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Algebraic Structures II (MAE724)

Algebraic Structures II (MAE724)

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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).
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