
Renzo's class 


MWF 12 – 12:50 am 


ENGRG E 105
// in the oval with good weather 







TEXTBOOK:
Abstract Algebra: Theory and Applications
by Thomas W Judson
Publisher:
available freely from:
http://abstract.ups.edu/index.
IMPORTANT TECHNICAL ANNOUNCEMENT:
MIDTERM MOVED TO NOVEMBER 13th
MOTIVATIONAL STUFF
If you want to
know why you should study abstract algebra, I think the best answer is: to train your brain to think! Just how when you do pushups at the
gym, your goal is to get stronger, not just to perform *the perfect pushup*.
However, if you stick with abstract math long enough (a lot longer than this
one semester course) – then you will find that there are powerful
applications of abstract algebra. Below is a small compilation of a few of
them, if you are curious!
RESOURCES
EXAMS
First midterm coming up Oct 4th!
LaTeX CHEATSHEET:
Office
hours : the official
office hours for this class are right after class. However, if these times are
not convenient for you, you are very welcome to make an appointment and come
ask questions, make comments, or just chat. You can also try showing up at my
door anytime. But I might tell you to come back at another time if I am
immersed into something else.
The tables of the law for this class are contained in the
following document:
Syllabus
Homework: math is not a sport for bystanders. Getting
your hands dirty is important to make sure that things sink in and you
are not just spending a semester assisting to my creative rambling. Homework
will be due pretty much every Friday (but see below for the uptodate
information). I will NOT grade all the problems I assign. If one of the
problems you feel unsure about doesn’t get graded, please don’t go
“Whew! Lucky one!” but rather come ask me about it. The point is
you understanding, not pretending to!!
Important: the number of exercises and pages
are mismatched between the electronic and paper versions of the book. I will
always refer to the electronic version available following the link above
(latest edition), since not everyone owns the paper version of the book!
DATE DUE: 

Wednedsday, Sep 4 
READ CHAPTER 1 in the book and
HAVE QUESTIONS for class. Wednesday’s class may be entirely devoted to
answering basic questions. 
Friday, Sep 6 

Friday, Sep 13 
1) Write down in full detail and paying great
care to your exposition two different proofs for the identity: 1+2+3+…+n= ½ n(n+1) 2) Compute the sum of the first n squares in two different ways: First, make a wild guess that the answer is a degree 3 polynomial in n 1+4+9+…+n^2= An^3+Bn^2+Cn +D Plug in values for n to determine A,B,C,D by solving a linear system
of 4 equations in 4 variables. Then prove the formula by induction. In the second case, use the identity (n+1)^3= n^3+3n^2+3n+1 to generalize to this case one of the proofs seen
in class for the sum of the first n
integers. This week’s hwk is only two problems, so
please put in a good effort to attempt to do them well!! This means that your
writeup should be complete, tidy, well expressed, and in one of the
languagues I can understand! 
Friday, Sep 20 
Exercise 12 page 33 
Friday, Sep 27 
Exercises
18, 19, 23, 25, 31 page 34 
Friday, Oct 4th 
No homework. Study for the exam! 
Friday,
Oct 11th 
Write up the answers to the following problems from the
handout on Rings Question 4 Sec 2.5 Theorem 2 Sec 3.3 Theorem 3 Sec 3.3 Theorem 5 Sec 4.1 (Careful! Make sure not to use theorem
2 in the proof of theorem 5!) 
Friday
Oct 18^{th} 
Write up the answers to the following problems from the
handout on Rings Problems 6,7,8 Section 4.2 Problems 10,11 Section 4.3 
Friday
Nov 1^{st} 
Exercises
7, 24, 30, 38, 44, 45, 47, 49, 54 pages 5355 
Friday
Nov 8th 
Exercises
14, 23, 26, 29, 30, 31, 37. Pages 7174. (1) Give a formula for the
order of a general element [m] in Z/nZ. Proceed
by first experimenting with small values of n until you understand what is
going on. Then write a general proof. (2) Complete and prove the
following statement. There exists a group homomorphism f: Z/nZ à G sending
[1]à g if and only if the order of g…(fill in).
If the order of g …(fill in),
then f is an isomorphism between Z/nZ and <g>. 
Monday Dec 2nd 

Friday Dec 6th 
Exercises
4, 5, 6, 8, 14 pages 166167 Challenge:
7,9 page 167. 

