Don’t forget that on Friday you have homework and a quiz. Info on those can be found above and to the right (under Homework and Quizzes).
First, try to complete pages 5-8 of your classroom worksheet, skipping writing the proofs, if you haven’t finished yet. The “cards” approach on page 6 is a way of visually formalizing the fact that you can “add” equations. For example, the equation ax + by = 1 can be added to the equation ax’ + by’ = 2 to get the equation a(x+x’) + b(y+y’) = 3. In the “cards” notation, this says that the card “(x,y) gives 1” can be added to the card “(x’,y’) gives 2” to get the card “(x+x’,y+y’) gives 3”. Notice that writing it this way emphasizes the fact that you are adding vectors (x,y)+(x’,y’)=(x+x’,y+y’) as well as numbers 1+2=3. So you should do the steps of the Euclidean algorithm on the “cards” instead of just the numbers. We’ll cover all this first thing on Wednesday.
Please read your text, pages 33-41. This covers the material we have been doing in class. He approaches linear Diophantine equations with “hops”, “skips” and “jumps”. If you find this better than the “cards” on page 6 of my worksheet, that’s fine! (Although I think my approach will make you much happier than his once you see it in action!) You may wish to spend more or less time on the reading depending on whether it is working for you compared to other things.
If time permits, try to fill in the proofs on the worksheet.
We will spend Wednesday in class finishing up the topic of solving linear Diophantine equations. This will complete Chapter 1 of the textbook.
I have office hours Tuesday at 10 am; please feel welcome! You are also welcome to just come and do your 45 minutes of work in my office, so I’m handy while you’re doing it.
Wednesday 5-6 pm in Math 350 is the first Math Club event of the semester! Danny Moritz will be talking about “Geodesic Domes, Graph Theory, and Beyond.”