Graduate Algebra II (MA501) Syllabus  (Fall 2022)

******************************************************************************************************************************************************************

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.