MATH 3110 Spring 2019

• I hope you had a chance to see James Grime speak on Friday; even if you didn’t, you can still take the quick canvas “Enigma” quiz (look up Enigma on wikipedia to learn the basics). I will grade it — sort of — participation matters more than correctness, but if you don’t know the answers that’s less indication of participation. 🙂
• Over the weekend, read pages 160-163 (about primality testing, material from before break), pages 166-167 (about Diffie-Hellman, which we finished on Friday), and pages 164-165 if you want a look-ahead to Monday’s lecture.
• Monday Task C is due; homework for next Friday and quiz material for next Friday have been posted.

• Office hours Thursday are 3 pm instead of 2 pm. I may be slightly late, and I may have to end early. But I’ll try to make it a full hour (I have several student defenses that day, so it’s very busy).
• You have homework due Friday.
• On the worksheet from class today, complete up to the end of Section 3.
• Friday in class we will begin by doing Section 4/5 in pairs. If you completed Section 4 on Wednesday, I’ll have a challenge task for you, so expect something fun.
• Please complete the Discrete Log Quiz on canvas, associated to our recent material. This is a quick concept check.
• I was asked by a former student to advertise a sort of tech start up competition for CU students.
• On Friday at 4 pm, James Grime (who does Numberphile) is giving a talk on “Alan Turing and the Enigma Machine” (click for poster). This is not one to be missed! It’s going to be really fun, and it is very relevant to our class. If you would like to earn a little extra credit toward the “Daily Tasks” portion of your grade, please attend this talk and there will be a quick canvas quiz on it open during the talk. There’s pizza and stuff afterward.

• Attendance during the Wed/Fri before break was abysmal. Students who were absent are responsible for covering and learning that material.
• We had two worksheets, one on Modular Dynamics and one on Primality Testing. Please complete these (the first up to end of Section 6 and the second up to end of Section 3) if you did not complete them in class.
• The material on Modular Dynamics is absolutely crucial for the rest of the course, so I reviewed it today in class. Please take some time now to revisit and understand it in conjunction with the worksheet and the textbook. Read pages 153-159.
• We have lately had several incidents of students breaking the honor code. First, I want to thank those of you who hold this code in high esteem. It is for those of you who care about bettering yourselves and embracing learning, that I teach this course. I also hope you will forgive those who err. Secondly, I want students who cheat to recognize that they are not only harming themselves, but disrespecting and harming their peers, teachers, community and university. Cheating will not be tolerated.
• The CU undergraduate Math Club (QED: quest-explore-discover) will have its next talk for Spring 2019 by Professor Jeanne Clelland, this Wednesday, April 3 from 5 – 6pm in MATH 350. Title: The Will of the People: How we vote and why it matters.
• Don’t forget TASK B is due today and we have homework due Friday. Your 4th and final quiz is already friday after this coming one (Apr 12).
• LATE ADDITION: Check the homework page, a typo was discovered in one problem.

• This week I will be gone at a conference, but you will have a substitute teacher. I am leaving worksheets and lecture notes etc. in my absence. Please attend class as regularly, as we are covering important material.
• I’m leaving up this one website post for the week. I will post under “Lectures” the worksheet material etc.
• Don’t forget that Monday (the 18th) you have Writing Assignment TASK A due; that’s your task for this weekend. I will be looking at these remotely via canvas and giving feedback (via canvas) as quickly as possible after you hand them in (so that everyone is on track with a good topic before spring break!).
• We will skip homework for this Friday and Homework will be due after spring break. (With the snow day and the quiz, we hardly covered any new material to test; and anyway it’s spring break.) Homework due after break has been posted.
• As for “45 minute tasks,” just keep the habit but use your 45 minutes to review worksheets, lecture notes, and associated textbook material.
• I may update this post with a little more detail on Saturday, March 16th.
• After that, enjoy your spring break!

