(last revision 5/02/14, 3:25 pm)
MATH 5331 INFORMATION SHEET FOR FINAL TEST SPRING 2014
(scroll down to see a summary of the course material)
The Final Test will be 5:30-8:00 pm on Tues May 6 in PKH 105; it is worth 40% of your course grade.
The relevant sections for the Final Test are all those covered on the homework throughout the semester together with the items listed in the summary below.
My office hours are Tues and Thurs 4:40-5:10 pm through Thurs May 1. In addition, I will have office hours 3:30-5:30 pm on Monday May 5.
As per the course information sheet, any student not obtaining a positive score on the Final Test for this class will not pass this class.
You should know the definitions of the concepts (and examples thereof) that arise frequently in class; the theorems etc that are used frequently or which have a name; how to apply the theorems to examples and at least one method for doing each homework question. Skimming over short proofs (at most 6 or so lines) from class could also be helpful. You should be ready to present examples like those occurring in the homework, and be able to show that a subset of a group is a subgroup, and that a subset of a ring is a subring or left/right ideal.
Any question in the homework or the Quiz or Tests 1-3 is game for the test. I recommend you look over the Quiz and Tests 1-3; the solutions to those are posted at my website. The ratio of old material (that tested already) to new material (that not tested yet) will likely be 70:30.
No calculators are allowed; no notes are allowed; no phones, no tablets. Your belongings will need to be by the wall as in the previous tests.
Bring some form of photo ID.
Try to keep your eyes on your own work during the Final Test.
If you wish to leave the room during the test, you should ask permission first & turn in your test to me. Only in exceptional circumstances will I let you continue the test should you return. (So it is better to be 3 minutes late to the test, rather than ask to go to the bathroom during the test.) If you finish early but prefer to stay in the room, then you should NOT get out any work, book nor item, no matter what the subject matter is, without first checking with me. Should you wish to leave the test early, then you may.
It is your responsibility to be on time.
See below for a summary of the course material.
Groups
Definition and examples
homomorphisms
group actions
subgroups
centralizers, etc
cyclic groups
generators
cosets & quotient groups
Lagrange's Theorem
isomorphism theorems
permutation representations
Cayley's theorem
class equation
Sylow theorems
fundamental theorem of finitely generated abelian groups
nilpotent/solvable groups
Rings
Definition and examples
homomorphisms
subrings and (1-sided & 2-sided) ideals
cosets & quotient rings
isomorphism theorems
rings of fractions
Modules
Definition and examples
homomorphisms
submodules
cosets & quotient modules
isomorphism theorems