14,577 reputation
11938
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 1 month
seen 5 hours ago

Aged mathematician


Nov
19
comment Polynominal odd function
What is $y$? If it’s a variable, I don’t see how $x-y$ can divide a polynomial without any $y$’s in it.
Nov
19
comment Questions about poles
This is my way of doing it, but it’s really “power-series division”, ’cause you write the terms in ascending order of degree rather than descending.
Nov
19
comment Questions about poles
Surely $g(z)=1/z$ has a pole of order one at the origin. So “our definition” is clearly wrong.
Nov
19
comment a question about integration $\int_{0}^{1} \int_{0}^{1} \sqrt{x dx - dx dy}$
Doesn’t look grammatical to me.
Nov
18
comment gcd of polynomials over Z_7
I was about to say the same thing as @Crostul, but in more words. Your error, if any, was to pay too much attention to the quotients. It’s just the remainders that count, here.
Nov
17
comment Implicit differentiation: $\ln(1+xy) = xy$
This is how I saw the problem, too.
Nov
17
answered Proving that the Gaussian integers have no zero divisors
Nov
15
comment Find all the values of $w$ ∈ C that satisfy the equation.
Yes I did. $a=1$, $b=-4i$, $c=-1$.
Nov
15
comment is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
This is kind of sketchy. At first I thought it was the way to go, now I’m not so sure.
Nov
15
answered Find all the values of $w$ ∈ C that satisfy the equation.
Nov
14
comment having trouble saying this in a rigorous way
One way is to go by contradiction. Suppose the negative of what you want to show, i.e. that $f(x)\ge0$ throughout some neighborhood of the form $[0,a\rangle$. Then the difference quotient is $f(x)/x$, quotient of a nonnegative by a positive, result being nonnegative. But nonnegative numbers can not have a negative limit $f'(0)$.
Nov
14
answered How do you find the imaginary roots of a fourth degree polynomial that cannot be simplified?
Nov
12
comment What is the name of this proof of, “$\sqrt{2}$ is irrational”?
Well, all the worse for the author, because the FTA does require a proof: it’s by no means trivial, as you’ll see when you go through a proof.
Nov
12
comment What is the name of this proof of, “$\sqrt{2}$ is irrational”?
This proof uses the Fundamental Theorem of Arithmetic, which says that there is essentially only one way of expressing an integer as a product of primes; in particular, the number of factors of the prime $2$ does not depend on how you factorize your original number. The proof of the irrationality of $\sqrt2$ is implicit, once one has the FTA. But I think your text is deficient in not pointing out that this Theorem has been used: it’s not so clear at the outset that the number of $2$’s in a number is well-defined.
Nov
12
comment Weak Mathematical Induction for Modulo Arithmetic
You have written some things that are not grammatical, and so show only a partial understanding of the concepts. When you write “$a|b$”, you have made a statement that’s either true or false. It doesn’t have a value. So, “$8|8$” is true, but nothing you have written is equal to zero.
Nov
11
comment Writing the sum of two rational functions as a single rational function.
For common denominator you can always use the product of the separate denominators.
Nov
11
answered How would I calculate the area of a rectangle on a sphere using vertical and horizontal angles?
Nov
11
comment How would I calculate the area of a rectangle on a sphere using vertical and horizontal angles?
Since the edges of the picture are straight lines, your “rectangle” is unquestionably bounded by geodesics. I’ll give a solution based on inputs that make the calculation comparatively easy. Soon.
Nov
10
comment Proving a surjection. Clarification
Very unclear indeed. But this is the way it always is when we’re just beginning to understand. One of the big challenges in mathematics is to improve our understanding so that we can explain with clarity.
Nov
10
comment How would I calculate the area of a rectangle on a sphere using vertical and horizontal angles?
Of course you can’t put a name tag on a balloon, because you would be making it crimp as you stuck it on. We need much more information. How do you describe your rectangle? By its vertices? By the lengths of its sides? By its height and its width? (This is not the same as the previous!) Are its sides “straight”, i.e. are its sides what you would get by looking at a straight line hanging in space? The lines of latitude, parallel to the equator, are not “straight” in this sense, i.e. they are not geodesics.