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- Author:
-
Artin, Michael
- Subject:
- Mathematics and Statistics
- Institution Name:
- M.I.T.
- Collection:
-
MIT OpenCourseWare
- Grade Level:
- Post-secondary
- Abstract:
More extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs helpful. First term: group theory, geometry, and linear algebra. Second term: group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, Galois theory. The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.
- Languages:
- English
- Material Type:
- Assessments, Full Course, Homework and Assignments, Lecture Notes, Syllabi
- Media Format:
- Text/HTML, Downloadable docs
- Conditions of Use:
-
Creative Commons Attribution-Noncommercial-Share Alike 3.0
No restrictions on your remixing, redistributing, or making derivative works.
Give credit to the author, as required.
Your remixing, redistributing, or making derivatives works comes with some
restrictions, including how it is shared.
Your redistributing comes with some restrictions. Do not remix or make
derivative works.
Copyrighted materials, available under Fair Use and the TEACH Act for US-based
educators, or other custom arrangements. Go to the resource provider to see
their individual restrictions.
Algebra II, Spring 2008
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