Month: February 2019

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.

To Do For Mon, Feb 25

  • IMPORTANT: Monday we will have a LaTeX lab in BESC 385. This is in Benson Earth Sciences, not in our regular room. There are not quite enough computers for everyone, but there is plenty of seating, so bring your laptop if possible. If you can’t bring your laptop, you can use one of the lab computers. I’ll give an intro/overview of LaTeX and then have a worksheet set up for you to work through easy-to-medium LaTeX challenges so you can learn the most important skills, while I circulate the room to help people with anything. You could use this as time to LaTeX up your homework, etc., if you already have the basics down. Please do attend if you are not familiar with LaTeX. If you are a LaTeX expert, you may feel free to do whatever is helpful to you (attend or not attend). Students can be working on whatever they like (as long as it is productive!) during the hour.
  • You’ve earned a brief rest this weekend, so use the time to catch up on reading or homework (new homework is assigned on the Homework page).

To Do for Fri, Feb 22

  • Do not forget that you have a quiz.
  • Do not forget that homework is due.
  • The Homework, Quizzes and Lectures pages are all up to date.
  • Don’t forget Thursday there are office hours (2 pm) and a study hour at the library at 4 pm (see “Course Info” for details on both).
  • Good luck!
  • THIS JUST IN: MONDAY WILL BE A LATEX LAB. Info to follow, but we will meet in BESC 385.

To Do for Wed, Feb 20

  • Please watch this Numberphile video (7 minutes). I decided not to spend time on greek constructions in class, but you should know a bit of the history and main idea, and this is a nicely done enjoyable video.
  • Please read your text, pages 78-85. You can just do a gentle read over the bit about constructible numbers (pages 78-80 and 85), without diving deeply; these are nice to know about but I won’t consider it a topic of the course. Focus on pages 81-84 as a complement to Monday’s lecture.
  • Log into canvas and complete the associated reading quiz there.
  • Here is a wonderful 3blue1brown video (15 minutes) that visualizes Pythagorean Triples. It is optional, but it’s highly recommended.
  • Wednesday we will cover pages 86-93. You may wish to read ahead on those.
  • I will likely assign Chapter 3, Exercises 2 and 3 on the next homework; you may wish to do them early to study for Friday’s quiz.

To Do for Mon, Feb 18

  • Read your text, pages 75-77, Proposition 3.5 and Problem 3.6 on page 82. Beyond that, read as you see fit; you will be reading ahead, which can be excellent.
  • Take this 15-second poll, just to help me prepare.
  • You may be curious for a proof that pi is irrational or that e is irrational.
  • I will shortly post homework for next week and some information on next week’s Quiz #2.
  • If you missed Wednesday and/or Friday’s classes, obtain class notes covering the material that isn’t in your text. See Lectures page (above, right) to find out what that is.

To Do for Wed, Feb 13

  • The Math Club is having another talk on Wednesday afternoon, about surprising mathematics. THIS JUST IN: Talk has been rescheduled.
  • The Mathematics Department REU projects have been announced. These are paid positions to do research in teams of 1-6 with a faculty mentor. Online application requires identikey, due March 1st.
  • Finish reading your text, Chapter 2. I will de-emphasize the bit on Mersenne primes and perfect numbers. It’s a nice story, but not central to anything. So you needn’t focus too much on those proofs.

To Do for Mon, Feb 11th

  • Watch this 20 minute 3blue1brown video giving a beautiful proof of the Basel problem using lighthouses. Watch actively: pause, rewind, take notes if that helps. Figure it out.
  • Today in class we discussed the intuition behind Corollary 2.22, 2.24 and a problem related to 2.25 in your text. Please read pages 60-62 carefully and solidify your understanding.
  • We proved Theorem 2.27 in class (modulo some details), but the textbook doesn’t. Although he does make a margin note (19) which could be turned into a different proof than the one I gave. For the source of the proof I gave in class, see ‘Lectures.’
  • Homework due next Friday has been posted.
  • On the Lectures page, I posted some links and further info to do with the Rabbit & Hare problem, and the Postage Stamp problem, which you may have enjoyed exploring on your recent homework.

To Do for Fri, Feb 8

  • Important note: office hours for Thur, Feb 9th are cancelled.
  • We have now covered the proofs of Results (Lemma/Corollary/Theorems) 2.3, 2.12, 2.13, 2.14, 2.15, 2.20. Please complete the reading of your text, pages 46-59. Pay special attention to the proofs of these items — they are core results of this section of the course. Compare my proofs to his; they should be essentially the same, so two voices may help clarify any confusion points. I may ask them on the next quiz. After this course, I want you, too, to be able to convince your friends unique prime factorization is surprising and cool, and to be able to explain why it is true.
  • Also please spend some time appreciating the Figures on p. 46, 52 and 55, as well as the rich historical context the author provides (e.g. 2.4, 2.5, 2.8-11, 2.17-19). One of the nice things about this text is that the author puts everything in context of what we know, don’t know, conjecture, and recent results. Mathematics is a living discipline!
  • If time remains: think of a question about primes that you are curious about, and see if you can find anything about it online. Many questions you might ask are still open!