368 reputation
616
bio website
location the virgo supercluster
age
visits member for 3 years, 4 months
seen Apr 17 at 16:39

Sep
3
awarded  Critic
Jun
8
awarded  Constituent
Jun
8
awarded  Caucus
May
30
comment Good books and lecture notes about category theory.
I wanted to add that his book is now available in paperback at half the price of the hardcover edition: Amazon
Jan
28
accepted Prove the composition of these map objects are consistent.
Jan
28
comment Prove the composition of these map objects are consistent.
The level of detail in your answer was perfect! You used the UMP to set up the two maps, brought them together by means of substitution, made a projection from the product to the exponent, and then switched the order, which is correct up to isomorphism (why is that, btw?).
Jan
27
asked Prove the composition of these map objects are consistent.
Jan
21
comment Which is the fastest way to find the remainder when $2^{400}$ is divided by $400$?
Excellent presentation. One thing I don't follow is how you equate 1/4 to -6 under mod25 arithmetic.
Jan
8
awarded  Yearling
Jan
7
accepted Prove that these two integer groups have equivalent Cayley tables.
Jan
6
comment Prove that these two integer groups have equivalent Cayley tables.
Could the same be done with 5, since it is an element of equal order?
Jan
6
comment Prove that these two integer groups have equivalent Cayley tables.
In your solution, the elements of the additive group are indices for the elements of the multiplicative group and it works because of a very simple algebraic equation e.g. i + j = ... Very slick!
Jan
6
asked Prove that these two integer groups have equivalent Cayley tables.
Jan
1
comment Baby Rudin: Advice
@analysisj, Henri Poincare supposedly only worked four hours a day on research, two hours in the morning and two in the evening. It was his conviction that our subconscious minds can be used to great benefit; it certainly benefited him to a great extent! If it worked for him, maybe it can work for you too.
Dec
24
comment Prove the determinants of these related matrices are zero.
...this explains why it takes n=3 to get a zero determinant. if you consider the plot of e.g. cosine vs. amplitude, the 2nd derivative shifts the function by pi, inverting the original. This is equivalent to making the n-2 row the opposite sign of the nth row!
Dec
23
comment Prove the determinants of these related matrices are zero.
Excelent. So the determinant is zero for any n greater than two. Two questions: would this result extend to the general case e.g. the matrices of trig functions? And, can this proof be expressed in terms of $S_n$?
Dec
23
comment Prove the determinants of these related matrices are zero.
for the purposes of this question, the elements of the matrix are cosine, whose derivative is -sine, whose derivative again is -cosine, whose derivative is sine, whose derivative is cosine again. This forms a ring. The "anti-derivative" is equivalent to incrementing to the next element on this ring, but in the opposite direction of the derivative. Now, is THAT clearer?
Dec
23
comment Prove the determinants of these related matrices are zero.
You iterate down the column by taking the derivative of the previous element. You iterate across the row by taking the anti-derivative of the previous element. Is that clearer?
Dec
23
revised Prove the determinants of these related matrices are zero.
added 158 characters in body
Dec
23
asked Prove the determinants of these related matrices are zero.