Math 366: Introduction to Abstract Algebra



Renzo's class



MWF 3 – 3:50 pm



ENGRG  E 204  // in the oval with good weather









Office Hours






Abstract Algebra: Theory and Applications
 by Thomas W Judson
2016 Edition
Publisher: Virginia Commonwealth University Mathematics

available freely from:





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 push-ups at the gym, your goal is to get stronger, not just to perform *the perfect push-up*. 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!


Applications of Group Theory

Chinese Remainder Theorem



Rings and Fields

(LaTeX source)




PDF file

LaTeX source file



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:


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!!

READ CAREFULLY!! In fact, here is the homework grading policy. For every assignment, you are supposed to write up all problems. However you need to identify two questions: the one that you feel have done best on (which will be graded), and the one where you feel you have done worst on (which will be looked at and commented but not graded). This is supposed to force you to self-evaluate your own understanding, and to maximize the efficiency with which I can give you the most needed feedback.

Important: the number of exercises and pages might be 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!



Jan 20th  READ CHAPTER 1 up to page 10 in the book and HAVE QUESTIONS for class. Wednesday’s class will be entirely devoted to answering your questions (so long as you bring them). Otherwise I will be asking you questions! 
Focus on the following key concepts:
1) What does it mean to proof a mathematical statement?
2) Make very good friends with the bulletted list on page 3 of the book.
3) Be OK with the basic set operations.
4) Are you cool with the concept of function? Do you know exactly what injective, surjective and bijective mean? What domain and range of a function are?
5) Composition of functions is an important concept. Make friends with it and then think about the definition of inverse function.
Jan 23rd READ pages 11-13 and think a lot about the concepts of equivalence relation, quotient set, and partition of a set.
Bring your questions to class.
Jan 27th Homework 1    (TeX file)
Feb 3rd Write up individual solutions to problems 1, 2, 3, 4, 5 on the worksheet on Newton Binomial's theorem. You can find that worksheet on Manuscripta (see below).
Feb 10th Write up individual solutions to problems 6, 7, 8, 9, 10 on the worksheet on Newton Binomial's theorem. You can find that worksheet on Manuscripta (see below).
Feb 17thExercises 18, 19, 23, 24, 25, 26, 31 page 24-26
Mar 3rd Write up solutions to Problems 3, 6, 7, 9, 11.
Mar 24th Find and carefully write up at least 7 isomorphisms of groups among the examples distributed in class (and available on manuscripta).
Mar 31st
Exercises 2, 4, 25, 31, 39, 46, 52, 53 pages 39-42
Apr 7th
Exercises 23, 26, 37, 45 pages 55-56 (cyclic groups)
Exercises 12,16 page 75 (cosets)
Apr 28th Exercises 6,7,8,9  page 124 (quotient groups)
Exercises 5,12  page 130 (homomorphism)

Manuscripta: this is an important tool  for this course. You can find here a worksheet with short summaries of the material, and you are encouraged to leave here your questions and comments, to make the class as usueful and interactive as possible.

Go to , log in with the information that I shared with you via email and find the document MATH 366. Then follow instructions as to how to input your questions and comments.

For any questions, comments, tips and especially to pass on feedback or problems about Manuscripta, feel free to contact Jim Carlson, the developer of this platform, at