2007-2008 Academic Year Colloquium Schedule

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(Faculty/Staff Only)

August 30, 2007

Title:An Introduction to Parallel Computing
Speaker:David A. Reimann
Associate Professor and Chair
Mathematics and Computer Science
Albion College
Albion, MI

Abstract:Parallel computing employs the use of multiple processors and specialized algorithms to solve problems.Using multiple processors has the potential to improve performance by dividing a task among several processors, thus reducing the amount of work each a processor, in turn reducing the time required to solve a problem.An overview of historical and modern parallel computer architectures will be given.Parallel computers are classified by their connection topology and control mechanisms. The recent development of multi-core machines has the potential to deliver inexpensive parallel computing.However, special algorithms must be developed that break a task into independent components. Because the number and speed of communication channels between processors influences performance, understanding how an algorithm affects communication of information among processors is critical in overall performance.Examples of sequential and parallel algorithms to solve several tasks will be presented to help illustrate these concepts.
Location:Palenske 227
Time:3:10 PM
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September 6, 2007

Title:Planning for Graduate Study in Mathematics and Computer Science
Speaker:David A. Reimann
Associate Professor and Chair
Mathematics and Computer Science
Albion College
Albion, MI

Abstract:A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation.
Location:Palenske 227
Time:3:10 PM
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September 13, 2007

Title:Decoding Nazi Secrets - Part 1
Speaker:NOVA Video

Abstract:Most historians agree that by enabling Allied commanders to eavesdrop on German plans, Station X shortened the war by 2 or 3 years. Its decoded messages played a vital role in defeating the U-boat menace, cutting off Rommel's supplies in North Africa, and launching the D-Day landings. Now, for the first time on television, a 2-hour NOVA Special tells the full story of Station X, drawing on vivid interviews with many of the colorful geniuses and eccentrics who attacked the Enigma. Wartime survivors recall such vivid episodes as the British capture of the German submarine U-110; one of its officers describes how he saved a book of love poems inscribed to his sweetheart but failed to destroy vital Enigma documents on board. Decoding Nazi Secrets also features meticulous period reenactments shot inside the original buildings at Station X, including recreations of the world's first computing devices that aided codebreakers with their breakthroughs. Station X not only helped reverse the onslaught of the Third Reich, but also laid the groundwork for the invention of the digital computer that continues to transform all our lives.See http://www.pbs.org/wgbh/nova/decoding/ for the companion website.

One important note: Cayley Rice has an ongoing research project related to codebreaking at Bletchly Park, the subject of this video. She is looking for students who might be interesting in working with her. Please come to the video and talk to her afterwards for more information.
Location:Palenske 227
Time:3:10 PM
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September 20, 2007

Title:Decoding Nazi Secrets - Part 2
Speaker:NOVA Video

Abstract:Most historians agree that by enabling Allied commanders to eavesdrop on German plans, Station X shortened the war by 2 or 3 years. Its decoded messages played a vital role in defeating the U-boat menace, cutting off Rommel's supplies in North Africa, and launching the D-Day landings. Now, for the first time on television, a 2-hour NOVA Special tells the full story of Station X, drawing on vivid interviews with many of the colorful geniuses and eccentrics who attacked the Enigma. Wartime survivors recall such vivid episodes as the British capture of the German submarine U-110; one of its officers describes how he saved a book of love poems inscribed to his sweetheart but failed to destroy vital Enigma documents on board. Decoding Nazi Secrets also features meticulous period reenactments shot inside the original buildings at Station X, including recreations of the world's first computing devices that aided codebreakers with their breakthroughs. Station X not only helped reverse the onslaught of the Third Reich, but also laid the groundwork for the invention of the digital computer that continues to transform all our lives.See http://www.pbs.org/wgbh/nova/decoding/ for the companion website.

One important note: Cayley Rice has an ongoing research project related to codebreaking at Bletchly Park, the subject of this video. She is looking for students who might be interesting in working with her. Please come to the video and talk to her afterwards for more information.
Location:Palenske 227
Time:3:10 PM
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September 27, 2007

Title:An introduction to Harmonic Analysis and Dispersive Estimates for Schrodinger Operators
Speaker:William Green, Class of `05
Graduate Student
Mathematics
University of Illinois
Urbana-Champaign, IL

