Advice to participants:
Timetable etc.: The page for this particular AFS on the ATM school website has some of these details (follow the links on that page).
Syllabus: Click here for the pdf file of the syllabi for all levels of the AFS: I, II, and III. Particularly relevant for us are sections 2.1 (ring theory or RT), 2.2 (functional analysis or FA), and 2.3 (differential topology or DT), for these are the ones to be covered in AFS-II. Each section has four subsections or "modules".
Notation: For subsections or modules, this is fixed as follows: DT-III refers to the third module of differential topology, etc. On the timetable, FA10 stands for the tenth lecture of section FA, etc. Assuming that the modules are covered one after another in succession (which may not be the case!) and that there are four lectures per module, FA10 would be the second lecture of the FA-III module.
Resource persons (listed, as is customary in mathematics literature, by alphabetical order on last name):
General advice to participants about RT-I: Revise linear algebra and basic facts about PIDs. The theorems will be proved for modules over a general PID although in the applications the PID will invariably be either the ring of integers or the ring of polynomials in one variable over a field. Specifically come prepared with knowledge of the following material:
Note on references for RT-II and RT-III:
The following
text is suggested as an additional important reference:
M. F. Atiyah and I. G. Macdonald: Introduction to Commutative Algebra, 1969.
Exercises for RT-II and RT-III:
from the book of Atiyah and Macdonald mentioned above:
Chapter 1 : 1-12, 14
Chapter 2 : 1-13
Chapter 3 : 1, 2, 5, 6, 7, 9, 12, 13, 14, 17
Chapter 4 : 2, 4, 5, 7, 8, 14, 15, 16
Chapter 5 : 2-7, 11-14
Chapter 7 : 2, 5, 6, 8, 10, 11, 15
Notes (click on the appropriate links):