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Florida Section Newsletter The Mathematical Association of America February 2006 Volume 27, Issue 2 |
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Florida Section Newsletter The Mathematical Association of America February 2006 Volume 27, Issue 2 |
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President's Message Florida Section Stephanie Fitchett |
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I hope you all had a relaxing and enjoyable holiday season and are now back in the groove of things. The most important message I can send is that you and your students should attend the Joint Meeting of FL-MAA and FTYCMA on February 17th and 18th on the Jupiter campus of Florida Atlantic University.
Our program chair, Li Zhou from Polk Community College, has developed a rich program of contributed papers, plenary sessions, and workshops. Many thanks to Li and to Terje Hoim and the local organizing committee at FAU-Jupiter. The meeting is clearly going to be terrific!
An advance copy of the preliminary program is available in this newsletter. As in previous meetings, a final hard-copy version of the program will be distributed with your registration materials.
I would like to highlight a few things about the Joint Meeting. The conference begins Friday morning with a FTYCMA workshop and luncheon, followed by the first of four outstanding speakers, Underwood Dudley, who will speak on "Formulas for Primes". There will be three sessions of contributed papers and a special problem-solving session in the afternoon. At the end of the afternoon, we have our second plenary address by Steve Dunbar, who will speak on "The MAA American Mathematics Competitions: Easy Problems, Hard Problems, History and Outcomes".
There will be a conference banquet and awards ceremony on Friday evening, at which I invite "professionally young" mathematicians (those in roughly the first five years since graduation) to join a table of similarly situated colleagues to discuss the possibility of some section-level activities for early-career professional development. Our banquet dinner will be followed by our third special speaker, Hans-Dietrich Gronau, speaking on "Mathematical Olympiads - International and National".
On Saturday morning, we have three sessions of contributed papers and a student integration contest, followed by our final invited speaker, James Tanton, whose title is "More than a Dozen Proofs that 1=2: A Misguided Review of all of Mathematics." We end the day with the MAA business meeting and luncheon.
Of course, an integral component of the meeting is the richness and depth of the contributed papers. As you can see in the program, every kind of school in the state is represented and the papers are arranged, time-wise, so that everyone can find something of interest to them.
And … remember the mystery raffle at last year’s meeting? There just may be another!
We are also grateful for the support and participation of several publishers. Please stop by the exhibits, take a look at the books, and thank our book representatives for their support!
Finally, a few logistical notes. Because of spring training and a local art festival, hotels in the Jupiter area fill early at this time of year, so PLEASE book your rooms as soon as possible. Also, it helps us tremendously in planning (and saves you money!), if you pre-register, so I encourage you to do so. Finally, because of a local art festival being held near campus on Saturday and Sunday, parking may be tricky on Saturday morning. Please let the police at the entrance to FAU’s parking lot know that you’re attending the MAA conference and they’ll let you in!
I look forward to seeing you all next month!
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Florida Section The Nominating Committee is pleased to forward the following slate of officers for election at the annual business meeting of the Florida Section of the MAA.
