
Renzo's class 


MWF 3 – 3:50 pm 


ENGRG E 204
// in the oval with good weather 







TEXTBOOK:
Abstract Algebra: Theory and Applications
by Thomas W Judson
2016 Edition
Publisher:
available freely from:
http://abstract.ups.edu/index.
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!
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!!
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
selfevaluate 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!
DATE DUE: 

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 1113 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 17th  Exercises 18, 19, 23, 24, 25, 26, 31 page 2426 
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 3942 
Apr 7th 
Exercises 23, 26, 37, 45 pages 5556 (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 http://www.manuscripta.io , 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 jxxcarlson@icloud.com