The Rose Mathematics Seminar

Overview

The Rose-Hulman Mathematics Seminar meets on a regular basis throughout the year per the schedule below. The seminar is quite informal and so the topics are likely to vary from week to week .  Anyone --- student, faculty, or visitor --- is encouraged to give a talk or series of talks on any topic of interest.  We're especially happy to have students attend or better yet, give talks! Students can get credit for attending and giving talks, by signing up for MA450. For seminars in past years go to the seminar history page. Here is a printable campus map if needed by our off-campus visitors.

Also of interest: Here is the seminar page for our sister institution Indiana State University.

• Regular Day and Time (Fall 2007-08): Wednesday, ninth hour 3:25 - 4:20 p.m
• Place: G219
• Organizer: David Finn dave.finn@rose-hulman.edu   (812) 877-8393

Current and Upcoming Schedule (latest first)

• Topic:  Generalizations of Niven Numbers
• Speaker:  Robert Lemke Oliver, Rose Student
• Date:  14 May 2008
• Abstract:  A Niven number is an integer that is divisible by the sum of its base q digits. For example, 2008 is Niven both in base 3 and in base 5 (see abstract). Several people have derived asymptotic formulae for the function N(x) that counts the number of Niven numbers less than x. We proceed in a more general case, studying functions that act only on the base q digits of an integer. An asymptotic formula for the counting function of these generalized Niven numbers is known, but the question of divisibility by multiple functions is still open. We present partial work toward acquiring an asymptotic formula in this case, as well as conjectures based off of numerical evidence.
  For more information see Announcement/Abstract/Paper in PDF form

• Topic:  A Generalization of the Fibonacci and Jacobsthal Sequences
• Speaker:  Ian Rogers, Rose Student
• Date:  07 May 2008
• Abstract:  Among the sequences of discrete mathematics, the Fibonacci sequence is probably the most well-known. Turning up in myriad areas from geometry to graph theory, seashells to the stock market, the Fibonacci numbers display an amazing number of interesting properties. The Jacobsthal numbers, another well-known sequence, are defined by a different, yet closely related, recurrence relation to that of the Fibonacci numbers. While slightly less popular, the Jacobsthal numbers too display many desirable properties. In this talk, we will describe a new class of generalizations of the Fibonacci and Jacobsthal numbers. We then look at a few examples in which the Fibonacci and Jacobsthal numbers are known to occur, and expand them to produce the new sequences. Finally, we show that many of the desirable properties of the Fibonacci numbers still hold in the general case, and provide suggestions for further research into this new family of sequences.

• Topic:  Total Variation Image Restoration
• Speaker:  Ely Spears, MIT Lincoln Labs - Rose Alum
• Date:  26 Mar 2008
• Abstract:  One of the most widely studied areas of applied mathematics is image processing. Image restoration, also called image inpainting, is one of the most prominent uses for these mathematical techniques. In this talk, a particular procedure for restoring damaged or corrupted images, called total variation, is discussed. Most of the material will be accessible to students familiar with linear algebra. A brief description of numerical methods, in particular the Fast Level Set Transform, is included.

• Topic:  Modeling a Slice of French Bread
• Speaker:  David Finn
• Date:  23 Jan 2008
• Abstract:  Why does a slice of French or Italian bread have a somewhat elliptical shape? In this talk, I will provide a heuristic model to describe the shape based on treating dough as a liquid. Then from data from slices of bread, I will show that this model provides a good description of a slice of bread.

• Topic:  Generalized Difference Sets on Positive Integers
• Speaker:  Tanya Jajcay
• Date:  16 Jan 2008
• Abstract: 
  For more information see Announcement/Abstract/Paper in PDF form

• Topic:  Introduction to the Life Table
• Speaker:  Casimir G.Ksiazek III, Rose Student, Mathematics
• Date:  19 Dec 2007
• Abstract:  Buying life insurance is a quite a common occurrence. But how do people determine how much life insurance premiums should cost? Historically, actuaries have used life tables to assist in pricing insurance and annuities. In this talk, the concept of a life table will be introduced. In addition, examples will be given to show how from seemingly simple data, quantities such as life expectancy and insurance premiums can be calculated. A knowledge of probability is recommended, but not required. Anyone interested in actuarial science is strongly encouraged to attend.

