5,556 reputation
1931
bio website
location Bergen, Norway
age 50
visits member for 1 year, 10 months
seen 11 hours ago

Apr
16
reviewed Leave Open Proving that $\sum_{k=0}^n\frac{1}{n\choose k}=\frac{n+1}{2^{n+1}}\sum_{k=1}^{n+1}\frac{2^k}{k}$
Apr
16
reviewed Close an example of almost uniformly convergence
Apr
9
comment Are infinitesimals dangerous?
@leonbloy The idea was put on an official list of censored opinions, kept by the Jesuits. It can be compared to the index of prohibited books, but with a more limited scope. Still, you'd better not teach atomism in science classes of any Jesuit college, if you cared about keeping your job.
Apr
6
comment doubt about definition of holomorphic polynomials
Surely, you are guessing it right. In other words, $f(z)=f(z_1,z_2)=az_1^2+bz_1z_2+z_2^2$. There is no other sensible interpretation.
Apr
4
comment Should I do all the exercises in a textbook?
@Graduate I'd probably skip that one too...
Apr
4
comment Should I do all the exercises in a textbook?
Two exercises that I skipped: "Pick up any book on homological algebra and prove all the theorems without looking at the proofs in the book" (Serge Lang's Algebra), and "Do any fifty problems in Kelley's book" (Reed and Simon about John Kelley's Topology).
Mar
20
comment Evaluating $\int \frac{\operatorname d \! x}{\sin^4{x}+\cos^4{x}+\sin^2{x}\cos^2{x}}$
I don't think that is correct. The substitution $u=\tan(x)$ would be the Weierstrass substitution, or the tangent half-angle substitution as Wikipedia calls it, since $x$ is half of $2x$. It always works for integrals of this type, but often leads to heavy work. The tangent substitution, which I have used, will work when all sines and cosines are raised to even powers, and can then be expected to give less work than the Weierstrass substitution, just as in this case.
Mar
20
comment Sources on Hamilton's Discovery of Quaternions
This story is told by van der Waerden (with the same references as in the link above) in A History of Algebra From al-Kwarizmi to Emmy Noether‌​, pp. 179-183.
Mar
20
answered Evaluating $\int \frac{\operatorname d \! x}{\sin^4{x}+\cos^4{x}+\sin^2{x}\cos^2{x}}$
Mar
20
comment Evaluating $\int \frac{\operatorname d \! x}{\sin^4{x}+\cos^4{x}+\sin^2{x}\cos^2{x}}$
The two expressions are not equal. Note that $1+({\sin(2x)\over 2})^2=1+\sin^2(x)\cos^2(x)\neq \sin^4(x)+\cos^4(x)+\sin^2(x)\cos^2(x)$.
Mar
7
awarded  Nice Answer
Mar
5
answered Examples of mathematical results discovered “late”
Feb
22
reviewed Leave Open Rational Number Proof
Feb
22
reviewed Close P(A) $\subset$ P(B) implies A $\subset $ B proof or disproof.
Feb
20
comment who invented division and why we do division in those steps told?
@HagenvonEitzen The Babylonians did not use long division. In fact, it would have been rather cumbersome in base 60. In computing $a/b$, they would use a table of inverses to find the sexagesimal expansion of $1\over b$, or at least a decent approximation of it, and then they would multiply $a\cdot{1\over b}$. For this they had rather extensive multiplication tables.
Feb
11
reviewed Leave Open combination and permutation !!!!
Feb
11
reviewed Leave Open What is the probability to win? Die game
Feb
11
reviewed Leave Open This question on right triangles.
Feb
11
reviewed Leave Open Prove: For any 2 coloring of 2-space, one of the color classes contains points at all distances
Feb
11
reviewed Leave Open Why can we assume that the expected value of the error term is zero?