Download OU B.Sc 2016 April 2nd Year Mathmatics Question Paper

S;::l: Lagrange's theorem in groups: Prove that every group of prime order is cyclic.

by 4 9 & 8 G)ignd -[“ t

o) e |4 i 3 ; 2 )aretwo permutations

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b) If o~

&, 0 AR R,

in S_e. Then find s o ?

U o

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3:'*':)) = efine an lntoaral do ?v‘i: m'gwe &

Prove that a commutative ring with unity is a field if and only if it has no non-trivial ideals.

M) Def\ne Rjngi homomorphism. Sh y ly t?Vl.al , .

ey oW,

d(a+ib) = (a, a) for all a, b ? R. Let f: C ? M₂(R) given by f(a+ib) = ... Show that f is an Isomorphism of ...

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b) If f(x) ? F[x] and f(x) is of degree 3

and Ol?w it | szm 7 F. '} then prove mm s wreducio\e over ¥

Vfg a) State and .

orem of integral calculus.

b) Define the i) pa tnr' , d interval [a, b] i) n

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orm sums

and iv) Riemann integrals (lower and upper).

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