• Topic:  Introduction to Infinity or Why Johnny Can't Add
• Speaker:  Bill Butske
• Date:  07 Nov 2007
• Abstract:  First I want emphasize that this talk is for anyone who has wondered what mathematics has to say about the concept of infinity. In particular non-math majors are encouraged to attend and the talk is aimed primarily at them. I'm going to talk about infinity in two ways, first in counting, where we will see that there are two different kinds of infinity (at least) and second in geometry where we know that parallel lines DO intersect, namely at infinity. Of course this is a math talk and the underlying intent is to warp your mind.

• Topic:  FETCHING WATER WITH MINIMUM RESIDUES: Generalization of a problem from Die Hard 3
• Speaker:  Herb Bailey, Emeritus Rose Math professor
• Date:  31 Oct 2007
• Abstract:  Bruce Willis can disarm a bomb if he is able to get exactly 4 gallons of water from a well using only a 3 gallon jug and a 5 gallon jug. This problem dates back to the 13th century. A generalization of this problem is to determine all possible integer gallons that can be obtained using an M gallon jug and an N gallon jug, with M < N. We solve the generalized problem using some congruence results. It turns out that there are only two distinct pouring sequences to get a given number of gallons. The shorter of the two can be determined by solving a linear congruence equation. Short is good since Bruce has but 5 minutes prior to detonation. Not to worry, no previous knowledge of number theory will be needed to enjoy this talk.

• Topic:  Blow-up Solutions to Differential Equations
• Speaker:  Kurt Bryan
• Date:  24 Oct 2007
• Abstract:  Nonlinear differential equations of the form u' = f(u) where u=u(t) are common in applied mathematics. Usually t is time, u(t) is the amount of some "stuff" in a system, and f(u) models the rate stuff is produced or destroyed, as a function of the amount present. If the function f is positive and increasing (the stuff catalyzes its own production) then solutions may grow to infinity in a finite time, a phenomena called "blow-up". In this talk I'll start with the simple ODE above, then describe some recent progress in analyzing blow-up phenomena for similar partial differential equations in which diffusion is present.

• Topic:  Models for Emergent Behavior
• Speaker:  Ely Spears, Rose Student, Mathematics
• Date:  17 Oct 2007
• Abstract:  Emergent behavior is a division of biology that seeks to understand and better explain phenomena that appear in group situations but not on an individual basis. Fish schooling, bacterial growth properties, and bird flocking are just a few prominent examples of this sort of behavior. The latter of these examples motivated summer research at the City University of Hong Kong, in China. This introductory presentation will give the details behind some popular mathematical models for bird flocking behavior. Additionally, numerical simulations of these models will be discussed at length and the various model parameters will be explored. The talk is such that students of any background are encouraged to attend.

• Topic:  Generalized Niven Numbers
• Speaker:  Robert Lemke-Oliver, Rose Student, Mathematics
• Date:  27 Sep 2007
• Abstract:  A base-q Niven number is one which is divisible by the sum of its digits. For example, 18 is a base 10 Niven number, since 9 divides 18. We will be interested in simultaneous Niven numbers, numbers that are Niven in more than one base. Returning to the example, 18 is also base 9 Niven, since 18 is 20 in base 9. Thus, 18 is a simultaneous base 9 and base 10 Niven number. We are interested in counting the number of simultaneous Niven numbers up to a point, x. One approach to this is to look at completely q-additive functions. These functions essentially act on the digits of a number, so that f(124)=f(1)+f(2)+f(4). Note that the sum of digits function is completely q-additive. If we can understand these generalized Niven numbers, we can hopefully gain some information about the standard Niven numbers. In this talk, we will prove an asymptotic formula for the number of generalized Niven numbers, and we will present the work that has been done to relate this to Niven numbers.