**DEPARTMENT OF MATHEMATICS**

**Graduate Algebra I (MA501) Syllabus (Spring 2024)**

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**Professor: **Yoonjin Lee

**Office: ** Science Complex Building B, 313

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

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

**Course requirements: ** Linear Algebra, Abstract Algebra I, Abstract Algebra II

**References:***Algebra* (Graduate Texts in Mathematics)
by Serge Lang, 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 :** Combination: Absolute + Relative

HW Assignment: 20%

Midterm Exam: 40%

Final Exam: 40%

Presentation: Bonus credit

**Schedule of Exams:**

Midterm on **April 22 ** (Mon.), 2024

Final on **June 12 ** (Mon.), 2024

**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.