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Midsemester Grades are posted

Hi everyone,

Your Midsemester Grades are available in the OpenLab Gradebook. These grades are not a part of your official academic record – they are intended as check-in on how you are doing in the class.

The Midsemester grade will be one of the following: P=Pass, BL=Borderline, U=Unsatisfactory. It is based on your Midsemester %, which is calculated as follows:

  • Homework 30% – this includes both WeBWorK and written assignments.
  • OpenLab 25% – this includes all writing assignments on the OpenLab
  • Exams 45% – this includes exams #1 and #2

Let me know if you have any questions or concerns,

Prof. Reitz

Lesson 15 bonus example: Proofs involving gcd

Hi everyone,

On Tuesday we introduced the idea of greatest common divisor and we looked at several theorems about properties of the gcd.

Definition. The greatest common divisor of integers $a$ and $b$, denoted $\gcd(a,b)$, is the largest integer that divides both $a$ and $b$.

In your homework, you are asked to prove propositions that involve the gcd. It may help to keep the following in mind:

To prove that a number $x$ is the gcd of $a$ and $b$

We need to show two things:

1.  $x$ is a common divisor of $a$ and $b$ (that is, $x|a$ and $x|b$)

2.  if  $y|a$ and $y|b$, then $x\geq y$ (“if $y$ is a common divisor of $a$ and $b$, then $x\geq y$”

Here is an example, so we can see how it works in practice:

Proposition. If $a, b$ are integers then $\gcd(a,b) = \gcd(a+b,b)$.

VIDEO: Example – proof with gcd

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