In accordance with our bylaws, this slate will be presented to the section for election on February 18, 2006, but nominations from the floor can be submitted for any of these positions. Scott Hochwald |
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FL-MAA
Florida Section |
Jupiter Campus |
 FTYCMA Florida Two-Year College Mathematics Association |
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February 17-18, 2006 |
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| The 2006 Joint Annual Meetings will
bring together Florida’s dedicated mathematicians, professional and
non-professional, for a weekend of exciting lectures, talks, and
discussions on a variety of mathematical topics. The plenary speakers for the conference will be Underwood Dudley, Steve Dunbar, Hans-Dietrich Gronau, and James Tanton. Underwood Dudley is a native of New York City, was an undergraduate at the Carnegie Institute of Technology, and was given a Ph.D. degree by the University of Michigan in 1965. After teaching in Ohio and Indiana for thirty-nine years, he saw the light and moved to Florida. He has edited the College Mathematics Journal, written four books, and is proud of having an Erdos number of 1. For more information, visit http://www.maa.org. Steve Dunbar received a bachelor's degree in mathematics at the University of Nebraska, doctorate at the University of Minnesota in 1981, and returned to the University of Nebraska-Lincoln in 1985. His research interests are in nonlinear differential equations and applications of mathematics in all areas. In 2001, Professor Dunbar was appointed as Director of the American Mathematics Competitions. For more information, visit http://www.math.unl.edu/~sdunbar/. Hans-Dietrich Gronau, President of Mathematik-Olympiaden e.V. and German IMO Team Leader, will give a talk on Mathematical Olympiads - International and National. He will also be one of the presenters during the Special Session on Problem Solving. For more information, visit http://www.mathematik-olympiaden.de/. James Tanton, after receiving his Ph.D. from Princeton in 1994, followed the usual track of Visiting/Assistant/Associate Professor at three different institutions New College of the University of South Florida, St. Mary’s College of Maryland, and Merrimack College. However, he was soon lured away by the joys of interacting with, teaching, being taught by, and publishing research articles with younger students, K – 12, at the Boston-based Math Circle. During those three years, Dr. Tanton also worked as a consultant for various teacher-training programs and college and secondary text-book editors, all under the pretext that he actually knew something about the state of secondary-level mathematics education. He didn’t. He eventually decided to try practicing what he preached by heading into the secondary scene. Dr. Tanton worked at Milton Academy for a short stint and now finds himself to be a regular high-school teacher at St. Mark’s School in Southborough, Massachusetts. He has never worked harder in any aspect of his mathematical career and is still in a state of shock over what he is really learning about life as a high-school math teacher. And just to keep sanity completely out of reach, Dr. Tanton is also the founding director of a new Institute of Mathematics at St. Mark’s School. For more information, visit http://www.stmarksschool.org/smtoday/math/. In addition to these four distinguished plenary speakers, there will be invited talks by some of the state’s leading mathematics professionals as well as student presentations. Other events include:
More information will be available soon. |
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
| Friday, February 17, 2006 | ||||
| 8:00-10:45 EC 101 & 102 |
FTYCMA Workshop Implementing the Developmental Plan - Let's Get Started! |
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| 11:00-12:30 EC 101 & 102 |
FTYCMA Business Meeting and Luncheon | |||
| 12:45-1:00 AD 119 |
Presidential Welcomes Stephanie Fitchett, President, FL-MAA Martha Goshaw, President, FTYCMA Kristen Murtaugh, Vice President, Florida Atlantic University - North Campuses Mark Tunick, Interim Associate Dean, Florida Atlantic University - Honors College |
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| Plenary Session 1:00-1:50 AD 119 |
Formulas for Primes Underwood Dudley, Tallahassee MAA Pólya Lecturer, 1995-96 & 1996-97 |
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| Contributed Paper Sessions | AD 204 | AD 205 | AD 206 | AD 102 (Special Sessions on Problem Solving) |
| 2:00-2:45 | Modeling Self-assembly
of Graphs Daniela Genova |
Student Success with
Online Homework Brooke P. Quinlan |
From Disk to Pyramid
Carl Hensley |
Problem Solving I -
Inequalities Hans-Dietrich Gronau |
| 3:00-3:45 | Integration as an
Averaging Process Mark E. Rupright |
Enhance and Improve
Your Teaching/Learning Environment with MERLOT Mathematics
James Rutledge |
Triangle Pyramids
Mike Keller |
Problem Solving II -
IMO Problems Hans-Dietrich Gronau
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| 4:00-4:45 | Round-table Discussion:
Planning Regional Meetings Hosted by Jacci White |
Using the TI-84+ in
Applied Calculus Martha Goshaw |
Just How Big Is Our
National Debt? Dennis C. Runde |
Triangle Geometry in
Recent MAA Journal Problems and Competitions Paul Yiu |
| Plenary Session 5:00-5:50 AD 119 |
The MAA American Mathematics
Competitions: Easy Problems, Hard Problems, History, and
Outcomes Steve Dunbar, University of Nebraska Director of the American Mathematics Competitions |
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| 5:50-6:40 | Hotel Check-in! | |||
| 6:40-7:30 DH |
Conference Banquet and Awards Ceremony | |||
| Plenary Session 7:40-8:30 AD 119 |
Mathematical Olympiads -
International and National Hans-Dietrich Gronau, University of Rostock President of Mathematik-Olympiaden e.V. and German IMO Team Leader |
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| Saturday, February 18, 2006 | ||||
| 9:00-9:45 AD 202 |
Student Integral Contest Dan Jelsovsky, Coordinator of Student Activities, FL-MAA |
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| Contributed Paper Sessions | AD 204 | AD 205 | AD 206 | AD 102 (Special Sessions on Problem Solving) |
| 9:00-9:45 | Complex Relationships
Among Coefficients, Zeros, and Critical Points Lubomir P.
