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B005490 - ALGEBRA II
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Academic Year 2014-15
Coorte 2013 - 3-years First Cycle Degree (DM 270/04) in MATHEMATICS
Course year
Second year - First Semester
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/02 - ALGEBRA
Credits
6
Teaching Hours
60
Teaching Term
22/09/2014 ⇒ 23/12/2014
Attendance required
No
Type of Evaluation
Final Grade
Course Content
show
Lectureship
Teaching Language
Italian
Course Content
Groups and subgroups. Normal subgroups. Factor groups. Isomorphism theorems. Actions and permutation groups. Sylow theorems. Field extensions. Algebraic and trascendental extensions. Degree of an extension. Splitting fields, normal extensions and Galois extensions. Galois group. Galois correspondence. Finite fields.
Suggested readings (Search our library's catalogue)
Course Handouts
Learning Objectives
Knowledge acquired:
Basics of group theory, concept of group action, elements of Galois’
theory, application of acquired knowledge for solving problems.
Skills acquired (at the end of the course):
The student will be able to solve basic problems in the theory of groups,
fields and equations
Basics of group theory, concept of group action, elements of Galois’
theory, application of acquired knowledge for solving problems.
Skills acquired (at the end of the course):
The student will be able to solve basic problems in the theory of groups,
fields and equations
Prerequisites
Courses required: Algebra I
Courses recommended: Geometry I
Courses recommended: Geometry I
Teaching Methods
CFU: 6
Total hours of the course (including the time spent in attending lectures,
seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities:
84
Total hours of the course (including the time spent in attending lectures,
seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities:
84
Further information
Frequency of lectures, practice and lab: Recommended
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Type of Assessment
Written and oral.