Here is my Euclidean algorithm spreadsheet calculator.

As a first approximation, I post links to past tests:

In Spring 2014, they did badly at the Euclidean algorithm on the first test. You all did not have that problem.

I suspect I may have provided the first question on this test as a makeup for people who did badly at the Euclidean algorithm question on the first test, as well.

Spring 2015 Test II handwritten solutions

Everything on these tests is fair game. I might ask about something on your test that you all did not do so well on on the first test. A variant on the last question comes to mind.

There is also stuff on this test which I could perfectly reasonably ask.

HERE is your **Test II Review Sheet**, which is a homework assignment due
on Wednesday after the test.

HERE are your **Test II Review Sheet Solutions**. Final version of solutions is up, unless you all report typos or errors which need correction. There well may be some. Though I decided to provide solutions, you may still turn in your worked review sheet for homework credit.

- Friday 13 April: The link for the Test II Review Sheet appears above.
Time on Wednesday will be partitioned between some progress on effectiveness of the Rabin-Miller test (which I will do first, to make sure it actually happens) and test review: best prepared for by studying the sample tests and the review sheet!

- Wednesday 11 April: In keeping with the exercise in class, I'll make the exercise delightfully informal. Choose three primes
of the form 4k+1, each larger than the last example 1549 done in class, and carry out the algorithm demonstrated in class (and found on p. 187 of the book) to find an expression for each of them as a sum of two squares. This will force me to build my own Python code to check your work, as between you all you will no doubt choose many different primes! Any student who writes their own Python code to execute this task may submit it for additional credit (one of you has submitted code to compute Legendre symbols, to which similar remarks apply).
This is due next Wednesday. It's very likely that I will come up with another homework set (possibly a set of problems for test review, possibly new stuff) on Friday.

Problem 7, if you do not recall, was this. Show that in a PPT (a,b,c), c cannot be divisible by 7. In addition, state a pattern in the behavior of the remainders on division by 7 of a and b in PPT's if you can see one. The secret is to use calculations of all possible values of the squares of a and b in mod 7 arithmetic (suitably, of course). If you want to explore and see if there is something to say about PPT's in mod 11, do so...I have no idea whether there is anything interesting about them.

Posted homework (on Sunday, sorry I'm slow): do the problems from the book listed in section 9.4 of the notes (p. 36). Problems are noted to be optional only individually! A lot of this is computational.

- Friday, February 2: Homework 3 will still be accepted next Wednesday due to confusion about which problems were optional (only two of them!).
Homework 4, due next Friday: do the exercises listed in section 8.3 of the notes (exercises from chapter 8 in the book).

- Friday, January 26: Homework 3, due next Friday: do the exercises in section 6.4 of the notes (these are problems from the book) Get started before Wednesday (don't slack off when you finish the previous assignment for Wed)...as you may have questions for me...

- Friday, January 19: Homework 2, due next Friday: do the exercises in section 4.3 of the notes (these are problems from the book).
Since this was not posted correctly, it is now due Wednesday the 31st rather than Friday the 26th. I really had edited the file correctly on Friday; I must have dropped it in the wrong directory. I would appreciate email if the homework doesn't appear by Friday at 6 pm or so (there might be factors which delay me) and certainly if it is not there on Saturday morning! There will be homework assigned on Friday the 26th, which will be due as usual the following Friday.

(Thanks to a student): Should this be the answer key to problem 5.5?

On a more serious note, you might like my Python functions in this file for explorations of the process in 5.5 (the guess that this process always terminates is called the Collatz Conjecture).

- Friday, January 12: Homework 1, due Friday January 19th: do the exercises on page 9. The last one is a challenge problem, and you should not worry unduly if you are not successful at it. Do be sure you are looking at the updated version of the file: if it has an exercise about the div and mod operations, it is updated.

This should give a very clear impression of what you need to know for the exam. I will probably have a little more to say on Wednesday.