# 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.

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.

```               hour exams average                100 points each