLE SPACES. FINITE DIMENSIONAL SPACES.

CONTINUOUS MAPPINGS (10 HOURS): CONTINUOUS MAPPINGS. TOPOLOGICALLY EQUIVALENT METRICS. ISOMETRIES. BOUNDED LINEAR OPERATOR AND THEIR CHARACTERIZATIONS. UNIFORMLY CONTINUOUS FUNCTIONS. LIPSCHITZ FUNCTIONS AND CONTRACTIVE MAPS. HÖLDER FUNCTIONS. LIPSCHITZ EQUIVALENT METRICS. INFINITE DIMENSIONAL SPACES AND RELEVANT ISTANCES.

COMPLETE METRIC SPACES AND BANACH SPACE (12 HOURS): COMPLETNESS AND CHARACTERIZATIONS. COMPLETATION OF A METRIC SPACE AND OF A NORM SPACE. RELEVANT ISTANCES OF COMPLETE AND UNCOMPLETE SPACES. EQUIVALENT NORMS. BANACH-CACCIOPPOLI FIXED POINT THEOREM AND SEVERAL APPLICATIONS.

COMPACTNESS IN METRIC SPACES (12 HOURS): COMPACT AND SEQUENTIALLY COMPACT SETS. COMPACTNESS IN FINITE DIMENSIONAL SPACES. CRITERIA FOR COMPACTNESS IN METRIC SPACES AND IN NORMED SPACES. CONTINUITY AND COMPACTNESS. WEIESTRASS AND CANTOR THEOREMS. EXTENSION OF CONTINUOUS AND UNIFORMLY CONTINUOUS FUNCTIONS. APPLICATIONS.

	Teaching Methods
	THE COURSE CONSISTS OF 48 HOURS OF LECTURED TEACHING. IT IS STRUCTURED AS A COMBINATION OF LECTURES AND PRATICAL SESSIONS. THE LAST ONES WILL SHOW THAT THE ABSTRACTION OF METRIC SPACES SETTING NOT ONLY SIMPLIFIES AND ELUCIDATES MATHEMATICAL IDEAS THAT RECUR IN DIFFERENT GUISES, BUT ALSO HELPS ECONOMIZE THE INTELLECTUAL EFFORT INVOLVED IN LEARNING THEM. THE FEEDBACK FROM STUDENTS WILL ALWAYS BE HIGHLY APPRECIATED.

Teaching Methods

THE COURSE CONSISTS OF 48 HOURS OF LECTURED TEACHING. IT IS STRUCTURED AS A COMBINATION OF LECTURES AND PRATICAL SESSIONS. THE LAST ONES WILL SHOW THAT THE ABSTRACTION OF METRIC SPACES SETTING NOT ONLY SIMPLIFIES AND ELUCIDATES MATHEMATICAL IDEAS THAT RECUR IN DIFFERENT GUISES, BUT ALSO HELPS ECONOMIZE THE INTELLECTUAL EFFORT INVOLVED IN LEARNING THEM. THE FEEDBACK FROM STUDENTS WILL ALWAYS BE HIGHLY APPRECIATED.

	Verification of learning
	THE FINAL EXAMINATION, EVALUATED ON A 0-30 SCALE, CONSISTS IN ONE WRITTEN TEST. THE EXAM PAPER INCLUDES 5 CLOSED QUESTIONS ON THE MAIN DEFINITIONS, 3 CLOSED QUESTIONS ON THE STATEMENTS OF THE THEOREMS, ON THEIR DEMONSTRATIONS AND APPLICATIONS AND 2 OPEN QUESTIONS. IT IS THE SAME FOR ALL STUDENTS, AND IT IS TO BE COMPLETED IN 180 MINUTES. DURING THE WRITTEN EXAMINATION, STUDENTS ARE NOT ALLOWED TO USE TEXTBOOKS, NOTES, SCIENTIFIC CALCULATORS OR OTHER ELECTRONIC DEVICES. STUDENTS WILL BE EVALUATED ON THEIR ABILITY TO DEVISE, ORGANIZE AND PRESENT THE MAIN TOPICS AND THEIR CONNECTIONS. THE MINIMUM GRADE OF 18/30 IS OBTAINED WHEN THE STUDENT EXHIBITS A SUFFICIENT KNOWLEDGE OF ALL THE PROGRAM, WITH THE EXCEPTION OF PROOFS. THE MAXIMUM GRADE OF 30/30 WHEN THE STUDENT EXHIBITS A DEEP AND EXTENDED KNOWLEDGE OF THE THEORY AND THE APPLICATIONS OF ALL THE ARGUMENTS OF THE COURSE. THE MAXIMUM GRADE CUM LAUDE WILL BE AWARDED TO PARTICULARLY DESERVING STUDENTS WHO, IN ADDITION TO HAVING COMPLIED WITH THE REQUISITES NECESSARY TO OBTAIN THE FULL EVALUATION, IN THE PERFORMANCE OF THE TEST HAVE OVERALL DEMONSTRATED AN APPRECIABLE SYSTEMATIC KNOWLEDGE OF THE TOPIC, AN EXCELLENT ABILITY TO APPLY THE KNOWLEDGE ACQUIRED TO THE SPECIFIC PROBLEM IN QUESTION, A CONSIDERABLE AUTONOMY OF JUDGMENT, AS WELL AS A PARTICULAR CARE IN WRITTEN EXPOSITION.

Verification of learning

THE FINAL EXAMINATION, EVALUATED ON A 0-30 SCALE, CONSISTS IN ONE WRITTEN TEST. THE EXAM PAPER INCLUDES 5 CLOSED QUESTIONS ON THE MAIN DEFINITIONS, 3 CLOSED QUESTIONS ON THE STATEMENTS OF THE THEOREMS, ON THEIR DEMONSTRATIONS AND APPLICATIONS AND 2 OPEN QUESTIONS. IT IS THE SAME FOR ALL STUDENTS, AND IT IS TO BE COMPLETED IN 180 MINUTES.

