Charles Weibel's Home Page
Teaching Stuff (for more information, see
Rutgers University, the Rutgers
Math Department, and its
Graduate Math Program.
- My schedule
(Addresses, courses, office hours)
- Undergraduate
Course Materials, as well as course material for
- Graduate Algebra Supplementary Materials
Research papers & stuff: This is a link to
some of my research papers. Here are
my research interests and
my Ph.D. Students.
Do you like the History of Mathematics? Here are some articles:
Definition: Proofiness is defined as
"the art of using bogus mathematical arguments to prove something that
you know in your heart is true — even when it's not."
-Charles Seife
I am often busy editing the
Journal of Pure and Applied Algebra (JPAA), the
Annals of K-theory
and the journals
HHA
and JHRS.
Note:
The
Journal of K-theory ceased publication in December 2014.
Link to submit to the
Annals of K-theory
Please donate to the
K-theory Foundation (a nonprofit organization)
Seminars I like:
Links to other WWW sites
Fun Question: How can you prove that
123456789098765432111 is a prime number?
note that 12345678987654321 = 111111111 x 111111111
Fun Facts about Mersenne primes:
In 1644, a French monk named Marin Mersenne
studied numbers of the form $N=2^p-1$,
where p is prime,
and published a list of 11 such numbers he claimed were prime numbers
(he got two wrong).
Such prime numbers are called Mersenne primes.
The first few Mersenne primes are $3,7,31,127$ (corresponding to $p=2,3,5,7$),
but not all numbers of the form $2^p-1$
are prime; Regius discovered in 1536 that p=11 gives the non-prime 2047=23*89.
The next few Mersenne primes are $8191,131071,524287$ (for $p=13,17,19$).
The next few primes $p$ for which
$2^p-1$
is not prime are p=23 and p=37
(discovered by Fermat in 1640), and p=29 (discovered by Euler in 1738).
Mersenne primes are the largest primes we know.
By 2014, the list of the first 44 Mersenne primes was verified;
we don't know what is the 45th smallest, even though a handful of
larger Mersenne primes are known.
For years, the Electronic Frontier Foundation (EFF) offered a $50,000 prize
for the first known prime with over 10 million digits.
The race to win this prize came down the wire in Summer 2008, as the
45th and 46th known Mersenne primes were discovered in within 2 weeks
of each other by the UCLA Math Department (who won the prize) and an
Electrical Engineer in Germany, respectively.
The largest known Mersenne primes are the
48th, which has 17 million digits and p=57,885,161;
the 45th has 13 million digits and p=43,112,609.
A new Mersenne prime was discovered in 2016 with p=74,207,281;
it has 22 million digits.
(Each prime $N=2^p-1$
has $p\log_{10}(2)$ digits.)
For more information, check out the
Mersenne site.
Charles Weibel /
weibel @
math.rutgers.edu /
May 31, 2015
MATHJAX test:
$\partial y/\partial t=\partial y/\partial x$, $\sqrt2=1.4141$,
$\forall n\in\mathbb{N}, e^n\in \mathbb R$
If $f(t)=\int_t^1 dx/x$ then $f(t)\to\infty$ as $t\to\infty$
HTML 4 font rednering:
∂y/∂t = ∂y/∂x √2 =1.414
If f(t)= ∫_{t} ^{1} dx/x then
f(t) → ∞ as t → 0. This really means:
(∀ε ∈ℝ, ε>0) (∃δ>0)
f(δ) > 1/ε .
ℕ (natural numbers), ℤ (integers), ℚ (rationals),
ℝ (reals), ℂ (complexes)
The ndash (–) is & #150; , & #8211; and & ndash; !
I prefer the longer —, which is & mdash; or & #151;.