1,071 reputation
47
bio website
location Chennai, India
age
visits member for 2 years
seen 8 hours ago

Interested in elementary algebra enter image description hereproblems, and teaching.


10h
answered same splittingfield of two polynomials $f(x)$ and $f(x+a)$
Apr
17
answered Is there a way to find a point on a circle, given another point and an arc length without using trig functions?
Apr
17
comment Subrings Between Integers and Rationals
On the other extreme, all fractions (in their simplest form) having odd denominators form a subring of the rationals and contain all integers.
Apr
16
comment Finding Number of Cyclic Sub groups of order $15$ in $Z_{30} \bigoplus Z_{20}$. The mistake in this method?
@Marc: I too missed the cases where $|g|=15, |h|=5$. So there are actually 6 subgroups. My earlier comment is wrong. Thanks for bringing in vector spaces over finite fields which allows us to see things clearly.
Apr
16
answered Automorphisms of group extensions
Apr
16
comment Showing that a set of units form a multiplicutive group
Associativity is assured. You have to just verify closure with respect to multiplication. Existence of inverse will also follow easily. Work with the well-known special case of rational numbers and it will give you an idea how to formalize. If two rational numbers have reciprocals, can you actually construct the reciprocal for their product?
Apr
16
comment Finding Number of Cyclic Sub groups of order $15$ in $Z_{30} \bigoplus Z_{20}$. The mistake in this method?
You are not making a mistake. The answer is not 6.
Apr
14
comment Are there contradictions in math?
Your first two sentences say different things. Saying someone is a liar is vastly different from saying that person does not know a few things. So if your friend thought "lot of things in mathematics are not well-defined" it does not mean mathematics has contradictions.
Apr
14
answered Find an $n\times n$ integer matrix with determinant 1 and $n$ distinct eigenvalues
Apr
13
answered Is there any book about inequality?
Apr
13
answered Number of lines/triangles determined by n points
Apr
12
awarded  Yearling
Apr
12
answered Topologically dense subgroup
Apr
12
comment Peculiar Matrix
Any $n\times n$ matrix whose $(n,n)$th entry is 1 arises this way. You can work-backwards construct an $(n^2-1)\times (n^2-1)$ matrix having this as characteristic polynomial (its companion matrix).
Apr
12
comment Is an onto homomorphism from G to itself an automorphism
You are right. Shortest path for this proof is the polar route. As nth roots exists for [positive reals. However, I feel that mathematician in their quest for brevity or economy, state FTA in that way. In my class I formulate it as surjectivity of polynomial functions. As zero is a special number I did not want my students to get the idea that zero value is always achieved as opposed to others. (The proof by appealing to Liouville's theorem exploits non-vanishing of the entire function and obscures the surjectivity).
Apr
12
comment Is an onto homomorphism from G to itself an automorphism
@Olivier. I noticed the slip in my language. Corrected it. Thanks.
Apr
12
revised Is an onto homomorphism from G to itself an automorphism
added 3 characters in body
Apr
12
answered Is an onto homomorphism from G to itself an automorphism
Apr
11
awarded  Enlightened
Apr
11
awarded  Nice Answer