MATH 3110 Spring 2019

• You have a quiz on Friday. It is in-class. You can find information on it under “Quizzes”, above. I’ve added a few general notes above the topics section, there.
• You have homework due Friday. It should help you study for the quiz, ideally. See “Homework,” above.
• You are welcome to attend office hours Thursday at 2 pm.
• Thursday 4 pm in Gemmill is a “homework hour” where you may meet your peers (see “Course Info” above, for details.)
• I’ve been continuously updating info in the “Lectures” section, above. You’ll now find today’s linear Diophantine equation example from class, as well as the handout summarizing linear Diophantine equations.
• I wish you all good luck!

• 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.”

• Next Friday Feb 1st you have homework due and your first quiz. The homework is posted under “Homework.” The material on the first quiz is posted under “Quizzes” (both on menu upper right). Look at the material and make a study plan.
• The quiz will take the full class. Arrangements for extra time, if applicable, should be made ASAP.
• Today in class, we worked on a worksheet, which is available for you under “Lectures” in the menu to the upper right. There is a typo corrected noted there; please make this correction on your copy. (Reminder: Lectures has info relevant to each lecture, including further reading, copies of handouts, etc. It will be updated frequently.).
  
• We discussed/completed pages 1-3 of the worksheet in class (at least). Please continue on to finish page 4 in advance of Monday’s lecture. In class, I suggested you skip the proof writing and concentrate on the rest of it. Now, please write the two proofs requested on pages 2 and 4. You may wish to print out a fresh copy and write neatly so you can have this as a reference later (in case your copy from class was messy.)
  
• Students responded to the Homework Hour poll and based on that and other feedback, I hereby declare 5 pm Mondays and 4 pm Thursdays in Gemmill a Math 3110 homework hour, where you can meet others who may be interested in collaborating on homework. (Let me know if this turns out to be useful.) I’m putting this info on the “Course Info” page.
• Some students took an interest in Sage; you can find getting-started info and resources on the “Resources” page. You have access to Sage using your identikey. We will do more with this later.
  

• You have homework due Friday, don’t forget. The homework is like a “standard course”, i.e. graded on correctness, and you take as much time as you need whenever during the week works for you (it’s not part of the 45-minute tasks).
• Read the Homework page (above, right for link). In particular, read the honour code rules. I have slightly unusual honour code rules, and you should email me if they aren’t clear at all.
• I have set office hours and they are now listed on the “Course Info” page. However, this starts next week. Thursday the 24th I’m completely booked up; email if you need me ASAP.
• If you want (optional!), please log in to the canvas and complete another when2meet poll for “homework hours”. That is, I will set designated study hours at Gemmill or the MARC, where you can all meet to work on homework during the week. By setting such hours, you can go there to work and will find people who are working on the same course. I won’t be there, and there’s no guarantee anyone else will either, but it will facilitate meeting your peers. Please send me your advice on location in email (Gemmill or MARC? should we designate a more specific location?).
• Today we formalized the Euclidean algorithm. The next task is to try to to solve equations of the form ax+by=c, in integers. You’ll find that our textbook unifies these problems, so today’s reading will review what we’ve done but simultaneously get you started on solving such equations.
• Read your text, Pages 25-32 inclusive. Take your time and read actively. It’s better to do just some of it well, than all of poorly.
• By the way, I’m recalling the library’s copy of the text, to put on course reserve, but it is taking time.
• Do at least one gcd computation for practice.
• If you are done the reading etc., find someone who doesn’t know the Euclidean algorithm and explain it to them.

• There’s a good chance we’ll move rooms (around the corner in ECCR), which would allow me to let the waitlist of students into the class. I will report more on this when I know more (perhaps Tuesday). It is not for sure.
• Please complete the when2meet poll with your availability for office hours. The link & explanation for the poll is available as an announcement in canvas (I didn’t want to put it on a public site).
• Allow me to remind you of the last proposition from class, which was this (restated here a little differently):

Proposition. Let a and b be integers. Then, for some integer k, define the quantity c = a + kb. Then gcd(a,b) = gcd(b,c).