DURING THE WRITTEN EXAMINATION, STUDENTS ARE NOT ALLOWED TO USE TEXTBOOKS, NOTES, SCIENTIFIC CALCULATORS OR OTHER ELECTRONIC DEVICES. STUDENTS WILL BE EVALUATED ON THEIR ABILITY TO DEVISE, ORGANIZE AND PRESENT THE MAIN TOPICS AND THEIR CONNECTIONS.

THE MINIMUM GRADE OF 18/30 IS OBTAINED WHEN THE STUDENT EXHIBITS A SUFFICIENT KNOWLEDGE OF ALL THE PROGRAM, WITH THE EXCEPTION OF PROOFS.

THE MAXIMUM GRADE OF 30/30 WHEN THE STUDENT EXHIBITS A DEEP AND EXTENDED KNOWLEDGE OF THE THEORY AND THE APPLICATIONS OF ALL THE ARGUMENTS OF THE COURSE.

THE MAXIMUM GRADE CUM LAUDE WILL BE AWARDED TO PARTICULARLY DESERVING STUDENTS WHO, IN ADDITION TO HAVING COMPLIED WITH THE REQUISITES NECESSARY TO OBTAIN THE FULL EVALUATION, IN THE PERFORMANCE OF THE TEST HAVE OVERALL DEMONSTRATED AN APPRECIABLE SYSTEMATIC KNOWLEDGE OF THE TOPIC, AN EXCELLENT ABILITY TO APPLY THE KNOWLEDGE ACQUIRED TO THE SPECIFIC PROBLEM IN QUESTION, A CONSIDERABLE AUTONOMY OF JUDGMENT, AS WELL AS A PARTICULAR CARE IN WRITTEN EXPOSITION.

	Texts
	- P. CAVALIERE: INTRODUZIONE ALLA TEORIA DEGLI SPAZI METRICI E DEGLI SPAZI NORMATI – FULL ITALIAN LECTURE NOTES FOR ATTENDING STUDENTS OF ‘TEORIA DELLE FUNZIONI’ COURSE - S.K. BERBERIAN: FUNDAMENTALS OF REAL ANALYSIS, SPRINGER-VERLAG, 1999, 479 PAGES, ISBN: 0-387-98480-1 A.N. KOLMOGOROV - S.V. FOMIN: INTRODUCTORY REAL ANALYSIS, COURIER CORPORATION, 2012, 416 PAGES, ISBN 0-486-13474-1 - W. RUDIN: PRINCIPLES OF MATHEMATICAL ANALYSIS, THIRD EDITION, MCGRAW-HILL, SINGAPORE, 1976, 351 PAGES, ISBN: 0-07-054235-X - W.A. SUTHERLAND: INTRODUCTION TO METRIC AND TOPOLOGICAL SPACES, OXFORD, NEWYORK, 1981, 181 PAGES, ISBN: 0-19-853161-3 THE STUDENT CAN USE ANY GOOD TEXT THAT CONTAINS THE ARGUMENTS OF THE PROGRAM, SINCE IT IS A STANDARD PROGRAM. STUDENTS ARE URGED TO CHECK IN ADVANCE WITH THE TEACHER THE APPROPRIATENESS OF THE CHOSEN TEXT.

Texts

- P. CAVALIERE: INTRODUZIONE ALLA TEORIA DEGLI SPAZI METRICI E DEGLI SPAZI NORMATI – FULL ITALIAN LECTURE NOTES FOR ATTENDING STUDENTS OF ‘TEORIA DELLE FUNZIONI’ COURSE

- S.K. BERBERIAN: FUNDAMENTALS OF REAL ANALYSIS, SPRINGER-VERLAG, 1999, 479 PAGES, ISBN: 0-387-98480-1
A.N. KOLMOGOROV - S.V. FOMIN: INTRODUCTORY REAL ANALYSIS, COURIER CORPORATION, 2012, 416 PAGES, ISBN 0-486-13474-1

- W. RUDIN: PRINCIPLES OF MATHEMATICAL ANALYSIS, THIRD EDITION, MCGRAW-HILL, SINGAPORE, 1976, 351 PAGES, ISBN: 0-07-054235-X

- W.A. SUTHERLAND: INTRODUCTION TO METRIC AND TOPOLOGICAL SPACES, OXFORD, NEWYORK, 1981, 181 PAGES, ISBN: 0-19-853161-3

THE STUDENT CAN USE ANY GOOD TEXT THAT CONTAINS THE ARGUMENTS OF THE PROGRAM, SINCE IT IS A STANDARD PROGRAM. STUDENTS ARE URGED TO CHECK IN ADVANCE WITH THE TEACHER THE APPROPRIATENESS OF THE CHOSEN TEXT.

	More Information
	FOR ANY ISSUE OR QUESTION REGARDING THE COURSE PROGRAM AND RELATED ACTIVITIES, STUDENTS CAN CONTACT THE TEACHER BY EMAIL. CLASS ATTENDANCE IS ADVISED. IN ORDER TO FOLLOW THE DEVELOPMENT OF THE LECTURES, IT IS STRONGLY RECOMMENDED TO SPEND FOUR HOURS PER WEEK OUTSIDE OF CLASS WORKING ON THIS COURSE.

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Paola CAVALIERE | FUCNTION THEORY

FUCNTION THEORY

PERCORSO SHARED STUDY PATHWAY

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Paola CAVALIERE | FUCNTION THEORY