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ALGEBRA 611. HOMEWORK 5. DUE IN CLASS ON OCTOBER 23
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutio
ALGEBRA 611. HOMEWORK 2. DUE IN CLASS ON SEP 25.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutions
HILBERTS 3D PROBLEM
JENIA TEVELEV
As a fun application of tensors, lets solve the Hilberts 3d problem:
P ROBLEM 0.0.1. Given two polytopes P, Q R3 of the same volume, is it always
possible to cut P into polyhedral pieces and then reassemble them into Q?
H
ALGEBRA 611. HOMEWORK 1. DUE IN CLASS ON SEP 18.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutions
ALGEBRA 611. HOMEWORK 8. DUE IN CLASS ON NOV 20.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutions
ALGEBRA 611. HOMEWORK 4. DUE IN CLASS ON OCT 16.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutions
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ALGEBRA 611. HOMEWORK 3. DUE IN CLASS ON OCT 9.
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b),
etc. counts as one problem. Please make sure that all solutions a
ALGEBRA 611. HOMEWORK 9. DUE IN CLASS ON NOV 27.
The same rules as in the previous homeworks.
Let R be a commutative ring with 1. Let k be a eld.
1. The purpose of this exercise is to show that any two bases A and B of a
vector space V have the same cardi
ALGEBRA 611. HOMEWORK 7. DUE IN CLASS ON NOV 6.
Announcement: the next midterm will be on Nov 13 (at 6pm, in 1322)
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a), (b)
ALGEBRA 611. HOMEWORK 6. DUE IN CLASS ON OCTOBER 30
Announcement: the next midterm will be on Nov 13 (at 6pm, in 1322)
The grader will grade six problems from this assignment determined by
my generator of random numbers. A problem with multiple parts (a),
ALGEBRA 611. HOMEWORK 10. DUE IN CLASS ON DEC 4.
The same rules as in the previous homeworks.
All rings are commutative with 1. Let k be a eld.
1. Compute the following n n determinant:
2 1 0
0 .
1 2 1 0 . . .
0 1 2 1 . . .
0
0 1 2 . . .
.
.
.
.
.
.
.
.
.