- 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.

## To Do for Fri Mar 5

- 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.

## To Do for Wed Apr 3

- 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.

## Week of March 18-22

- 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!

## To Do for Wed Mar 13

- 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).

## To Do for Mon, Mar 11

- 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.

## To Do for Fri, Mar 8

- 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.**

## To Do For Mon, Mar 4

**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 2
^{100}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.

## To Do for Fri, Mar 1

- 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.**

## To Do for Wed, Feb 27

- 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.**