Abstract:Harmonic Analysis can be defined as roughly the branch of analysis that arose from the study of Fourier Series and the Fourier Transform. An overview of necessary concepts in analysis, harmonic analysis and spectral theory will be given with an eye towards discussing estimates of certain Schrodinger operators. We will discuss certain estimates of the solution operator to the Schrodinger equation, generally concentrating on results in dimensions 3 and higher. We will end with a discussion of some open questions in the field.
Location:Palenske 227
Time:3:10 PM
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October 11, 2007

Title:Exploring the Best Joke of the 19th Century: The History of Mathematics in Action
Speaker:Deborah A. Kent
Assistant Professor of Mathematics
Mathematics and Computer Science
Hillsdale College
Hillsdale, Michigan

Abstract:The story surrounding of Neptune's discovery provides an excitingillustration of what historians of mathematics do. Neptune was first sightedas a new planet on 23 September 1846 at the Berlin observatory. Thesensational news reached London a week later and the ensuing dispute createdone of the great (and ongoing) priority debates in the history of science.About a month after the initial observation, word of the new planet alsoarrived in America where the controversy captured both popular interest andscientific attention. A handful of nineteenth-century scientists who shareda vision for professionalizing science in America viewed the Neptune affairas an opportunity to establish the legitimacy of American science inresponse to perceived European scientific superiority. While Europeanadministrators of science quibbled over the priority question, the Harvardmathematician Benjamin Peirce — considered an upstart Americanscientist — dared to question the mathematical particulars of the discovery.Recent twentieth-century events and manuscript discoveries furtherilluminate the story of planetary controversy.
Location:Palenske 227
Time:3:10 PM
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October 25, 2007

Title:Image reconstruction in multi-channel model under Gaussian noise
Speaker:Veera Holdai
Doctoral Student
Mathematics
Wayne State University
Detroit, Michigan

Abstract:We will consider the problem of image reconstruction. Starting from some classical problems, we will gradually add some features to them. The main problem of image boundary reconstruction is double nonparametric due to multi-channel model and due to the object of estimation. The large sample asymptotics of the minimax risk will be discussed and asymptotically optimal estimator will be suggested.
Location:Palenske 227
Time:3:10 PM
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November 1, 2007

Title:Abel's Impossibility Theorem
Speaker:Susan J. Sierra
Graduate Student
Mathematics
University of Michigan
Ann Arbor, Michigan

Abstract:

You know the quadratic formula, but what about the cubic formula: if

\begin{displaymath}x^3 + px + q = 0\end{displaymath}

then

\begin{displaymath}x = \omega^i \sqrt[3]{ ‑ \frac{q}{2} + \sqrt{\left( \frac{q......{\left( \frac{q}{2} \right)^2 + \left( \frac{p}{3}\right)^3}}\end{displaymath}

(for $i$ = 0, 1, or 2). Imagine having to memorize that for an exam!

There's also a quartic formula for fourth degree equations. You may have heard, however, that there is no formula to solve a quintic polynomial by adding, subtracting, multiplying, dividing, and taking roots of the coefficients. This was proved by the great Norwegian mathematican Niels Henrik Abel in 1824.

We'll talk about the elegant algebraic structures that encode information about solving polynomials, do a bit of basic group theory and Galois theory, and prove Abel's "impossibility theorem." Time permitting, we'll end with some intriguing mathematical puzzles.

Location:Palenske 227
Time:3:10 PM
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November 8, 2007

Title:How the DFA (deterministic finite automaton) is not
Speaker:Thomas F. Piatkowski
Professor of Computer Science and Electrical and Computer Engineering
Department of Computer Science
Western Michigan University
Kalamazoo, Michigan

Abstract:Automata theory is one of the most mathematical areas of computerscience. Two of the important uses of automata are:
  1. to assist in the study and categorization of formal (computer) languages, and
  2. to specify system behavior standards for implementable discrete systems.
One of the simplest types of automaton is the deterministic finiteautomaton (DFA) — the type used to recognize "regular" languages.Interestingly enough, the classical DFA is
  • not deterministic,
  • not finite, and
  • not an automaton.
The details of this paradoxical contention will be explored usingconcepts of state-system specification.
Location:Palenske 227
Time:3:10 PM
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November 15, 2007

Title:The Fractal Calculus Project
Speaker:Mark M. Meerschaert
Professor and Chairperson
Department of Statistics and Probability
Michigan State University
East Lansing, Michigan

Abstract:

