08-401/Homework Assignment 8

08-401/Navigation Panel   # Week of... Links 1 Jan 9 About, Notes, HW1 2 Jan 16 HW2, Notes 3 Jan 23 HW3, Photo, Notes 4 Jan 30 HW4, Notes 5 Feb 6 HW5, Notes 6 Feb 13 On TT, Notes R Feb 20 Reading week 7 Feb 27 Term Test (and solution) 8 Mar 5 HW6, Notes 9 Mar 12 HW7, Notes 10 Mar 19 HW8, Notes, RC (PDF) 11 Mar 26 HW9, Notes 12 Apr 2 FT, HW10, Notes 13 Apr 9 Notes S Apr 14-25 Study Period: blackboards F Apr 28 Final Add your name / see who's in! Register of Good Deeds

Announcements go here

In Preparation

The information below is preliminary and cannot be trusted! (v)

Reading

Read chapters ?? and ?? of Gallian's book (6th edition) three times:

• First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
• Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
• And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

Doing

Solve problems ?? in Chapter ?? of Gallian's book (6th edition) and problems ?? in Chapter ?? of the same book, but submit only the solutions of the problems marked with the letter "S".

Due Date

This assignment is due in class on Wednesday March 26, 2008.

Just for Fun

Let $x$ be some root of the equation

$x^{5}+({\sqrt[{3}]{2}}-{\sqrt {3}})x^{4}+{\frac {1}{\sqrt {{\sqrt {3}}+{\sqrt {5}}}}}x^{3}-1=0.$

We know that $x$ is algebraic. Can you find a polynomial $f$ with rational coefficients whose roots include $x$? Can you find the minimal polynomial $p$ of $x$? What is $\deg p$?

Warning. "Can you find?" should be interpreted as "How would you find?" and not as "Please find.". The latter is doable, but not by hand!

Prize. Though if you do actually find such a polynomial $f$ through your own efforts, post it on this site along with your detailed and repeatable computations leading to it (a computer program, I presume, fully documented so that anybody else could run it too), and you will receive up to 60 bonus points for the feat, counted towards your final grade in the same manner as the "good deed" points. The due date for prize claims is the last day of classes.