Math 302 Learning Objectives
... o integral formula for the volume of a solid bounded between a region Ω in o the xy-plane and the graph of a non-negative function z=f(x,y) defined on Ω. o integral formula for the area of region in a plane o integral formula for the average of a function defined on a region Ω. o projection of a reg ...
... o integral formula for the volume of a solid bounded between a region Ω in o the xy-plane and the graph of a non-negative function z=f(x,y) defined on Ω. o integral formula for the area of region in a plane o integral formula for the average of a function defined on a region Ω. o projection of a reg ...
HOMOLOGY ISOMORPHISMS BETWEEN ALGEBRAIC GROUPS MADE DISCRETE
... Proof. Since tensor product commutes with direct sums, we can assume that U = U (α, r) and V = V (β, s) for r, s ∈ Q. It is then enough to show that for any u ∈ U and v ∈ V there exists a positive integer k such that (α ⊗ β − rs)k (u ⊗ v) = 0. By assumption there exist positive integers i and j such ...
... Proof. Since tensor product commutes with direct sums, we can assume that U = U (α, r) and V = V (β, s) for r, s ∈ Q. It is then enough to show that for any u ∈ U and v ∈ V there exists a positive integer k such that (α ⊗ β − rs)k (u ⊗ v) = 0. By assumption there exist positive integers i and j such ...
Math 194 Clicker Questions
... relatively straightforward. If at least two of the equations represent the same plane and the third plane intersects this plane or is the same as this plane, then you’ll have infinitely many solutions. So it’s possible that response (b) could be true. As for response (d), if the planes are parallel ...
... relatively straightforward. If at least two of the equations represent the same plane and the third plane intersects this plane or is the same as this plane, then you’ll have infinitely many solutions. So it’s possible that response (b) could be true. As for response (d), if the planes are parallel ...
Factorization in Integral Domains II
... Proof. There are at most n roots of the polynomial xn − 1 in F , and hence µn (F ) is finite. It is a subgroup of F ∗ (under multiplication): if ζ1 and ζ2 are nth roots of unity, then ζ1n = ζ2n = 1, and thus (ζ1 ζ2 )n = ζ1n ζ2n = 1 as well. Thus µn (F ) is closed under multiplication. Since 1n = 1, ...
... Proof. There are at most n roots of the polynomial xn − 1 in F , and hence µn (F ) is finite. It is a subgroup of F ∗ (under multiplication): if ζ1 and ζ2 are nth roots of unity, then ζ1n = ζ2n = 1, and thus (ζ1 ζ2 )n = ζ1n ζ2n = 1 as well. Thus µn (F ) is closed under multiplication. Since 1n = 1, ...