Math 165
Homework/Lab #6 Solutions
due Wednesday, November 18
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrar
Math 165
Homework/Lab #3
due Friday, October 21
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
eld.
(1) Wri
Math 165
Homework/Lab #3 (Solutions)
due Friday, October 21
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
Math 165
Homework/Lab #2 (Solutions)
due Friday, October 14
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
Math 165
Homework/Lab #1 (Solutions)
due Friday, October 7
Complete the following problems. If you use Maple for any computations, be sure to attach a
printout of your worksheet.
(1) Plot the following varieties (over R) in Maple. Your plots should displa
MAT 165
Homework #0 (Solutions)
Due September 30, 2011
(1) Let K be a eld. Prove that if x, y K satisfy x y = 0, then either x = 0 or y = 0.
Proof: Suppose for contradiction that x y = 0 and x, y = 0. Since x and y are nonzero elements
of the eld K , they
Math 165
Homework/Lab #1
due Friday, October 7
Complete the following problems. If you use Maple for any computations, be sure to attach a
printout of your worksheet.
(1) Plot the following varieties (over R) in Maple. Your plots should display the releva
Math 165
Homework/Lab #4
due
The following problems will not be collected. It may be in your best interest to complete them
before the midterm exam.
(1) (a) Write Maple code that will implement the Euclidean algorithm for polynomials over
the rational nu
Math 165
Homework/Lab #5
due Wednesday, November 9
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
eld.
(1)
Math 165
Lab #5
due Wednesday, November 9
Please submit the following coding assignment with Homework assignment #5 that is due on
Wednesday, November 9.
(1) Find a polynomial f Q[x, y, z ] with the property that the lead term of f is dierent in
each of t
Math 165
Lab #6
due Wednesday, November 23
Please email a le called lab6-yourlastname.mw to me that contains the solutions to the following problems.
(1) Write a function called Buchsberger(F,T) whose input consists of a list of polynomials
F = (f1 , . .
Math 165
Lab #2
Friday, October 7
Complete the following problems. Be sure to justify all of your answers. Throughout, K denotes
an arbitrary eld. Please submit solutions to these problems with Homework assignment #2, which
will be due on Friday, October
Math 165
Homework #8
due Tuesday, December 6
(1) The game of Shidoku is a 4 4 analogue of the classical Sudoku. The objective is to ll the
table with the numbers 1-4 such that each row and column, along with the 2 2 squares in
the upper/lower left/right c
Math 165
Homework/Lab #5
due Wednesday, November 9
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
eld.
(1)
Math 165
Homework/Lab #6
due Friday, November 18
Complete the following problems. Be sure to justify all of your answers. If you use Maple for any
computations, be sure to attach a printout of your worksheet. Throughout, K denotes an arbitrary
eld.
(1) Wr
Math 165
Homework #0
due Friday, September 30
Note: Dont forget to register for a math department computer account before Friday, September
30!
(1) Let K be a eld. Prove that if x, y K satisfy x y = 0, then either x = 0 or y = 0.
(2) Let F2 denote the eld