Markov |
The Significant Yet
Overlooked Role of Personality in the Mathematics Classroom
Craig D. Hardesty |
The Student Portfolio -
Accepting Responsibility to Learn Julie Miller & |
Conducting a Problem of
the Week Contest by Email Patrick Bibby |
| 10:00-10:45 | Fascinating
Mathematics Problems and Their Solutions Scott Hochwald |
Engaging
Your Students and Helping Them to Become Rocket Scientists
(OK...maybe just passing the class will do!) Jana Bryant, |
Rings in Automated
Proof Robert Lamar |
A Viewpoint
on Problem Solving Stephen C. Locke |
| Foundations for Number
Analysis Martin Storm |
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| 11:00-11:45 | Minimal Representations
of Non-well-founded Sets Taje Ramsamujh |
Concept Mapping in
Algebra I Matt Campese |
Discriminants and
Polynomials Sam Sakmar |
Some Sets Based on
Lucas's Theorem and Some Recent Work of George Andrews
Shanzhen Gao |
| Plenary Session 12:00-12:50 AD 119 |
More than a Dozen Proofs that 1=2:
A Misguided Review of all of Mathematics James Tanton, St. Mark's School MAA Beckenbach Book Prize Winner |
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| 12:50-1:00 AD 119 |
Presidential Farewells Stephanie Fitchett, President, FL-MAA Martha Goshaw, President, FTYCMA |
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| 1:00-2:30 DH |
Conference Luncheon Annual Business Meeting of FL-MAA |
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Abstracts
| Friday, February 17, 2006 | |
| 8:00-10:45 EC 101 & 102 |
FTYCMA Workshop Implementing the Developmental Plan - Let's Get Started! Abstract: A panel of two year college mathematics educators from across the state will describe implementation strategies they are using at their colleges to address the Developmental Plan. |
| 1:00-1:50 AD 119 |
Plenary Session Formulas for Primes Underwood Dudley, Tallahassee MAA Pólya Lecturer, 1995-96 & 1996-97 Abstract: Formulas are nice and primes are fascinating, so formulas for primes should be nice and fascinating. This talk will give a survey of the field and contains two moral conclusions. Exactly one theorem will be proved. |
| 2:00-2:45 | Contributed Paper Sessions |
| AD 204 | Modeling Self-assembly of Graphs Daniela Genova, University of South Florida Abstract: Inspired by the process of self-assembly, we present a new way of defining classes of graphs based on boundary conditions. We discuss some properties of the new model and present several examples. |
| AD 205 | Student Success with Online Homework Brooke P. Quinlan, Hillsborough Community College Abstract: Hillsborough Community College's Dale Mabry Campus instituted mandatory online homework in MAT-0012, Prealgebra, for Fall 2005. MathXL, an online homework, tutorial, and assessment system, was used for this purpose. While working exercises, the multimedia resources and immediate feedback resulted in students' better understanding of the content and improved overall grades. |
| AD 206 | From Disk to Pyramid Carl Hensley, Indian River Community College Abstract: This is a demonstration using paper folding for introduction or review of geometric terms, definitions and examples. This is appropriate for Liberal Arts Mathematics, Algebras, Geometry, CLAST and other courses. |
| AD 102 (Special Session on Problem Solving) |
Problem Solving I - Inequalities Hans-Dietrich Gronau, University of Rostock Abstract: I will present some essential problem solving strategies, which I use in the preparation of our German students for IMO, but also for lower levels. In this first part, I will focus on inequalities. |
| 3:00-3:45 | Contributed Paper Sessions |
| AD 204 | Integration as an Averaging Process Mark E. Rupright, Florida Atlantic University - Honors College Abstract: The definition of the average value of a function in terms of the integral is presented in introductory calculus courses, but often without examples of how this relationship is useful. I will present a number of examples where the relationship between integration and averaging proves useful in teaching concepts in physics and numerical computing. |
