Syllabus for 2022 AIMS Lie Groups

Course name:
Lie Groups and Lie Algebras
Course number:
AIMS 22.
Instructor:
Tevian Dray
Course credits:
0
Class meeting times:
10 hours per week
Prerequisites:
Familiarity with linear algebra, including matrix mutiplication, change of basis, determinant, trace, eigenvalues and eigenvectors; Some exposure to abstract algebra, including vector spaces and groups; Comfort with elementary differential calculus; Some acquaintance with complex numbers.
Course description:
Lie groups are groups of continuous symmetries, generalizing the familiar notion of rotation groups; Lie algebras are their infinitesimal versions. Lie groups describe the symmetries of many physical henomena, combining algebra and geometry in beautiful ways. This course provides an introduction to the rich theory of Lie groups and Lie algebras, using explicit matrix groups to demonstrate concepts from differential geometry and abstract algebra. In particular, the properties of the orthogonal and unitary groups will be studied, along with several applications.
Learning resources:
Textbook 1 (PDF available): Lie Groups: A Problem-Oriented Approach via Matrix Groups (HP); Textbook 2 (online only): The Geometry of the Exceptional Lie Groups (GELG).
Learning outcomes:
  • 1) (none yet)
Course content:
  • 1) (none yet)
See also course schedule.
Evaluation of student performance:

The best way to learn the material of this course is to attend class, participate in the class activities, and do the exercises.

Your course mark will be determined by your marks on three required assignments, at least one of which will be given in class as a quiz; the others will be turned in via Gradescope (instructions will be shared in class).

In preparation for these assignments, we will provide daily practice exercises with solutions. You will NOT turn in these exercises.

Additional Guidance

  • You are encouraged to discuss assignments with each other and with the teaching team. Science is inherently a social and collaborative effort. So that we can best support your learning, you are required to turn in assignments that you have written up independently, and to acknowledge those with whom you consulted.
  • Appropriate resources on assignments include: working with each other, the course tutor(s), and/or the course instructors; textbooks; other online materials, etc. Do not use homework solutions from previous versions of this course, or those associated officially with the textbook(s) (such as those from an instructor's manual). Do not share your completed homework solutions with other students (in other words, collaborate through discussion, not copying).
  • Document your resources appropriately. If you find a homework problem worked out somewhere other than those sources listed above, you may use that resource, just make sure you reference it properly. If someone else helps you solve a problem, reference that too. An appropriate reference might be“Tevian Dray (private communication, 1/15/21)” or “I worked with Tevian Dray on this problem”. Representing someone else's work as your own without reference -- also known as plagiarism -- is unethical, but collaboration and exchange of ideas is healthy. You can avoid having collaborative efforts take on the look of plagiarism by acknowledging sources as described above and by writing up your work independently.
  • The problems in this course will likely take longer than problems you've seen in previous courses. If you find that you have worked on a problem for 1/2 hour WITHOUT MAKING FORWARD PROGRESS, it's time to pause, take a break, sleep, and seek help from classmates or the instructional team.

PLEASE IGNORE THE ITEMS BELOW, WHICH ARE THE OSU DEFAULTS

Academic calendar:
All students are subject to the registration and refund deadlines as stated in the Academic Calendar: https://registrar.oregonstate.edu/osu-academic-calendar
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Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.
Expectations of student conduct:
Students are expected to comply with the University code of conduct, available at https://beav.es/codeofconduct.
Student bill of rights

OSU has twelve established student rights. They include due process in all university disciplinary processes, an equal opportunity to learn, and grading in accordance with the course syllabus: https://asosu.oregonstate.edu/advocacy/rights

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