Fractional derivatives are almost as old as their integer-order cousins. Recently, fractional derivatives have found new applications in engineering, physics, finance, and hydrology. In physics, fractional derivatives are used to model anomalous diffusion, where a cloud of particles spreads differently than the classical Brownian motion model predicts. A probability model for anomalous diffusion is based on particle jumps with power law tails. The probability of a jump length larger than $r$ falls off like $r^{-\alpha}$ as $r\to\infty$. For $0<\alpha<2$ these particle jumps have infinite variance, indicating a faster than usual spreading rate. Particle traces are random fractals whose dimension $\alpha$ equals the power law tail exponent. A fractional diffusion equation for the concentration of particles $c(x,t)$ at time $t$ and location $x$ takes a form


\begin{displaymath}\frac{\partial c(x,t)}{\partial t}=\frac{\partial^\alpha c(x,t)}{\partial x^\alpha}\end{displaymath}

that can be solved via Fourier transforms. Fractional time derivatives model particle sticking or trapping in a porous medium. In finance, price jumps replace particle jumps, and the same models apply. In this talk, we give an introduction to this new area, starting from the beginning and ending with a look at ongoing research.

Location:Palenske 227
Time:3:10 PM
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November 29, 2007

Title:Summer and Off-Campus Programs
Speaker:David A. Reimann
Associate Professor
Department of Mathematics and Computer Science
Albion College

Abstract:Have you ever wondered if you can study mathematics and/or computer science off-campus? Either during the summer or during the academic year? Each year a number of high-quality academic opportunities are availableto Albion College students. Options include research/study internships at
  • academic institutions both within the United States and abroad,
  • numerous federal government agencies, and
  • a number of government scientific laboratories.
In this presentation we will tour a new portion of the Albion College Math/CS website that illustrates these various opportunities as well as provide adviceon how to apply, deadlines, any other pertinent information.
Location:Palenske 227
Time:3:10 PM
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January 31, 2008

Title:Non-Inferiority: the Basics, a Saga, and Maybe an Opportunity
Speaker:Tom C. Venable, Ph.D.
Lecturer
Department of Statistics
University of Michigan
Ann Arbor, Michigan
Abstract:In clinical trials, using placebo is unethical in many therapeutic areas. In turn, non-inferiority studies are common. An experimental drug is compared against an active-control, that is, a gold standard. Simply said, we move from hypothesis testing to demonstrate that a new drug is superior to placebo to the use of confidence intervals to demonstrate that a new drug is not-inferior to the standard. However, these studies are challenging, especially in the necessary sample size, the choice of the standard and the margin itself, plus doing so in an extremely regulated environment.

This non-technical presentation includes the basics of superiority and non-inferiority study designs, their pros and cons, their methodologies, a non-inferiority story, plus an opportunity for continued research.
Location:Palenske 227
Time:3:10 PM
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February 7, 2008

Title:Computer Generated Effects for Film
Speaker:Joseph Cavanaugh
Visual Effects Technical Director
Sony Imageworks
Los Angeles,, CA
Abstract:The speaker will give an overview of how a blend of art and technology is used to create computer generated effects for film. These effects range from elemental effects such as fire and water to dynamics effects such as crumbling and breaking objects. He will touch on the basic application of the mathematics used to create computer generated effects. He will show examples from recent movies such as Beowulf and Spiderman 3.
Location:Palenske 227
Time:3:10 PM
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February 14, 2008

Title:A Brief Introduction to Monte Carlo Simulations
Speaker:Fatih Celiker
Assistant Professor
Mathematics
Wayne State University
Detroit, Michigan, USA
Abstract:In this talk I will give a brief introduction to Monte Carlosimulations. A short overview of some theoretical considerations willbe followed by numerous examples coming from various areas of math,science, engineering, and finance. In their basic form, thesesimulations are extremely easy to generate, and for that matter theyhave found numerous applications in areas where randomness play acrucial role. Some examples are, simulation of Bernoulli's experiments(coin flip), the birthday problem, traffic flow, random walk, Brownianmotion, neutron shielding, financial option pricing, and insurancepricing. Moreover, applications generalize to deterministic problemssuch as computation of areas and volumes, approximating solutions ofpartial differential equations, approximating the value of the numbermathematical constants such as pi and e, and optimization problems areonly some of these.
Location:Palenske 227
Time:3:10 PM
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February 21, 2008

