Instructor: Jingjun Han

Office: Krieger 221

Email: jhan[at]math.jhu.edu

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 (zzhao25@math.jhu.edu), 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.

Syllabus

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 integrity@jhu.edu. For more information, see the Homewood
Student Affairs site on academic ethics: https://studentaffairs.jhu.

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, studentdisabilityservices@jhu.

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 http://studentaffairs.jhu.edu/