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B005490 - ALGEBRA II
Main information
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2013-14
Coorte 2012 - 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
23/09/2013 ⇒ 20/12/2013
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
Groups and subgroups. Normal subgroups. Quotients. Isomorphism theorems. Actions and permutation groups. Sylow’s theorems. Field extensions. Algebraic and transcendental extensions. Degree of an extension. Splitting fileds, normal field extensions, Galois extensions. Galois group. Galois connection. Finite fields.
Suggested readings (Search our library's catalogue)
Lecture notes by Prof. Casolo.
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
Contact hours for: Lectures (hours): 30
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 30
Seminars (hours): 0
Stages: 0
Intermediate examinations: 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
Contact hours for: Lectures (hours): 30
Contact hours for: Laboratory (hours): 0
Contact hours for: Laboratory-field/practice (hours): 30
Seminars (hours): 0
Stages: 0
Intermediate examinations: 6
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.
Course program
Group and subgroup. Normal subgroup. Quotient. Isomorphism theorem. Action and permutation group. Sylow’s theorem. Field extension. Algebraic and transcendent extension. Extension degree. Normal extensions, Galois extension. Galois group. Galois connection. Finite field. Compass and straightedge constructions.