| AD 205 | Enhance and Improve Your Teaching/Learning
Environment with MERLOT Mathematics James Rutledge, St. Petersburg College Abstract: MERLOT (Multimedia Educational Resource for Learning and Online Teaching, http://ww.merlot.org ) has become one of the nation’s premiere educational resources. Learn about its newly added features, award-winning content, learning resource portfolios, Mathematics Web portal, RSS feeds, Journal of Online Learning and Teaching, Virtual Speakers Bureau, newsletter, free membership, and opportunities to participate in various ways. |
| AD 206 | Triangle Pyramids Mike Keller, St. Johns River Community College Abstract: Participants will use plastic cups to construct triangular pyramids. Data will be collected and analyzed to determine the relationship between the number of levels and the number of cups. A graphing calculator will be used to find curves of best fit. |
| AD 102 (Special Session on Problem Solving) |
Problem Solving II - IMO Problems Hans-Dietrich Gronau, University of Rostock Abtract: In this second part, I would like to talk on mathematics which were initiated or is in connection with some IMO-problems. |
| 4:00-4:45 | Contributed Paper Sessions |
| AD 204 | Round-table Discussion: Planning Regional
Meetings Hosted by Jacci White, Saint Leo University Abstract: In this session, participants will share ideas for hosting a meeting in any of the six regions of the Florida section of the MAA. The FL-MAA section President-elect will facilitate the discussion as a way to support individuals and departments who would like to learn more about hosting a small MAA meeting. |
| AD 205 | Using the TI-84+ in Applied Calculus Martha Goshaw, Seminole Community College Abstract: The TI-84+ can be used quite effectively in an applied or business calculus course to introduce and enhance the topics. The presenter will share a variety of applications and projects that make use of the TI-84+. BYOC |
| AD 206 | Just How Big Is Our National Debt? Dennis C. Runde, Manatee Community College Abstract: Economic numbers such as the national debt, revenues, expenditures, the gross domestic product, and the U.S. population are a rich source of meaningful application problems for mathematics students of all levels. This talk will use these data in various mathematics applications including scientific notation, ratio and proportion, and linear regression. |
| AD 102 (Special Session on Problem Solving) |
Triangle Geometry in Recent MAA Journal Problems and
Competitions Paul Yiu, Florida Atlantic University Abstract: I shall try to advocate the use of directed angles and homogeneous barycentric coordinates in geometry. |
| 5:00-5:50 AD 119 |
Plenary Session The MAA American Mathematics Competitions: Easy Problems, Hard Problems, History, and Outcomes Steve Dunbar, University of Nebraska Director of the American Mathematics Competitions Abstract: The MAA has continuously sponsored nationwide high-school level math contests since 1952. The sequence of contests now spans 5 different contests at increasing levels of mathematical sophistication. Students who succeed at the top level on these contests become the team representing the U.S. at the annual International Mathematical Olympiad. I'll survey the history and organization of the contests, along with the outcomes and some notable mathematicians whose early indications of talent came on these contests. I'll comment about the intersection of these contests with the school mathematics curriculum. Along the way, I'll showcase some interesting, easy, and hard mathematical problems from these contests. |
| 7:40-8:30 AD 119 |