Title:What is an Actuary?
Speaker:Dustin Turner, ’06
Actuarial Analyst
Actuarial Department
North Pointe Holdings Corporation
Southfield,, MI
Abstract:In this talk I will give a broad overview of the actuarial profession. Many math majors have heard of the actuarial profession, but few are quite sure of what it entails. I will discuss the process of becoming a credentialed Actuary, while focusing on the responsibilities and perks of entry-level Actuarial Analyst positions. I will also be presenting examples of some fundamental actuarial exercises, including insurance pricing and loss reserving.
Location:Palenske 227
Time:3:10 PM
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February 28, 2008

Title:Careers in Mathematics and Computer Science
Speaker:David A. Reimann
,
Associate Professor and Chair
Mathematics and Computer Science
Albion College
Albion, MI
Abstract:A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation. Slides from the talk are available at http://zeta.albion.edu/~dreimann/talks/careers/careers.html.
Location:Palenske 227
Time:3:10 PM
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March 6, 2008

Title:Conjecture and Proof
Speaker:Dennis Ross, ’08
Senior Mathematics Major
Mathematics and Computer Science
Albion College
Albion,, MI
Abstract:Problem solving is a fundamental skill in mathematics. However, not all problems are created equally. In this interactive colloquium we will explore several seemingly innocuous problems and discover the underlying combinatorial or number theoretic structures. We will also explore the concept of Grundy Numbers (Nimbers) and their relation to bizarre combinatorial games.
This is an accessible talk to mathematicians and computer scientists of all levels, and remember to bring a pencil.
Location:Palenske 227
Time:3:10 PM
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March 27, 2008

Title:Markov Processes: Markov Chains, Poisson Processes, Brownian Motion
Speaker:Nadiya Fink
Visiting Assistant Professor
Mathematics and Computer Science
Albion College
Albion,, MI
Abstract:The Markov property indicates that, with knowledge of the current state, previous trajectories are irrelevant for predicting the probability of the future of a process. A Markov chain is a discrete-time stochastic (i.e. random) process possessing the Markov property. Probabilities and expected values on a Markov chain can be evaluated by a technique called First Step Analysis. An analogous technique can be applied to continuous-time processes. We will discuss an elementary introduction to Markov chains and First Step Analysis, followed by a broader description and discussion of the long-term behavior of Markov chains. Further, we will get acquainted with the Poisson Processes which are continuous-time processes with finite number of states, and, finally, will overview the continuous processes and their applications.
Location:Palenske 227
Time:3:10 PM
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April 3, 2008

Title:Arctangent Identities for Pi
Speaker:Jack Calcut
Research Scientist
Interactic Holdings
Austin,, TX
Abstract:Is there a better identity for pi than pi=4arctan(1)? Are the degree angle measures ever rational in a triangle whose side lengths form a Pythagorean triple? Which regular polygons may be built on a geoboard? The answers to these questions are intimately related to arctangent identities for pi, which we will explore using the number theory of the Gaussian integers. We will present some of the historical context as well as some directions for further research.
Location:Palenske 227
Time:3:10 PM
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April 17, 2008

Title:Life isn't Fair: A Mathematical Argument in Favor of Benevolent Dictatorships
Speaker:Cayley Rice
Assistant Professor
Mathematics and Computer Science
Albion College
Albion, Michigan, USA
Abstract:Arrow's theorem, proved in the '50s, suggests that under very reasonable restrictions, the only sensible method of societal decision making is dictatorial. In this talk we'll explore a few different models of voting, how theoretical math can be applied to models of voting, and just how un-sensible voting models can get. A part of the talk will develop notation to discuss voting scenarios in mathematical notation. We'll see how the language of abstract mathematics can be deftly applied to problems like this and, while the notation may be quite complicated, the subsequent mathematics is often already understood. This talk is in recognition of Math Awareness Month (as determined by the AMS, MAA, and SIAM to be April), whose theme this year is math and voting.
Location:Palenske 227
Time:3:10 PM
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May 1, 2008

Title:How the 2007 LMMC Albion Math Team captured the infamous Klein Cup
Speaker:Jeremy Troisi, '08
Student, Mathematics Major and Economics and Management Major
Albion Colleg
Albion, Michigan, USA
Abstract:The test administered for the Lower Michigan Mathematics Competition (LMMC) in the Spring of 2007 contained a very strong focus on Proof by Mathematical Induction, often dubbed 'Induction', compared to past LMMC examinations. Being able to solve such problems quickly as well as a simple combinatorics problem, a simple bounding problem, and a college geometry problem within three hours assured victory. I will go over a complete solution process through a few of these problems and describe a few other problems time permitting.
Location:Palenske 227
Time:3:10 PM
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