
Renzo's class 


MWF 12 – 12:50 pm 


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.
MOTIVATIONAL STUFF
PROJECTS AND SUCH
FINAL EXAM PREPARATION WORKSHEET
LaTeX CHEATSHEET:
Office
hours : the official
office hours for this class are right after class (and you should let me know
at the end of class that you want to stop by or else I’ll go to lunch).
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!!
DATE DUE: 

Aug 26^{th} 
Exercises 1, 2, 6, 8 pages 1820. 
Sep 2^{rd} 
Exercises 18, 19, 20, 22 pages 1820. 
Sep 9^{th} 
Exercise 29, page 20. Let X={Albert, Bob,
Betty, Carl, Cecil, David, Diane, Donald, Edward} and f be the function that associates to each
person the initial letter of their name. What set is f a surjective function
on? Describe the equivalence relation induced by f. How many elements does
the quotient set have? Let X={A,B,C,D,E,F,G,H,O}
and consider V={A,E,O}, Con={B,C,D,F,G,H}. Do the two subsets V and C define
a partition of X? If so, describe the corresponding equivalence relation, the
quotient set and the projection function. 
Sep 16^{th} 
Exercises 1, 3, 8, 9, 12 page 33. REDO: exercise 19 page 20. 
Sep 23^{th} 
Exercises 18, 23 page 34. Describe ALL possible order relations on a set with three elements X={a,b,c}. 
Sep 30^{th} 
Exercises 25, don’t do 29, 30, 31 page 34. 
Oct 7^{th} 
I forgot to post these guys…oh well, one week of deserved rest after the exam! 
Oct 14^{th} 
Do Problem 2, questions 1,2,3,4,5 from the handout “Rings and
Fields”. Hint for question 2. First concentrate only on addition and show that, since any positive integer n= 1+1+…+1 (ntimes) and any negative integer m= 111…1 (m times), the morphisms that behave well with respect with addition must have a special form. Then see which one of those behave well with multiplication…and don’t get too depressed with the answer. It is a bit disappointing, but oh well…this is to show that being a ring homomorphism is indeed a strong requirement on functions! 
Oct 24^{th} 
Exercises 7, 10, 24, 29, 30, 38, 44, 45, 47. 
Oct 28^{th} 
Exercises 23, 26 page 73. 
Nov 4th 
Exercises 1, 2 ,3, 4, 18 pages 90, 91. 
Nov 11^{th} 
Exercises 23, 33, 34, 35 pages 9193. Describe when a permutation is even or odd in terms of its cycle type. 
Nov 30^{th} 
Exercises 1(a),(b),(e), 5, 6, 14 (a),(c),(d) pages 163164. 