Plenary Session Mathematical Olympiads - International and National Hans-Dietrich Gronau, University of Rostock President of Mathematik-Olympiaden e.V. and German IMO Team Leader Abstract: I will give a survey on IMOs with many statistics (several new ones), experiences (the IMO 2005 was my 20th), including short videos. I will also give a short survey on the German competitions. A few special IMO problems will be discussed in detail. |
| Saturday, February 18, 2006 | |||||
| 9:00-9:45 | Contributed Paper Sessions | ||||
| AD 204 | Complex Relationships Among Coefficients, Zeros, and
Critical Points Lubomir P. Markov, Barry University Abstract: The theorems of Descartes and Rolle rank among the most beautiful accomplishments of classical polynomial theory and calculus of functions of a real variable. There are many interesting generalizations and results of similar nature that are not as well known as they deserve to be. Our talk will address some of them. |
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| AD 205 | The Significant Yet Overlooked Role of Personality in
the Mathematics Classroom Craig D. Hardesty, Manatee Community College Abstract: Results of personal research regarding personality types of math teachers and math students will be presented. Significant differences and similarities will be discussed as well as how teachers can apply this knowledge to increase success in the classroom. |
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| AD 206 | The Student Portfolio - Accepting Responsibility to
Learn Julie Miller & Molly O'Neill, Daytona Beach Community College Abstract: Help your students organize course materials and accept responsibility for their own learning. The student portfolio provides a structured approach to homework, vocabulary, and testing, while guiding students to an honest self-assessment of their effort. |
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| AD 102 (Special Session on Problem Solving) |
Conducting a Problem of the Week Contest by Email Patrick Bibby, Miami Dade College Abstract: Every major semester since January 2005, the Miami Dade Kendall Campus Mathematics Department has been conducting a problem-of-the-week contest. This contest is unique in that it is conducted by email. The presenter will provide a rationale for such a contest, rules, format, problem archives, and sources for problems, results, and suggestions for conducting such a contest. |
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| 10:00-10:45 | Contributed Paper Sessions | ||||
| AD 204 | Fascinating Mathematics Problems and Their Solutions Scott Hochwald, University of North Florida Abstract: The problems primarily come from number theory, calculus, linear algebra, and geometry. Three examples are followed by a link to all the problems.
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| AD 205 | Engaging Your Students and Helping Them to Become
Rocket Scientists (OK...maybe just passing the class will do!) Jana Bryant, Nancy Johnson, & Mike Mears, Manatee Community College Abstract: Studies have shown that students who attend class end up with better grades. While attendance is important, we believe having activities that help engage students in the learning process will actually have more of an effect on the final outcome. The presenters will share some ideas for classroom use and allow attendees to participate. |
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| AD 206 (20-minute Student Presentations) |
Rings in Automated Proof Robert Lamar, Stetson University Abstract: The formalization of mathematics in computer proof systems relies on much rigor for its survival. One proof system is Isabelle, a proof assistant built on the ML programming language. Within the framework of Isabelle, ring theory is developed and shown to be consistent with classical ring theory from abstract algebra.
