# Math 310: Intro Modern Algebra

## Course Review Topics

- Know what a relation is
- Know what it means for a relation to be symmetric, reflexive or transitive
- Know when a relation is an equivalence relation
- Be able to write out an induction proof
- Be able to perform Euclid's algorithm
- Be able to solve mx + ny = gcd(m,n) for x and y
- Know relation between lcm(m,n) and gcd(m,n)
- Know what the prime number theorem says about number of primes
- Be able to do modular arithmetic
- Be able to sove ax = b mod m for x
- Be bale to solve simultaneous equations: x = a mod m, x = b mod n
- Be able to solve quadratic modular equations
- Know the definitions and examples of groups, rings and fields
- Know how RSA encryption works
- Understand the statement of Fermat's Little Theorem
- Understand the statement of Euler's Theorem
- Be able to computing the phi-function
- Understand the statement of Fermat's Christmas Theorem
- Understand the statement of the Binomial Theorem
- Know the definition of homomorphisms
- Be able to tell when a map is or is not a homomorphism

Instructor: Brian Harbourne
Class Time: 11:30-12:20 MWF
Class Room: Burnett Hall 204
Office: 331 AvH
Tel.: 402-472-4476
Office Hours: Tentatively, 1:30-2:30 p.m. M W F, or some other time by appointment, but feel free
to drop by my office anytime. If I'm busy, we can make an arrangement for later.
email: bharbour@math.unl.edu
web: http://www.math.unl.edu/~bharbour/

**Text**: * A concrete introduction to higher algebra*, Lindsay Childs, 2nd ed.
We will cover most of the first 12 chapters, and then several additional chapters,
chosen partly based on class interest.

**Homework**: We will have weekly assigned homework.

- Homework 1: due Friday, January 13, 2006
- Homework 2: due Friday, January 20, 2006
- Homework 3: due Friday, January 27, 2006
- Homework 4: due Friday, February 3, 2006
- (Here is a
Renaissance fresco by Raphael including a figure representing
Euclid.)
- (Here is a
web form to compute gcd's. You can use it to check your work,
but to get credit you must show your work.)
- Homework 5: due Friday, February 10, 2006
- (Here is a
web form to find prime factors.)
- Homework 6: due Friday, February 17, 2006
- Homework 7: due Friday, February 24, 2006
- Homework 8: due Friday, March 3, 2006
- Homework 9: due Friday, March 10, 2006
- (Here is a
web form to find least positive residues of powers.)
- Homework 10: due Friday, March 31, 2006
- Homework 11: due Friday, April 7, 2006
- Homework 12: due Friday, April 14, 2006

**Quizzes**: Each Wednesday we will have a short in-class quiz.

**Tests**: We will have three in-class hour exams.
[Sometimes an exam just doesn't go well; who knows why! To help take this into
account, your lowest hour exam will be replaced by the final
exam percentage IF that improves your average (so as not to punish someone
whose final does not go well).]

**Final Exam**: Monday,
May 1, 2006, 10:00am - Noon, in our usual room.
Everyone must take the final exam;
do not make plans to leave town before the
final. You are expected to
arrange your personal and work schedules to
allow you to take the final
exam at the scheduled time. No student will be
allowed to take the final exam early.
### Grade Scales, Averages and Semester Grades

There are three hour exams.
In addition, there are weekly quizzes, homework
and the Final Exam. Your Semester Grade
is determined by averaging your grades on these items with the following
weights:

hour exams average 100 points each
quiz average worth 100 points
homework average worth 100 points
Final Exam worth 200 points
Total 700 points

**Departmental grading appeals policy**: Students who believe their
academic evaluation has been prejudiced or capricious have recourse for
appeals to (in order) the instructor, the departmental chair, the departmental
appeals committee, and the college appeals committee.