Math 366: Introduction to Abstract Algebra



Renzo's class



MWF 12 – 12:50 pm



ENGRG  E 105  // in the oval with good weather








Office Hours






Abstract Algebra: Theory and Applications
 by Thomas W Judson

Publisher: Virginia Commonwealth University Mathematics

available freely from:




Applications of Group Theory





Rings and Fields



Study hard!





PDF file

LaTeX source file



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:


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 up-to-date 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!!



Aug 26th

Exercises 1, 2, 6, 8 pages 18-20.

Sep 2rd

Exercises 18, 19, 20, 22 pages 18-20.

Sep 9th

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 16th

Exercises 1, 3, 8, 9, 12 page 33.

REDO: exercise 19 page 20.

Sep 23th

Exercises 18, 23 page 34.

Describe ALL possible order relations on a set with three elements X={a,b,c}.

Sep 30th

Exercises 25, don’t do 29, 30, 31 page 34.

Oct 7th

I forgot to post these guys…oh well, one week of deserved rest after the exam!

Oct 14th

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 (n-times) and any negative integer m= -1-1-1…-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 24th

Exercises  7, 10, 24, 29, 30, 38, 44, 45, 47.

Oct 28th

Exercises 23, 26 page 73.

Nov 4th

Exercises 1, 2 ,3, 4, 18 pages 90, 91.

Nov 11th

Exercises 23, 33, 34, 35 pages 91-93.


Describe when a permutation is even or odd in terms of its cycle type.

Nov 30th

 Exercises 1(a),(b),(e), 5, 6, 14 (a),(c),(d) pages 163-164.



  • First Midterm: Monday, Oct 3rd .
  • Second Midterm: Friday, Nov 18th.