Welcome to Group Theory!
Office Hours: Office 736, Wexler Hall. 2:15 on MW.
TA: S. Alex Bradt
Office Hours of TA: (Check out MC^2)
Textbooks: We will use Armstrong's "Groups and Symmetry" extensively, but also go through Conway et al's "The symmetries of things" during class.
Class format: A lecture on Armstrong, homework presentation, a lecture on Conway.
Exams: There will be two midterms, on Oct 6 (in class) and on Nov 10 (in class) and a final (on the appropriate final exam date).
Grade breakdown: Five components, each consisting of 20%. Midterms: 2x20%, Final 40% (even questions and odd questions each 20%), homeworks and homework presentation 15%+5%=20%. Lowest of the five components will be dropped.
Homeworks:
(no HW due 10/6)
(no HW due 11/10)
Homework Presentations: During each lecture, there will be one homework presentation on one problem (10-15 minutes). Please work as a group with everyone else who has signed up for that day. You may choose any problem that no other group has presented.
What we'll cover: If we didn't live in strange Covid times, there would be a detailed description of the first 24 chapters of Armstrong here. Since the pandemic might get much worse again, the aim for now is to cover at least the first half of Armstrong's book, and as much as possible from Conway's book. You will learn how to recognize symmetry patterns and relate them to group theory. In addition, you will learn the basic concepts of group theory, including definition of groups, subgroups, morphisms of groups, cosets, quotients, examples of groups, focusing on the geometric examples.
Calendar:
Week 1: Symmetries of the tetrahedron
Week 2: Definition of groups
Week 3: Example: The integers and dihedral groups
Week 4: Subgroups and Generators
Week 5: Permutations
Week 6: Isomorphisms
Week 7: Plato's solids and Cayley's theorem
Week 8: Matrix groups
Week 9: Products and Lagrange's Theorem
Week 10: Partitions and equivalence relations
Week 11: Cauchy's Theorem
Week 13: Conjugacy
Week 13: Quotient Groups and Homomorphisms
Absences
The conditions under which assigned work or tests can be made up, including:
o No late homework is permitted, however the lowest homework score will be dropped.
o If you have to miss an exam due to religious observances/practices, please contact me beforehand.
Academic integrity
Academic honesty is expected of all students in all examinations, papers, and laboratory
work, academic transactions and records. The possible sanctions include, but are not
limited to, appropriate grade penalties, course failure (indicated on the transcript as a
grade of E), course failure due to academic dishonesty (indicated on the transcript as a
grade of XE), loss of registration privileges, disqualification and dismissal. For more
information, see http://provost.asu.edu/academic-integrity
Accommodating students with disabilities
Students who feel they will need disability accommodations in this class but have not
registered with the Student Accessibility and Inclusive Learning Services Office (SAILS)
should contact SAILS immediately. The SAILS Tempe office is located on the first floor of
the Matthews Center Building. SAILS staff can also be reached at: (480) 965-1234 (V) or
(480) 965-9000 (TTY). For additional information, visit:
https://eoss.asu.edu/accessibility
Expected classroom behavior
Classroom behavior: Under no circumstances should you allow your cell phone to ring
during class. Any disruptive behavior, which includes ringing cell phones, listening to
your mp3/iPod player, text messaging, constant talking, eating food noisily, reading a
newspaper will not be tolerated. The use of laptops (unless for note taking), cell phones,
MP3, IPOD, etc. are strictly prohibited during class.
Policy against threatening behavior
All incidents and allegations of violent or threatening conduct by an ASU student
(whether on-or off campus) must be reported to the ASU Police Department (ASU PD)
and the Office of the Dean of Students. If either office determines that the behavior
poses or has posed a serious threat to personal safety or to the welfare of the campus,
the student will not be permitted to return to campus or reside in any ASU residence hall
until an appropriate threat assessment has been completed and, if necessary,
conditions for return are imposed. ASU PD, the Office of the Dean of Students, and
other appropriate offices will coordinate the assessment in light of the relevant
circumstances.
Policy on Sexual Discrimination
Arizona State University is committed to providing an environment free of discrimination,
harassment, or retaliation for the entire university community, including all students,
faculty members, staff employees, and guests. ASU expressly prohibits discrimination ,
harassment , and retaliation by employees, students, contractors, or agents of the
university based on any protected status: race, color, religion, sex, national origin, age,
disability, veteran status, sexual orientation, gender identity, and genetic information.
As a mandated reporter, I am obligated to report any information I become aware of
regarding alleged acts of sexual discrimination, including sexual violence and dating
violence. ASU Counseling Services, https://eoss.asu.edu/counseling , is available if you
wish discuss any concerns confidentially and privately.
Copyrighted materials
A warning to students that they must refrain from uploading to any course shell,
discussion board, or website used by the course instructor or other course forum,
material that is not the student's original work, unless the students first comply with all
applicable copyright laws; faculty members reserve the right to delete materials on the
grounds of suspected copyright infringement.
Title IX is a federal law that provides that no person be excluded on the basis of sex from participation in, be denied benefits of, or be subjected to discrimination under any education program or activity. Both Title IX and university policy make clear that sexual violence and harassment based on sex is prohibited. An individual who believes they have been subjected to sexual violence or harassed on the basis of sex can seek support, including counseling and academic support, from the university. If you or someone you know has been harassed on the basis of sex or sexually assaulted, you can find information and resources at https://sexualviolenceprevention.asu.edu/faqs.
As a mandated reporter, I am obligated to report any information I become aware of regarding alleged acts of sexual discrimination, including sexual violence and dating violence. ASU Counseling Services,https://eoss.asu.edu/counseling is available if you wish to discuss any concerns confidentially and privately. ASU online students may access 360 Life Services, https://goto.asuonline.asu.edu/success/online-resources.html.