Math 4340

 

HW1)    D&F p.22 #8,9,18,22,26,27  p.27 #1,2  p.32 #1  p.39 #1,2 due Friday, Feb 3 in class.

HW2)    D&F  p.40 #13,14  p.44 #1,2,4,5-8  p.85 #1  due Friday, Feb.10 in class.

HW3)    D&F p.52 #5a,b,6 (hint - 6a, 2nd half - let H consist of 2 transpositions in S_3) 
 p.60 #2,8,9,11  p.101 #2,3,7,8  due Friday, Feb. 17 in class.

HW4)   D&F p.60 #1,13,18     p.101 #2,3,7,8   due Friday, Feb.  24 in class.  (The last 4 problems were
assigned  last week so this means you have an extension till next week to turn those in. Reason:  we
didn't get far enough in class. Also it means you will have a  much shorter assignment than usual which
fits well with the  break next Monday & Tuesday.)

HW5)  D&F p.28 #10-13  p.65 #2,7,8  p.86 #18  p.111 #8,9,11 (in #8 show only that A_4 has no subgroup of order 6;
in #11 consider the elements of order 4 and their squares)  due Friday, March 3  in class.

HW6)   D&F  p.45 #21-23   p.122 #7-9 (in #8 show that [G:K] divides n!; use this in #9)  p.146 #5,6,7  
due Friday, March 10  in class.

NOTE: This week Beihui is changing her office hours to  2-4PM Tuesday (the 14th) because of the prelim on Wednesday.
PRELIM  in class on Wed. March 15 (closed book). POSTPONED till Friday, 17th March because of likely Cornell
closure due to winter storm.

HW7)    D&F p.146 # 8,13 p.106 # 6,7,9,10 (you may use the results of other exercises on this page without proof)
 p.230 # 1,4  p.247 # 2,5,6,8 (all rings are assumed to have multiplicative identities which are preserved
 by ring homomorphisms; all subrings have the same mult. id. as the parent ring; answers may differ from
 D&F which doesn't have these conventions.) due in class, Friday, March 24.

HW8) D&F p.277 #2-6, p.301 #1-5 due in class, Friday, March 31
(Euclidean domains will be covered in class on Monday. Wait until then to do the hw or read enough about the topic
on your own to get started earlier.)

HW9) D&F p.278 #10,11  p.282 #1,2,3,5,6 due in class, Friday, April 14.

Note:  As announced in the first week of class, and mentioned several times since, the course material is largely what
is covered in class. The textbook (Dummit & Foote) and the homework are supplementary. A primary purpose of
the course is to teach a new way of thinking: how to use abstract concepts and the axiomatic method to study  a wide
variety of mathematical objects.  This is very hard to learn well entirely from books.

HW10) D&F p.278 #9,12  p.292 #2,8a,8c(1st part)  p.529 #1,2 due in class, Friday, April 21.

HW11)  D&F p.344 #7,8,9,18,19 p.356 #3 p.165 #1a,b,2a,b,3a,b due in class, Friday, April 28.

To get started you will need the definition of a R-module M where R is a commutative ring. Think
of M as a 'vector space ' over R (i.e. the scalars are from R and the 'vectors' form an abelian gtoup M)
and you won't go wrong. See D&F for the formal definition. A 'cyclic module' is one which is generated
by a single element (analogous to a cyclic group or a 1-dimensional vector space). The Fundamental
Theorem of Abelian Groups, needed for the problems on p.165, will be covered next week along with
modules.

HW12) D&F p.166 4a,b,c  p.356 2,4,5,7  p.469 10,11,12  p.488 3,4  p.499 #4 (need not find P) .
(p.469 #12 and p.499 #4 were added on Friday, May 5.) Due in class, Wed., May 10.

Note:  The Final Exam will be on  Thursday, May 18   7:00 PM - 9:PM  in  MLT406: Malott Hall 406.
It will be closed book and cumulative, with about one-third  of the questions on group theory  and  the
rest  on material covered since.

Office Hours (Exam week): I will have office hours on Tuesday, May 16,  11a.m.-12noon in Malott 505.
Beihui's office hours: Wednesday, May 17, 2 - 4p.m. in Malott  218.

Solutions

HW1 Solutions
HW2 Solutions
HW3 Solutions
HW4 Solutions
HW5 Solutions
HW6 Solutions
HW7 Solutions
HW8 Solutions
HW9 Solutions
HW10 Solutions
HW11 Solutions
HW12 Solutions


General Information
Text: Dummit and  Foote, 3rd. ed., John Wiley & Sons
Exams: Final,  Prelim in class  about half way through, possible 2nd Prelim (take-home)
    near the end of the term.
HW:  Approximately weekly (perhaps 11 or12 assignments).  You may collaborate with a couple of other
 students from the class but are encouraged to try every problem yourself first.  If you do collaborate
 state the names of the other students.  The grading won't depend on whether you collaborate, but make
 sure to write the solutions in your own words.
Grading policy: The final grade will depend approximately 15% on the hw and the remaining 85% on the
 exams (whether 2 or 3).

Instructor: (Prof.) Shankar Sen
Office Hours: MWF  11.10 - 11.50,  Malott 505   (and  by appointment)

TA:  Beihui Yuan  
email:  by238@cornell.edu
Office Hours:  Thursdays, 2-4 PM,  Malott 218