Algebraic Structures II (MAE724)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE823
Semester	8
Course Title	Algebraic Structures II
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	https://sites.google.com/site/apostolosthomamath/teaching

Learning Outcomes

Learning outcomes	The students will acquire with the successful completion of the course the skills to solve equations of small degree, the skills to find splitting fields and compute Galois groups, understand the problem of solving polynomial equations by radicals, understand the impossibility or not of certain constructions by ruler and compass.
General Competences	The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in Field Theory and produces free, creative and inductive thinking.

Syllabus

• Rings
• Integral Domains, Fields, Homomorphisms and Ideals
• Quotient Rings
• Polynomial Rings over fields
• Prime and Maximal Ideals
• Irreducible Polynomials
• The classical methods of solving polynomial equations
• Splitting fields
• The Galois Group
• Roots of unity
• Solvability by Radicals
• Independence of characters
• Galois extensions
• The Fundamental Theorem of Galois Theory
• Discriminants
• Polynomials of degree less than 4 and Galois Groups
• Ruler and Compass constructions

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures (13X3) 39 Working independently 78 Exercises-Homeworks 33 Course total 150
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

• S. Andreadakis:  "Galois Theory", (Greek), Symmetria Publishing Company, (1999).
• M. Holz: "Repetition in Algebra", Greek Edition, Symmetria Publishing Company, (2015).
• J. Rotman:  "Galois Theory", Greek edition, Leader Books, (2000).
• Th. Theochari-Apostolidou and C. M. A. Charalambous:  "Galois Theory", (Greek), Kallipos Publishing (2015).