Lecture Time and Office Hours

Instructor: Raul Gomez Malott 593 gomez@cornell.edu Lecture Time: T, Th, 10:10–11:25am Morrill Hall 111 Office Hours: W 8 am–9 am Malott 593

TA: Tair Akhmejanov Malott 120 ta328@cornell.edu Office Hours: T 3 pm–4 pm Malott 120

About the Course

MATH 3560 is a geometric introduction to the algebraic theory of groups, through the study of symmetries of planar patterns and 3–dimensional regular polyhedra. Besides studying these algebraic and geometric objects themselves, the course also provides an introduction to abstract mathematical thinking and mathematical proofs, serving as a bridge to the more advanced 4000–level courses. Abstract concepts covered include: axioms for groups; subgroups and quotient groups; isomorphisms and homomorphisms; conjugacy; group actions, orbits, and stabilizers. These are all illustrated concretely through the visual medium of geometry.

Book

The course will be based on the book "Groups and symmetry" by Mark Armstrong.

Homework

There will be a weekly homework to be handed in every Thursday during lecture time. The homework with the lower score will be dropped before computing your final grade. You can check the homework for this week by clicking the appropriate link at the top of this page or, if you are still reading this, you can just click here.

Exams

There will be a two preliminary exam. The first one will take place on Tuesday October 7th during lecture time. The second will be on Thursday november 20th, also during lecture time. You will not be allowed to bring notes to any of the exams.

Final presentation

There will be 6 final group presentations this semester. They will take place during the following days:

• Final Presentation 1, Tuesday   Nov. 25th 10:10–10:40
• Final Presentation 2, Tuesday   Nov. 25th 10:50–11:20
• Final Presentation 3, Tuesday   Dec.  2nd  10:10–10:40
• Final Presentation 4, Tuesday   Dec.  2nd  10:50–11:20
• Final Presentation 5, Thursday Dec.  4th 10:10–10:40
• Final Presentation 6, Thursday Dec.  4th 10:40–11:20

With the current enrollment, this means that each groups should consist of 3–4 persons. The possible topics to choose from are:

1. Group theory and Klein's Erlangen program.
2. Galois theory for finite fields.
3. Unramified extensions of local fields.
4. Quick-sort and other sorting algorithms.
5. Möbious transformations: symmetries and conformal transformations of the hyperbolic plane.
6. Low dimensional groups of isometries and Hamilton's quaternions.
7. Lie algebras of the classical algebraic groups.
8. Algebraic groups over local fields.
9. Introduction to representation theory of finite groups.

In addition to this presentation, each group should also produce a 2,000–2500 words essay to be handed in on Tuesday Nov. 25th

Grades

Final grades will be calculated using the formula:

20% Homework + 20% 1st Preliminary Exam + 20% 2nd Preliminary Exam + %40 Final Presentation.

Letter grades will be curved.