LUCA SPADA | UNIVERSAL ALGEBRA
LUCA SPADA UNIVERSAL ALGEBRA
cod. 0522200035
UNIVERSAL ALGEBRA
| 0522200035 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF7 | |
| MATHEMATICS | |
| 2020/2021 |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/01 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| CRITICAL KNOWLEDGE OF THE FUNDAMENTAL LAWS OF ALGEBRA THAT ARE COMMON TO ALL EQUATIONALLY DEFINED CLASSES OF STRUCTURES AND OF THE MAIN TOOLS FOR THEIR GENERAL STUDY. ** EXPECTED LEARNING OUTCOMES: * KNOWLEDGE AND UNDERSTANDING - KNOWLEDGE OF THE CONCEPT OF LATTICE AND ITS MAIN CLASSIFICATIONS. - KNOWLEDGE OF THE GENERAL CONCEPT OF HOMOMORPHISM, SUBALGEBRA, QUOTIENT. - KNOWLEDGE OF THE CONGRUENCE LATTICE OF AN ALGEBRA AND ITS CONNECTIONS WITH THE ALGEBRA ITSELF. - KNOWLEDGE OF THE MAIN ALGEBRAIC CONSTRUCTIONS: PRODUCTS, COMPRODUCTS, DIRECT LIMITS AND INVERSE LIMITS. - KNOWLEDGE OF THE CONCEPT OF FREE ALGEBRA AND ALGEBRA OF POLYNOMIALS. * ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING - ABILITY TO RIGOROUSLY REPRODUCE THE PROOFS OF THE MAIN RESULTS OF THE COURSE. - ABILITY TO APPLY THE TECHNIQUES AND TOOLS OF THE COURSE IN SIMILAR CASES. - ABILITY TO CLASSIFY EQUATIONALLY DEFINED CLASSES OF ALGEBRAS ON THE BASIS OF THEIR MAIN PROPERTIES. - ABILITY TO EXTRAPOLATE THE CRUCIAL ASPECTS OF AN ARBITRARY CLASS OF EQUATIONAL STRUCTURES. ** AUTONOMY OF JUDGMENT THE STUDENT MUST BE ABLE TO CONNECT THE COURSE TOPICS WITH THOSE OF ANALYSIS, ALGEBRA, GEOMETRY AND THEORETICAL COMPUTER THEMES. ** COMMUNICATION SKILLS THE STUDENT WILL BE ABLE TO HOLD CONVERSATIONS WITH PRECISION AND RIGOR ON ISSUES RELATED TO UNIVERSAL ALGEBRA. |
| Prerequisites | |
|---|---|
| BASIC KNOWLEDGE OF ALGEBRA AND SET THEORY |
| Contents | |
|---|---|
| - FUNDAMENTALS ON LATTICE THEORY (4 HOURS) - EQUATIONAL CLASSES. (4 HOURS) - SUBALGEBRAS, HOMOMORPHISMS AND CONGRUENCES. (8 HOURS) - POLYNOMIALS AND POLYNOMIAL ALGEBRAS. (4 HOURS) - DIRECT AND SUBDIRECT PRODUCTS. (4 HOURS) - DIRECT AND INVERSE LIMITS. (4 HOURS) - FREE ALGEBRAS. (6 HOURS) - HSP THEOREM. (6 HOURS) MAL'CEV TYPE THEOREMS (4 HOURS) THE WORD PROBLEM. (4 HOURS) |
| Teaching Methods | |
|---|---|
| THE 48-HOUR COURSE TAKE PLACE IN THE II SEMESTER. THE COURSE INCLUDES THEORETICAL LESSONS WITH GROUP DISCUSSIONS (6CFU) IN THE CLASSROOM. DURING THE DISCUSSIONS, STUDENTS (POSSIBLY IN GROUPS) SOLVE THEORETICAL PROBLEMS WHICH WILL THEN BE USED TO ACHIEVE MORE INVOLVED RESULTS. THIS LAST PHASE PROMOTES THE ABILITY TO IMAGINE POSSIBLE STRATEGIES TO FORMALIZE INTUITIONS AND TO BUILD COMPLEX CONCEPTS STARTING FROM BASIC ONES. |
| Verification of learning | |
|---|---|
| THE EXAM AIMS TO EVALUATE THE WHOLE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS INTRODUCED DURING THE LECTURES, AS WELL AS THE ACCURACY AND INDEPENDENCE IN USING SUCH TOOLS. THE EXAMINATION CONSISTS OF AN ORAL INTERVIEW WHERE IT WILL BE EVALUATED THE KNOWLEDGE ACQUIRED ON BASIC AND MOST ADVANCED CONCEPTS IN UNIVERSAL ALGEBRA. THE FINAL MARK IS UP TO THIRTY. LAUDEM WILL BE ATTRIBUTED TO STUDENTS THAT PROVE THEMSELVES TO BE ABLE TO INDEPENDENTLY USE THE KNOWLEDGE AND SKILLS ACQUIRED ON THE MOST ADVANCED TOPICS OF THE COURSE, AND ARE ABLE TO FIND CONNECTIONS WITH CONTEXTS DIFFERENT THAN THOSE PRESENTED IN THE LECTURES. |
| Texts | |
|---|---|
| CLIFFORD BERGMAN. UNIVERSAL ALGEBRA - FUNDAMENTALS AND SELECTED TOPICS. TAYLOR&FRANCIS 2012. S. BURRIS, H. P. SANKAPPANAVAR - A COURSE ON UNIVERSAL ALGEBRA. ONLINE HTTP://WWW.MATH.HAWAII.EDU/~RALPH/CLASSES/619/UNIV-ALGEBRA.PDF G. GRÄTZER. UNIVERSAL ALGEBRA. SECOND EDITION. SPRINGER 2008. |
| More Information | |
|---|---|
| LECTURER'S WEBSITE : HTTP://LOGICA.DIPMAT.UNISA.IT/LUCASPADA/ |
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