• Suppose you want to compute the gcd of 1925 and 931. The Proposition lets you make a “move” that replaces that big problem with a smaller one. For example, using k=-2, we get c=63 and learn that:

gcd(1925, 931) = gcd(931, 63)

• So, by clever choices of moves, we can replace the original big problem with smaller and smaller ones, until the gcd is obvious. We can go like this:

gcd(1925, 931) = gcd(931, 63) = gcd(63,49) = gcd(49,14) = gcd(14,7) = gcd(7,0) = 7

• First, please verify the set of moves above (recreate it for yourself).
• Your task is to find the “slickest” / “fastest” series of moves to discover the gcd of 4181 and 6765 that you can. On Wednesday bring it to class and we will see who can get to the gcd in the fewest moves (when you get to gcd(a,0)=a, you are done).
• Please read all of Chapter 0 in your textbook (you have already read a selection; now please finish it).
• There’s a new static page called “Homework” on the website. Please read and understand the honor code rules and general rules there. Email me if you have any questions.
• Your homework due Friday, January 25th is now assigned on that page. Don’t forget that regular homework assignments are assigned each Friday due the following Friday.

• Make sure you will have your text by the weekend ideally, or Monday at the latest.
• If you haven’t completed the tasks for previous days, in particular the “get-to-know-you” quiz on canvas, please catch up now.
• First take a look at, but don’t yet complete, the online quiz on canvas entitled “Reading p.10-17.” Just get a sense of the questions being asked.
• Now actively read pages 10-17 of your textbook (this was handed out as a photocopy in class on Wednesday, for those who do not have it yet; if you don’t have a copy or the text, please email me). By actively, I mean as modeled in class Wednesday. You might also find it useful to check out the links for Wednesday’s lecture on the “Lectures” page at right, for more guidance. Make notes in the margin or your notebook, of your active reading process.
• Now please complete the online quiz “Reading p.10-17” on canvas after reading. You can have your text open while working on this, together with any notes you’ve made during the reading or class, and you can look up resources if you find it helpful.
• In class we did an activity in the last ten minutes. Please bring your thoughts on that activity to start Friday’s class. Here is the activity, in case you need a review: It is a two player game. The board contains some number of positive integers to start. Players take turns. Each player attempts to find two numbers on the board, whose positive difference is not yet written on the board. Then he adds that number to the board. He who cannot add a number loses. The question is to analyse who wins this game, for a given set of starting numbers. For example, try “10, 15, 50” or “3, 5, 7”.
• Note that in class Monday, I wrote the wrong error term for the prime number theorem. Check out “Lectures” at right for some typed notes relating to that, including the correct error term. You might like to peruse these further to follow up on any of Monday’s motivating questions that interested you. In particular, they explain the cool pictures on the back of the question sheet.

• Please read the static pages on this website. You’ll find them listed at right, “Course Info”, “Goals”, etc.
• Please make inroads to obtaining your textbook. If you have it, please give it a look. It’s quite nice.
• Please figure out how to log into canvas and fill out the “get to know you” quiz you’ll find there. If you are not waitlisted or registered, you may not be able to access this (although I think you should be able to). If this is the case, please write me an email briefly letting me know (1) whether you attended on Monday, January 14th, (2) your registration situation, and (3) whether you have read the website in detail.
• Our course looked very crowded on day one. But it tends to clear up a bit. Please keep in mind that I will administratively drop students who are not attending (I will take attendance) and participating in these daily tasks. I will be posting a “to-do” post on this website by 5:30 after each day of classes, and you are expected to budget 45 minutes to do whatever I ask of you before the next lecture.
• Finally, I plan to post notes from the first-day lecture’s questions sheet. You will find them under “Lectures” at right, but this may take a little longer than 5:30 pm today, since I’m updating them a bit. One note: I wrote the error term on the Prime Number Theorem incorrectly in class. This will be corrected in the notes.

Please read through this website and come to class!