Fall2016_Math411

MATH 411 Introduction to Abstract algebra I, Fall 2016

Instructor Yaping Yang

Office: LGRT 1242

Office Hours:

Tuesday: 1:00 pm-2:00pm (Location : CTC calculus tutoring center)

and Thursday 10 am-11:00am (Location: LGRT 1242), or by appointment.

Email: yangyaping@umass.edu, or yaping@math.umass.edu

Class meeting

Math 411 TuTh 8:30am-9:45am, LGRT 171

Prerequisites:

Linear algebra (Math 235) and an introductory proof course (Math 300 or CS 250).

I will assume you have seen the following: multiplication and addition of matrices; the determinant of a matrix; the inverse of a matrix; definition of a vector space; definition of a linear operator; representing a linear operator by a matrix; associativity of matrix addition and multiplication; properties of complex numbers; proof by induction; equivalence relations and equivalence classes; properties of the integers (division algorithm, Euclidean algorithm, unique factorization); functions (injective= one-to-one, surjective = onto, bijective, inverse, composing functions).

Course Text:

Abstract algebra by Dan Saracino. A first Course. Second Edition.

We will cover material from chapters 0-14, An additional topic: Actions of groups on sets, and chapter 15(?).

Homework:

The homework will be collected on days indicated in the course schedule table below. No late homework will be accepted.

All solutions should be written in complete English sentences.

In mathematics, solution of every problem is always a two-step process. First you have this aha moment when you realize that you know how to solve the problem. But don't rush into putting your thoughts to paper. Now you have to convince another person (for example the grader) that you know how to solve the problem. This may require polishing your argument, rearranging its parts, adding extra details and introducing the right notation to make the argument look good on paper.

Each time you use a special proof technique such as proof by induction or proof by contradiction, say so (for example, you may say "I want to argue by contradiction. Suppose x is not equal to zero...").

If you want to use a known theorem or lemma in your homework, simply quote its number from the textbook, for example you may say "By Theorem 16.7, ..." On the test, either state the theorem you are using or refer to it by its name if it has one (for example, you may say "By Lagrange Theorem...", or "By the structure theorem of finitely generated abelian groups...", or "By a theorem I remember from the textbook that the order of k in Zn is equal to n/gcd(n,k)..."

Exams and Quizzes:

There will be two in-class midterms and four 20-minute quizzes. The dates are in the course schedule table below.

The date for the final exam will be determined by the Registrar office.

Grade Weights:

Two lowest HW grades and one lowest quiz grade will be dropped.

Grading Scale:

Tentative Schedule for Math 411:

Final Exam:

12/16/16, 8:00am-10:00am, LGRC A301