**DEPARTMENT OF MATHEMATICS**

**Graduate Algebra II (MA501) Syllabus (Fall 2022)**

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**Professor: **Yoonjin Lee

**Office: ** Science Complex Building B, 313 (Tel: extension 6653)

**E-mail: ** yoonjinl@ewha.ac.kr

**Text: ***Algebra* (Graduate Texts in Mathematics)
by Thomas W. Hungerford, Springer

**Course requirements: ** Linear Algebra and Abstract Algebra

**References:***Algebra* (Graduate Texts in Mathematics)
by Serge Lang (3rd ed.), Springer

**Course Description:**

Throughout this course, we study comprehensive and advanced
concepts of **Groups**, **Rings** and **Field Theory,
**assuming students have the basic knowledge
of Abstract Algebra I, II and Elementary Linear Algebra.
In more detail, we learn basic properties
and the structure of Groups and Rings. We also study Field Theory which covers
field extensions, Galois theory, cyclic extensions and so forth.
If time permits, we learn the basics of commutative algebra (Chinese
Remainder theorem, Nakayama Lemma, Rings of fractions, Noetherian modules,
Hilbert basis theorem and etc).

**Course Outline:**

Chapter I. Groups

Chapter II. The Structure of Groups

Chapter III. Rings

Chapter IV. Modules

Chapter V. Fields and Galois Theory

**Grading Scheme:**

HW Assignments: 20%

Presentations: 10%

Midterm: 35%

Final Exam: 35%

**Schedule of Exams:**

Midterm on **October 25** (Tues.)

Final Exam on **December 13** (Tues.)

**Grades and policy:**

* You will be evaluated throughout
the whole semester by means of one midterm exam, a comprehensive final exam,
homeworks and presentations .

* Make-up exams will not be given.
No late homeworks will be accepted.

**Class expectations:**

Students are expected to attend all the
lectures. You have to spend enough time for reviewing the material on a
regular
basis. The best way to learn the material is to spend enough time thinking
about
the homework problems virtually every day as our class progresses. In
addition,
you are encouraged to discuss the homework assignments with others, but
you must
write up your own solutions and turn them in individually.