• Today (Monday) we had a worksheet, but we only just started it. Please complete the section titled “Additive Dynamics” (up to end of page 5) and then compare to this brief cheatsheet: For item 1, it should look like one big cycle; item 2 you should have two cycles; for item 3, 5 pairs; for item 4, 3 cycles; finish to the end of page 5 at home. We will pick up there on Wednesday. Also, there was a typo on the second diagram on page 6, fixed in the online version here.
• Don’t forget to bring your worksheet back to class on Wed.
• You have homework and a QUIZ on Friday.
• YOU HAVE A TASK DUE ON MONDAY. Read all about the Writing Assignment on the menu above, including Task A. Please let me know if you have questions. Right now, spend a little time looking through the suggested topics or googling or wikipedia-crawling around, and start to zero in on a topic.
• For reading, we have covered Chapter 5 up to page 139, and are now starting on Chapter 6 (we have skipped pages 140-146 for now).

• This Friday we did a worksheet in class. Please continue it, getting to the end of Section 5.
• Do associated reading in the textbook, p. 134-139.
• Invent and solve a couple linear congruential equations. You should be able to solve any linear congruential equation at this point (ax = b mod n).
• Homework has been posted.
• Material to study for the quiz (next Friday!) has been posted. It will be updated on Monday/Wednesday after lectures to reflect the newest material we cover those days, so check back.

• Take the quiz on canvas about the Sage workshop (this helps me assess where the class is and also improve the worksheet for next time).
• Read Chapter 5, from beginning to page 136 inclusive. Keep reading if you have time (if so, this will preview our next material).
• Contemplate the question when can you solve a linear congruential equation (i.e. solve ax = b mod N)? Try to rephrase this problem into one just about integers.
• Note, on the Resources page I now list tutors in MARC (and hours) where they know and are willing to teach number theory. Near the bottom.
• IMPORTANT: Thursday’s office hours are 10:30-11:30 instead of 2-3 pm.

• DON’T FORGET: Monday is a Sage workshop in BESC 385.
• Finish writing up the proof that congruence is an equivalence relation (from class; we just had transitivity to go).
• Contemplate how to compute 2¹⁰⁰ modulo 11 by hand. How can you do this with the fewest operations?
• Contemplate what 1/2 should be modulo 7, if we are going to define it in some useful way. Why?
• Now, read p. 127-133 of your text (This is Chapter 5, the first 7 pages).
• Homework for next week has been posted.

• If you haven’t already, compare your quiz with solutions.
• Convince yourself, with the sum of geometric series, that 1 + 1/2 + 1/4 + 1/8 + … = 2. (We’ll use this in class Friday.)
• Watch this Mathologer video about approximating numbers with rationals. (Forgive him for his weird obsession with Fibonacci numbers.)
• Use the rest of your 45 minutes for any catch-up things you might need.
• Reminder that MONDAY will be a Sage Workshop in BESC 385.
• Friday’s class will be very important material (modular arithmetic done right).
• UPDATE: Thursday office hours are cancelled due to illness.
• THIS JUST IN: I corrected the statement of the homework problem on commensurability on the Homework page.

• Please compare your quiz (handed back on Mon) with the solutions. Spend a little time learning what you missed or were confused about.
• If you didn’t attend the LaTeX tutorial, check out the Tutorial Page (in the menu above), just to check out what you missed. You might find something useful.
• Finish reading Chapter 3 of your textbook. We will finish it in class Wednesday, so this is reading ahead. (Note: sometimes I assign reading ahead and sometimes afterward. Figure out what works for you and read ahead more if that’s best for you.)
• I have uploaded grades to Canvas so you know what they are. You should be able to see how individual grades compare to the mean in the course. Please double-check your homework and quiz grades are correct.
• UPDATE: I’m planning a Sage workshop Monday in BESC 385 (same room). (This is mandatory, not optional.)
• THIS JUST IN: Math Club talk on Wednesday titled “Are Random Algebras Really `Random’ ?” in Math 350, 5-6 pm.
• NOTICE: Office hours Tuesday, Feb 26th have been cancelled due to illness.