REU Number Theory Seminar
Wednesdays and/or Thursdays, 1 pm - 2 pm, Room 159 Altgeld Hall
This seminar is aimed primarily at the participants of the
REU Number Theory Program, but anyone is welcome to attend.
The purpose of the seminar is twofold:
- Give participants of the program an opportunity
to present research they have done and serve as a practice forum
for possible talks at national meetings.
- Expose program participants to the local number theory scene by
having faculty and perhaps graduate students present accessible talks
on topics related to their research interest.
The seminar will be held Thursdays, with additional sessions on
Wednesdays if necessary, and will continue through the end of July.
Schedule
- Thursday, June 20, 1 - 2 pm, 159 AH:
Jeremy Rouse (Harvey Mudd College), Recounting Fibonacci Identities
- Thursday, June 27, 1 - 2 pm, 159 AH:
Sharon Chuba (Penn State University), Partitions for dummies.
Abstract.
This talk is an introduction to Partitions and MacMahon's Omega function.
The first part will be a basic introduction to Paritions for those
unfamiliar with the subject. The remainder of the talk will feature
MacMahon's Omega function, found in his book "Introduction to Combinatory
Analysis" (1920), and include a basic overview of the function and examples
of its use. Those unfamiliar with this function might want to click
here for a sneak peak.
This talk is based on a 2001 MASS course (Penn State) taught by Prof.
George E. Andrews.
- Wednesday, July 3, 1 - 2 pm, 159 AH: Professor Scott
Ahlgren, Three term recurrences for the coefficients of infinite
products
- Wednesday, July 10, 1 - 2 pm, 159 AH:
Professor Doug Bowman, Adding fractions the wrong way: an introduction
to Farey series
- Thursday, July 11, 1 - 2 pm, 159 AH:
Professor Harold Diamond, Elementary methods in prime number theory
Abstract.
The Prime Number Theorem provides an asymptotic estimate of
how many prime numbers lie in an interval. This is a survey of prime
number theory by `elementary' (= real variable) methods. We start
with Euclid, take a big jump to Euler, and then move on to work of
Chebyshev, and the proofs of the Prime Number Theorem of Selberg and
Erdos.
- Wednesday, July 17, 10 am - 11 am, 345 AH:
Special Talk:
Professor Bruce Reznick, "You've proved a theorem, now
what?"
Abstract. For the last several years, the speaker has offered a
seminar here called "Introduction to Mathematical Research". This talk
will present some techniques for assisting in the three key activities
of problem-solving, question-asking, and knowledge-finding. Specific
examples will be stressed.
- Wednesday, July 17, 1 - 2 pm, 159 AH:
David Dueber (UIUC), Harmonic Numbers
- Thursday, July 18, 1 - 2 pm, 159 AH:
A.J. Hildebrand, How to sum $\sum_{n=1}^\infty \mu (n)$
- Wednesday, July 24, 1 - 2 pm, 159 AH:
Paul Pollack (Univ. of Georgia),
Some consequences of the prime k-tuples conjecture
- Thursday, July 25, 1:30 - 2:30 pm, 159 AH:
Professor Ken Stolarsky, Euler, Fibonacci, and the Great GCD mystery
- Friday, July 26, 1:00 - 2:30 pm, 159 AH:
Double header:
Aleck Johnsen (UIUC), Differentiating sequences;
Rich Astudillo (UIUC), Change sequences and palindromes
in Thue-Morse type sequences, with a splash of derivatives
Friday, August 2, 1:00 - 2:40 pm, 341 AH (note date and room
change!): Final presentations
1:00 - 1:30 pm:
Sharon Chuba and Jeremy Rouse, On palindromes and prepalindromes
1:40 - 2:40 pm:
Aleck Johnsen, The Thue-Morse sequence on progressions
David Dueber and Erin Wolf, The Thue-Morse sequence on primes
Paul Pollack, Consecutive values of the Thue-Morse sequence
Last modified: Mon 29 Jul 2002 02:27:44 PM CDT
ajh@uiuc.edu