Algebra II (MATH 512)

2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Ayesha Asloob Qureshi aqureshi@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
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CONTENT

Modules. Fields, extension fields, Galois theory. Categories and functors.

OBJECTIVE

Studying modules, fields, field extensions, Galois Theory

LEARNING OUTCOME

At the end of the course, the student should understand the following topics:
- field extensions, in particular finite algebraic extensions
- normal, separable extensions, splitting fields
- the notion of extending field embeddings
- Galois extensions and Galois groups
- the fundamental theorem of Galois theory, examples and some of its applications:
- cyclic and abelian extensions
- solving equations by radicals
- the fundamental theorem of Algebra
-Basics of Module theory
- tensor product of modules
- free, projective and injective modules

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 40
Midterm 60

RECOMENDED or REQUIRED READINGS

Textbook

Dummit and Foote: Abstract Algebra, Wiley and Sons

Morandi: Field and Galois Theory, Springer Verlag, Addison-Wesley

Lang: Algebra