Carmine MONETTA | UN' INTRODUZIONE ALLA TEORIA COMBINATORIA DEI GRUPPI
Carmine MONETTA UN' INTRODUZIONE ALLA TEORIA COMBINATORIA DEI GRUPPI
cod. 8860300028
UN' INTRODUZIONE ALLA TEORIA COMBINATORIA DEI GRUPPI
| 8860300028 | |
| DEPARTMENT OF MATHEMATICS | |
| Corso di Dottorato (D.M.226/2021) | |
| MATHEMATICS | |
| 2023/2024 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2023 | |
| FULL ACADEMIC YEAR |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/02 | 2 | 10 | LESSONS |
| Objectives | |
|---|---|
| THE COURSE AIMS TO PROVIDE STUDENTS WITH AN INTRODUCTION TO COMBINATORIAL GROUP THEORY, DISCUSSING IN PARTICULAR DECISION PROBLEMS IN GROUP THEORY. |
| Prerequisites | |
|---|---|
| BASIC CONCEPTS OF ABSTRACT ALGEBRA AND GROUP THEORY. |
| Contents | |
|---|---|
| COMBINATORIAL GROUP THEORY IS A BRANCH OF MATHEMATICS THAT DEALS WITH STUDYING GROUPS THROUGH COMBINATORIAL METHODS. IT ORIGINATED FROM ATTEMPTS TO UNDERSTAND AND SOLVE PROBLEMS IN TOPOLOGY, AND MANY SIGNIFICANT MATHEMATICIANS CONTRIBUTED TO THIS FIELD, SUCH AS POINCARÉ, DEHN, AND TIETZE. IN FACT, GROUPS ARISING FROM TOPOLOGICAL CONTEXTS, SUCH AS FUNDAMENTAL GROUPS OF SURFACES OR SPACES, OFTEN APPEAR IN THE FORM OF GENERATORS AND RELATIONS. THE COMBINATORIAL THEORY OF GROUPS HAS APPLICATIONS IN VARIOUS AREAS OF MATHEMATICS, COMPUTER SCIENCE, CRYPTOGRAPHY, AND THEORETICAL PHYSICS. THE AIM OF THIS COURSE IS TO PROVIDE AN INTRODUCTION TO THIS THEORY, DEMONSTRATING SOME PROPERTIES OF FREE GROUPS AND GROUP PRESENTATIONS, AND THEN DISCUSSING DECISION PROBLEMS IN GROUP THEORY, SUCH AS THE WORD PROBLEM |
| Teaching Methods | |
|---|---|
| THE TEACHING ACTIVITY INCLUDES LECTURES AND POSSIBLE PRACTICE SESSIONS, FOR A TOTAL OF 10 HOURS. |
| Verification of learning | |
|---|---|
| THE FINAL TEST INVOLVES THE PRESENTATION OF A TOPIC AGREED WITH THE PROFESSOR IN THE FORM OF A SEMINAR. |
| Texts | |
|---|---|
| MAGNUS, WILHELM, ABRAHAM KARRASS, AND DONALD SOLITAR. COMBINATORIAL GROUP THEORY: PRESENTATIONS OF GROUPS IN TERMS OF GENERATORS AND RELATIONS. COURIER CORPORATION, 2004. ROBINSON, DEREK JS. A COURSE IN THE THEORY OF GROUPS. VOL. 80. SPRINGER SCIENCE & BUSINESS MEDIA, 2012. ROTMAN, JOSEPH J. AN INTRODUCTION TO THE THEORY OF GROUPS. VOL. 148. SPRINGER SCIENCE & BUSINESS MEDIA, 2012. |
| More Information | |
|---|---|
| PROFESSOR'S EMAIL ADDRESS: CMONETTA@UNISA.IT |
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