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:
I am often busy editing the
Journal of Pure and Applied Algebra (JPAA), the
Journal of
K-theory
and the journals
HHA
and JHRS.
Seminars I like:
Links to other WWW sites
Fun Question: How can you prove that
123456789098765432111 is a prime number?
Fun Facts about Mersenne primes:
In 1644, a French monk named Marin Mersenne
studied numbers of the form N=2p-1, where p is prime,
and published a list of 11 such numbers he claimed were prime numbers.
Such prime numbers are called Mersenne primes. (He got two wrong.)
The first few Mersenne primes (p=2,3,5,7) are 3,7,31,127, and p=11
gives the non-prime 2047=23*89 (as was discovered in 1536 by Regius).
Not all numbers of the form N=2p-1) are prime, as Regius'
example 2047 (p=11) shows. The next few primes for which N is not prime
are p=23 and p=37 (discovered by Fermat in 1640), and p=29 (discovered by
Euler in 1738).
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 is the
45th, which has 13 million digits and p=43,112,609; the 46th
has 11 million digits.
(Each prime N has p log10(2) digits.)
More recently, the 47th known Mersenne prime was discovered in April 2009
by a Norwegian named Odd Magner Stridmo, with p=42,643,801. Surprisingly,
it is slightly smaller (by 141,000 digits) than the 45th Mersenne prime.
For more information, check out the
Mersenne site.
Charles Weibel /
weibel @
math.rutgers.edu /
July 1, 2009
HTML 3 font test:
∂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)
8810-2 are: ≪ ≫ ≬ while
& sube; is &# 8838; ;
&8838-41; (⊆ ⊇ ⊈ ⊉) &8712; is ∈
Here are some more html fonts: ∗
& #130; – & #139; are
‚ ƒ „ … † ‡ ˆ ‰ Š ‹
The ndash (–) is & #150; , & #8211; and & ndash; !
I prefer the longer —, which is & mdash; or & #151;.
& #160;–& #169; are
¡ ¢ £ ¤ ¥ ¦ § ¨ ©
(& #128; = €)
& #170;–& #191; are
ª « ¬ ® ¯ ° ± ² ³
and
´ µ ¶ · ¸¹º »¼ ½
¾ ¿
& #192; – & #269; are obsolete alphabet font codes.
They are replaced by codes like: & Egrave; for È;
& Eacute; for É; & Euml; for Ë.
(Ì, Ö, Ú are similar.)
For example, & #192;–& #199; are:
À Á ÂÃÄ ÅÆ Ç