Foundations for Number Analysis |
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| AD 102 (Special Session on Problem Solving) |
A Viewpoint on Problem Solving Stephen C. Locke, Florida Atlantic University Abstract: We look at the solution and construction of mathematical problems, interspersed with a few comments about problem solving in general. |
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| 11:00-11:45 | Contributed Paper Sessions | ||||
| AD 204 | Minimal Representations of Non-well-founded Sets Taje Ramsamujh, Florida International University Abstract: Minimal representations of Scott & Finsler pseudo-sets are obtained by using transfinite algorithms on their unfolded trees & directed trees, respectively. Two pseudo-sets will be equal iff their minimal representations are isomorphic. This extends earlier work on Aczel pseudo-sets and enable us to count the three kinds of hereditarily finite pseudo-sets. |
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| AD 205 | Concept Mapping in Algebra I Matt Campese, Sandalwood High School; Della Caldwell, Nease High School; & Bill Caldwell, University of North Florida Abstract: A team of high school mathematics teachers and UNF mathematics faculty is developing an analysis of high school Algebra I (Beginning Algebra in the community colleges). The analysis begins with constructing a set of expert “Concept Maps” describing the course. The process, the software used, and some of the maps that have been developed will be presented. |
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| AD 206 | Discriminants and Polynomials Sam Sakmar, University of South Florida Abstract: We view the discriminants of the polynomials from two different perspectives, analyze them and try to bring them in agreement. |
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| AD 102 (Special Session on Problem Solving) |
Some Sets Based on Lucas's Theorem and Some Recent
Work of George Andrews Shanzhen Gao, Florida Atlantic University Abstract: Let p be a prime number. We will discuss the sets
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| 12:00-12:50 AD 119 |
Plenary Session More than a Dozen Proofs that 1=2: A Misguided Review of all of Mathematics James Tanton, St. Mark's School MAA Beckenbach Book Prize Winner Abstract: Guidobaldo del Monte (1545 – 1647), a patron and friend of Galileo Galilei, believed he had witnessed the creation of something out of nothing when he established mathematically that zero equals one. He thereby thought that he had proven the existence of God! Although I daren’t be so bold with my claims, I am willing to prove instead that one equals two. And moreover, just to convince you that I am right, I will do so multiple times over, drawing upon a wide spectrum of mathematical techniques, from algebra and arithmetic, to probability theory, calculus, mechanics, propositional logic, and more! Will you be able to find fault with any of my “proofs?” |
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
Accommodations
We have blocked rooms at the following three
properties under an FAU designation (some of them also have MAA on
the records, but ask for the FAU group). Rooms will be held
only until January 16th, so
please make your reservations early!!! All hotels have a 10.5%
room tax in addition to the quoted rates.
Here are some other possibilities. These places will not block rooms in high season, so the rates below are those that were available when we called. Ask for a AAA discount if you’re a member, and don’t be surprised if rooms are more expensive (or not available) at later dates.
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
Food Service
Banquet: Friday, February 17th,
6:40 PM
Luncheon: Saturday, February 18th, 1:00 PM
For those planning to eat on their own, there are several restaurants within a few blocks of FAU. They are all in the Abacoa Town Center (northeast of FAU), which is the area bounded by University Drive, Main Street, and Central Boulevard. |
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
Directions
From I-95
From Florida's Turnpike - South
From Florida's Turnpike - North
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Florida Atlantic University • 5353 Parkside Drive • Jupiter, FL 33458
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
Campus Map
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Florida Atlantic University • 5353 Parkside Drive • Jupiter, FL 33458
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FL-MAA
Florida Section |
Jupiter Campus |
FTYCMA Florida Two-Year College Mathematics Association |
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| February 17-18, 2006 | |||||
Local Map
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| For more details, please visit http://mappoint.msn.com/. |
Circle all that apply.
Send check and Pre-registration Form by February 2, 2006 to:
Note: Pre-register by February 2, 2006, to be entered into a random drawing for six $50.00 awards. Only one entry per person is allowed. For additional information, contact John Waters Jr. at watersj@mccfl.edu or (941) 408-1492. |
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Circle all that apply.
Send check and Pre-registration Form by February 2, 2006 to:
For additional information, contact John Waters Jr. at watersj@mccfl.edu or (941) 408-1492. |
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There is little doubt within the Miami Dade College (MDC) family that Hurricanes Katrina, Rita, and Wilma tested our resolve. But we have risen from the aftermath renewed, refreshed, and revitalized in the planning of the fourth annual Mathematics Retreat (MR)! MR ’06 is scheduled for March 2nd and 3rd, 2006. This year’s theme is Enriching Students’ Experiences: New Perspectives. A discussion of institutional research statistics will serve as a backdrop to presentations on topics such as research and best practices, general education initiatives, and global issues in the classroom. There will be an update on the faculty-driven Quality Enhancement Plan (QEP). The traditional process to apply for continued accreditation was transformed into the first discipline-based QEP submitted to the Southern Association of Colleges and Universities Commission on Colleges (SACS). With its focus on the success and retention of mathematics students, the QEP is a College-wide course of action for institutional improvement on all levels and across disciplines.
