Math 401: Introduction to Abstract Algebra

Instructor: Jingjun Han
Office: Krieger 221 
Email: jhan[at]
Lectures: MW 12:00-1:15pm, Krieger 308
Office Hours: Wednesdays 11-noon or by appointment 

Section: F 12:00-12:50pm, Krieger 302
TA: Zehua Zhao (, Krieger 201.

Textbook: Groups and Symmetry by M.A. Armstrong 
Description: This course is an introduction to the basic structure of abstract algebra as well as  an introduction to proofs. We will be covering most of the book (all but chapters 24-28). The prerequisite for this course is Linear Algebra. 

Homework: Problem sets will generally be posted here each Wednesday and due in class the following Monday. Late homework will not be accepted without a valid reason, but your two lowest homework scores will be dropped. Collaboration on homework is allowed and encouraged. However, each student must write up their solutions individually and in their own words. Copying from another student's paper is prohibited.

·       HW1, due Monday 9/17

·       HW2, due Monday 9/24

·       HW3, due Monday 10/01

·       HW4, due Monday 10/08

·       HW5, due Monday 10/15

·       HW6, due Monday 10/22

·       HW7, due Monday 11/5

·       HW8, due Monday 11/12

·       HW9, due Monday 11/26

·       HW10. due Monday 12/03




Attention: There will be a quiz on Oct. 3 (in Class).

                There will be a quiz on Oct. 22 (in Class).

                There will be a quiz on Nov. 26 (in Class).


                Midterm (20%) is on Oct. 29 (in Class), at least 15% will comes from homework and quizzes. There will be no homework on the previous week.




Aug 30. Introduction.

Sep 5. Mathematical Statement + Some proof techniques

Sep 10. Some proof techniques + Division Theorem

Sep 12. Bezout identity + fundamental theorem of arithmetic

Sep 17. Groups: Definition and first examples

Sep 19. Some families of finite groups (1): Integers modulo n, Dihedral groups

Sep 24. Some families of finite groups (2): Dihedral groups, Symmetric groups, group structure on elliptic curves (not required)

Sep 26. Subgroups (1): Definition and examples

Oct 1. Subgroups (2): examples and cyclic groups

Oct 3. Quiz, Lagrange’s Theorem

Oct 8. Isomorphism

Oct 10. Direct sum (direct product): Definition and properties

Oct 15. Direct sum (2): examples

Oct 17. Permutation (1): Definition and properties

Oct 22. Quiz, Permutation (2): even and odd permutation, puzzle game

Oct 24. Permutation (3): alternating group

Oct 31. Classification of groups with small orders

Nov 5. Cayley’s Theorem and Cauchy’ Theorem

Nov 7. Quotient group (1)

Nov 12. Quotient group (2)

Nov 14. Isomorphism theorems

Nov 19. An introduction to ring theory (1)

Nov 28. An introduction to ring theory (2)





Middle Exam: Monday October 29 (in class)

Final Exam: Saturday December 15 from 10am-1pm

There will be three quizzes throughout the semester. The problems for the quizzes will be very similar to homework problems. Quizzes count for 5% each of your grade.

Exams and grades: There will be one in-class midterm, on Monday October 29. Grades will be assigned based on the following formula: 10% quizzes (lowest dropped), 30% homework, plus either 20% midterm and 40% final exam, or else 60% final exam, whichever is higher. (Make-up exams for the midterm will not be offered. If you miss the midterm with a valid excuse, then your exam grades will be determined by the final exam. The grade for an unexcused absence from any exam will be zero.) 

Ethics statement: In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Report any violations you witness to the instructor. You may consult the associate dean of student conduct (or designee) by calling the Office of the Dean of Students at 410-516-8208 or via email at For more information, see the Homewood Student Affairs site on academic ethics: or the e-catalog entry on the undergraduate academic ethics board:

Disability services: Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 385 Garland, (410) 516-4720, To obtain accommodations for an exam, please give me a copy of your letter at least one week in advance of the exam. 

Anxiety, stress, and mental health: If you are struggling with anxiety, stress, depression or other mental health related concerns, please consider visiting the JHU Counseling Center. If you are concerned about a friend, please encourage that person to seek out their services. The Counseling Center is located at 3003 North Charles Street in Suite S-200 and can be reached at 410-516-8278 and online at