Annamaria MIRANDA | TOPOLOGIA
Annamaria MIRANDA TOPOLOGIA
cod. 0512300036
TOPOLOGIA
| 0512300036 | |
| DIPARTIMENTO DI MATEMATICA | |
| MATHEMATICS | |
| 2014/2015 |
| YEAR OF COURSE 3 | |
| YEAR OF DIDACTIC SYSTEM 2010 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/03 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| -KNOWLEDGE AND UNDERSTANDING THE COURSE "TOPOLOGY" AIMS TO INTRODUCE STUDENTS TO THE FUNDAMENTAL CONCEPTS OF GENERAL TOPOLOGY AND ALGEBRAIC TOPOLOGY. THE FIRST PART IS CONCERNED WITH THE STUDY OF TOPOLOGICAL SPACES AND THEIR STRUCTURE-PRESERVING FUNCTIONS (CONTINUOUS FUNCTIONS). THE STUDENTS WILL BE INTRODUCED TO THE GENERAL STRUCTURE OF A TOPOLOGICAL SPACE, THE CONSTRUCTION OF NEW TOPOLOGICAL SPACES FROM OLD, THE TOPOLOGICAL PROPERTIES INVARIANTS UNDER CONTINUOUS MAPPINGS (AMONG OTHERS COMPACTNESS AND CONNECTEDNESS). THE BASIC GOAL OF THE SECOND PART IS TO STUDY SOME PROPERTIES OF TOPOLOGICAL SPACES AND MAPS BETWEEN THEM BY ASSOCIATING ALGEBRAIC INVARIANTS TO EACH SPACE. TWO WAYS IN WHICH THIS CAN BE DONE ARE THROUGH FUNDAMENTAL GROUPS, OR MORE GENERALLY HOMOTOPY THEORY, AND THROUGH HOMOLOGY AND COHOMOLOGY GROUPS. ON SATISFYING THE REQUIREMENTS OF THIS COURSE, THE STUDENT WILL HAVE THE FOLLOWING KNOWLEDGE AND SKILLS. •UNDERSTAND THE FUNDAMENTAL IDEAS IN GENERAL AND ALGEBRAIC TOPOLOGY. •EXPLAIN CLEARLY THE FUNDAMENTAL CONCEPTS OF GENERAL AND ALGEBRAIC TOPOLOGY. -APPLICATION SKILLS THE STUDENT WILL BE ABLE TO: •DEMONSTRATE EFFICIENT USE OF TOPOLOGY TECHNIQUES, BY APPLYING THEM TO PROBLEM-SOLVING. •DEMONSTRATE CAPACITY FOR MATHEMATICAL REASONING THROUGH ANALYZING, PROVING AND EXPLAINING PROPOSITIONS AND CONCEPTS FROM TOPOLOGY. -JUDGEMENT AUTONOMY STUDENTS WILL BE GUIDED TO IMPROVE THEIR CRITICAL ABILITIES BY LEARNING ALL WHAT WILL BE DEALT WITH IN CLASS, AND TO ENRICH THEIR JUDGEMENT THROUGH THE STUDY OF THE DIDACTIC MATERIAL INDICATED BY THE PROFESSOR. -COMMUNICATION SKILLS THE STUDENT WILL HAVE TO PRESENT IN A CLEAR AND RIGOROUS WAY BOTH THEORETICAL AND APPLICATIVE ACQUIRED KNOWLEDGE. |
| Prerequisites | |
|---|---|
| PREVIOUS COURSES CONTAINING BASIC CONCEPTS OF MATHEMATICAL ANALYSIS AND ALGEBRA ARE PRESUPPOSED. |
| Contents | |
|---|---|
| GENERAL TOPOLOGY: 1.TOPOLOGICAL SPACES. 2.CONTINUITY AND HOMEOMORPHISMS, TOPOLOGICAL INVARIANCE. 3.CONSTRUCTION OF TOPOLOGICAL SPACES FROM DIFFERENT POINTS OF VIEW (AMONG OTHERS PRODUCT TOPOLOGY, QUOTIENT TOPOLOGY, TOPOLOGY DETERMINED BY A BASIS). 4.SEPARATION PROPERTIES, COMPACTNESS, CONNECTEDNESS. ALGEBRAIC TOPOLOGY: 5.FOUNDAMENTAL GROUP. 6.HOMOTOPY THEORY. 7.CLASSIFICATION OF TOPOLOGICAL SURFACES. |
| Teaching Methods | |
|---|---|
| LESSONS |
| Verification of learning | |
|---|---|
ORAL EXAMINATION THE PROFESSOR WILL VERIFY, BY AN ORAL EXAMINATION, ALL THE GOALS REACHED BY THE STUDENT AND HE WILL EXPRESS HIS KNOWLEDGE AND COMPETENCE BY AN OPPORTUNE GRADE. |
| Texts | |
|---|---|
1.C. KOSNIOWSKI "INTRODUZIONE ALLA TOPOLOGIA ALGEBRICA" ZANICHELLI. 2. GIUSEPPE TALLINI "STRUTTURE GEOMETRICHE. SPAZI TOPOLOGICI E VARIETÀ DIFFERENZIALI", LIGUORI 3.M.A. ARMSTRONG BASIC TOPOLOGY UNDERGRADUATE TEXTS IN MATHEMATICS SPRINGER-VERLAG 1983 .. 4. R. ENGELKING GENERAL TOPOLOGY HELDERMANN VERLAG 1989. 5. W.S.MASSEY ALGEBRAIC TOPOLOGY: AN INTRODUCTION SPRINGER-VERLAG 1991. 6.S. WILLARD GENERAL TOPOLOGY ADDISON -WESLEY PUBLISHING COMPANY 1970. |
| More Information | |
|---|---|
| E-MAIL ADDRESS OF THE PROFESSOR: AMIRANDA@UNISA.IT •WEBSITE ADDRESS OF THE PROFESSOR: HTTP://WWW.UNISA.IT/DOCENTI/ANNAMARIAMIRANDA/INDEX |
BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2016-09-30]