Our agenda will facilitate an introspective look at our students, our institution, and ourselves. As we peer into the future, we see our students’ experiences enriched as a result MR ’06. For further information concerning MR ’06 and the QEP, please contact Linda Burton at lburton@mdc.edu and Patrick Bibby at pbibby@mdc.edu , respectively.
Jim Rutledge gave a presentation entitled Enhance and Improve your Teaching/Learning Environment with MERLOT Mathematics at the MAA Suncoast Regional meeting at New College in December. MERLOT Mathematics now offers a number of new features and a Web portal at http://taste.merlot.org/portal/mathematics.
The Mathematics Department of the University of South Florida is proud to present Louis H. Kauffman of the University of Illinois, who will speak on
Unknots, Collapsing Tangles and DNA Recombination
Magicians often present their audience with a knotted rope that miraculously unties itself. The secret to this trick is not always in a sleight of hand, but rather in topology! One can make “knots” that look knotted but are really not knotted. How can we recognize if a knot is really knotted? This is the fundamental question in knot theory. In this talk we begin with a discussion of the basics of knot theory and some very intriguing questions about the complexity of diagrams for unknots. We follow this path and find ourselves in the subject of rational tangles (certain weaving patterns that correspond to rational numbers) and some elementary number theory. Returning, we find that we have constructed infinitely many unknot diagrams that are “hard” to untie in the sense that they have to be made more complicated before they simplify. We find the smallest such unknot and we apply these ideas to DNA. The DNA molecule can start in an unknotted state and get knotted by the repeated application recombination enzymes. The theory of tangles and knots applies to unlocking the mechanisms of DNA recombination. This work is done in collaboration with Sofia Lambropoulou of NTUA, Athens, Greece.
Louis H. Kauffman is a professor of Mathematics at University of Illinois at Chicago. He received his Ph.D. from Princeton, and has worked at many places as a visiting professor and researcher, including the University of Zaragoza in Spain, the University of Iowa in Iowa City USA, the Institute Hautes Etudes Scientifiques in Bures Sur Yevette, France, the Institute Henri Poincare in Paris, France, the Univesidad de Pernambuco in Recife, Brasil, and the Newton Institute in Cambridge England. He is the founding editor and one of the managing editors of the Journal of Knot Theory and its Ramifications, and editor of the World Scientific Book Series On Knots and Everything. He is the author of the books “Formal Knot Theory”, “On Knots”, “Temperley Lieb Recoupling Theory and Invariants of 3-Manifolds” (Princeton University Press), and “Knots and Physics” (World Scientific Pub. Co.). He has been a prominent leader in Knot Theory, one of the most active research areas in mathematics today. His discoveries include a state sum model for the Alexander-Conway Polynomial, the bracket state sum model for the Jones polynomial, the Kauffman polynomial and Virtual Knot Theory. Many important concepts in the field bear his name. His publication list numbers over 170 and continues to grow, and with intriguing new results and concepts. He continues to inspire young mathematicians in the field.
About the Lectures
The Nagle Lecture Series was established in honor of the late R. Kent Nagle, a mathematician deeply interested not only in mathematics in itself, but also in mathematics education and the impact of mathematics on society. In this spirit, the NLS has invited world renowned scholars to speak on such matters in lectures designed for the general public.
About the Department
The Department of Mathematics at USF–Tampa consists of thirty-one faculty who teach courses ranging from the freshman to the doctoral level, while doing research in analysis, probability and statistics, discrete mathematics, and other areas of mathematics. We are also the home of the Center for Mathematical Services (which reaches out to the mathematics education community) and two research journals.
Date: Thursday, February 16, 2006
Time: 7:30–8:30 PM
Place: BSF 100, at USF-Tampa, located in front of the Physics Building
Parking: There is free parking available in the Lots 2A and 2B, adjacent to the lecture hall. Additional free parking will be available in Lot 1 (adjacent to the Administration Building) if necessary.
Contact: Mathematics Department (813) 974-2643 fax (813) 974-2700
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