Math 2710 First Exam Study Guide

The exam will cover Chapters One and Two. This means that you are responsible for all of the material in those chapters, With the exception of the Extended Euclidean Algorithm, presented on pages 31, 32, and the top of page 33 in the book. I will, however, expect you to know that, given integers \(a\) and \(b\), you can find \(x\) and \(y\) so that \(ax+by=gcd(a,b)\) using the (regular) Euclidean algorithm via backsubstitution; and know how to calculate this in simple cases.
Strictly speaking this fact is buried in the discussion in the book immediately following Theorem 2.24 on page 30.

Key topics from Chapter One

In parentheses I indicate problems from the book that are related.

Key Topics from Chapter Two

In Chapter Two, you should:

Because of time, I will not ask you for a complete proof of, for example, the Euclidean algorithm. I could:

or many other smaller results that are buried in the proofs of the bigger results.

Sample problems from Chapter 2: 9, 10, 11, 27, 28, 47-50, 67, 73, 74, 75, 83, 93, 99-102