Teaching Stuff (for more information, see Rutgers University, the Rutgers Math Department, and its Graduate Math Program.
Research papers & stuff: This is a link to some of my research papers. Here are my research interests and my Ph.D. Students.
I am often busy editing the Journal of Pure and Applied Algebra (JPAA), the Annals of K-theory and the journals HHA and JHRS.
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
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 in his honor.
The first few Mersenne primes are 3,7,31,127 (corresponding to p=2,3,5,7),
The next few Mersenne primes are 8191, 131071, 524287 (for p=13,17,19).
(Each prime N=2^{p}-1
has p log_{10}(2) digits.)
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 primes p for which 2^{p}-1
is not prime are p=23 and p=37 (both discovered by Fermat in 1640),
and p=29 (discovered by Euler in 1738).
Mersenne primes are the largest primes we know.
The largest known prime is the 51st Mersenne prime,
with p=82,589,933; it has over 24 million digits
and was discovered by an IT professional in December 2018.
The next largest known prime is the 50th Mersenne prime,
discovered in December 2017 using a Tennessee church computer;
it has 23 million digits and p=77,232,917.
Other recently discovered Mersenne primes are the
49th (2016) with 22 million digits and p=74,207,281;
the 48th (2013) with 17 million digits and p=57,885,161;
and the 47th, which has 13 million digits and p=43,112,609.
For years, the Electronic Frontier Foundation (EFF) offered a $50,000 prize
for the first known prime with over 10 million digits;
the 44th had 9.8 million digits and p=32,582,657.
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 46th had p=42,643,801 and the 45th has p=37,156,667.)
For more information, check out the
Mersenne site.
HTML 4 font rendering:
∂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;.