Math 3345 — Autumn 2016
10/31

Future class announcements and homework posts will be made through Carmen.

10/10

I've updated the notes to cover the material we have done, as well as the final pieces of material we'll cover before the next exam (there won't be any questions about section 8 on the exam). You don't have homework from the final parts of the notes. I have prepared some practice problems for you. I do expect you to be able to do most of the practice problems on the test. Like last time, I will put one or more of these problems on the test.

WARNING: I won't be able to make office hours next Tuesday. I will try to be as flexible as possible on Monday of next week to accomodate any discussion. Class next Monday will effectively be office hours. Please bring any questions on the material or practice problems to class on Monday.

10/3

The complete homework assignment list is given on the left, and the notes have been updated as of today. I added some additional problems, so if you're looking at an older version of the notes, be sure to look at the problems in the current list.

I can not be in office hours this Tuesday. Office hours for this week are Wednesday morning, 8:30-10:00 and Thursday afternoon 1:30 - 3:00.

9/26

The complete homework assignment list is given on the left. No new additional problems were added after the initial bunch.

9/26

Test corrections are due next Monday 10/3. Problems 2 and 4/5 are eligible. Please turn in complete solutions to whichever problems you are correcting. There is no real opportunity here for partial credit here: please turn in fully correct solutions. A fully correct solution to 2 will be worth half the missing points in Problem 2. A fully correct solution to either 4 or 5 will be worth half the missing points on whichever problem you attempted. Your instructor will think very highly of you if you choose 5, but he will not award more points (it looks much harder than it is!).

Here are a new set of notes for the combinatorics section. Homework is due Friday, as usual, but it will be shorter than usual. A few more problems will be assigned Wednesday.

Office hours are updated: T/Th 1:00-3:00.

9/19

I've written up some sample test problems here. I've mostly put number theory exercises, because those were what was demanded in class. I also put two sample induction problems. There will also be one question (or a group of related questions) on formal logic.

I will be available in my office between 1-3pm today and tomorrow to talk about anything related to the class.

9/16

I've written up some sample solutions to the third homework. I did not write the proofs to all the problems, but I gave at least one solution for each type of problem on the homework.

For the purposes of scoring the problems, a correct proof is one which demonstrates that you have reduced (or can reduce) the statement you want to prove to the axioms of the integers (or already proven facts). You don't need to state every axiom every time you use it, but it should be clear at every step which one(s) you are using.

At the end of the day, a proof is meant as a demonstration. While all proofs, in some sense, could be reduced all the way to the axioms, this would make most proofs useless and unreadable. The key to understanding how to write a good proof is knowing what new information you need to demonstrate. In general, both in this class and in life, it's good to err slightly on the side of demonstrating too much, rather than too little.

9/12

I've updated the notes to include all the lectures through to the exam on Wednesday 9/21. This includes all the homework due on Friday and all of the proof of the fundamental theorem of arithmetic.

For your exam, I will ask you to prove at least one of the following theorems:

  • Division algorithm
  • Bezout's lemma
  • The existence of a prime factorization
  • Euclid's lemma
  • The uniqueness of the prime factorization
In so doing, you will be allowed to use the tools off of which it builds. The remainder of the exam will consist of exercises similar to those you have seen on your homework (including the sections from the book).

9/7

I've updated the notes to include today's lecture on divisibility as well as the exercise mentioned in class today.

Try to get an early start on this homework. It's a fair bit more formal than the first two homework assignments, and you'll want to try things as soon as possible to see if it's making sense. Come to office hours or arrange a time to talk to me if it's not!

9/7

I've decided I will write lecture notes for the material we're discussing right now, since I can't find a good resource for exactly what we're doing. I'll update these notes as we go through our section on elementary number theory. At the moment, I've put everything we had in class today and a little bit more.

Your exercises will be placed in the lecture notes in the same fashion as in the textbook for the course, and your exercises for the third HW will come from these. The additional problems are for your practice.

On the midterm exam on September 21, at least one of your exam problems will be to reproduce a proof of one of the theorems (or lemmas) from this course. I will give you a list of the theorems and lemmas that might appear after all are written in the lecture notes.

8/31

Your second homework assignment has been posted. You should have everything you need to complete this homework after class on 9/2, before Labor Day weekend. So, try to do some of it before the next class on Wednesday of next week.

A calendar is now available at the link at the top of the page. This calendar will update whenever I post new homework, showing what has been covered. It will also have a little bit of the planned material, though this is subject to change depending on quickly or slowly we're going.

8/26

Welcome back to class! This site is intended as a resource for all information regarding Math 3345. Your homework will be posted on the sidebar (your first homework is due at the start of class Friday, September 2). A class calendar will be available, as will a link to the gradebook, soon.

The syllabus handed out in class on the first day had an incorrect room for the location of the final. The final exam will be in the instruction room.