Mathematics & Actuarial Science Spring Colloquium

"Computing Symbolic Dynamics for Polynomial Periodic Points"

Presented by Anna Durham, Paige Smith, and Sarah Stoops
Tuesday, March 17, 2015
Jordan Hall 183 at 3:30 pm

durham, smith, stoops
Anna Durham, Sarah Stoops, Paige Smith

Imagine entering an equation into a calculator and pressing
the equals button many times.  Each time the button is pressed, the calculator repeats the function, changing the input with each new application of the function.  The function and an initial value determine a dynamical system.  Depending on the starting input to the function, several outcomes may occur: for example, the output value may diverge to infinity, or it may cycle between several different values.  Cycles between one or more values
are called periodic points, and largely characterize the behavior of our system.  In this study, we introduce an algorithm based on Newton's method to find periodic points of a polynomial
zn + an-1zn-1 + … + a1z + c.  As the parameter |c| approcaches infinity, periodic points collapse to nth roots of unity, revealing a natural correspondence to symbolic dynamics.  In this way each periodic point has a symbolic address that can be tracked as we move about parameter space.  Using our algorithm, we take steps through parameter space to identify various symbolic automorphisms.

The talk is open to the public.

This research is due to a mini-grant from CURM.  CURM is funded by the National Science Foundation (NSF) grant #DMS-0636648/#DMS-1148695, by Brigham Young University(BYU), and by sponsors.

 

BUTLER MATHEMATICS RESEARCH CAMP (MRC)
A FOCUSED RESEARCH EXPERIENCE FOR MATHEMATICS MAJORS

faculty mrc 2015

The Opportunity:This summer, Butler's Mathematics Summer Research Faculty will again provide an MRC experience for our current freshman through senior majors-a first research experience in mathematics. Prior research experience is not required. We hopeyoumight join us! The MRC provides a dedicated, focused research investigation in mathematics that could lead toward further research.  For example, you could continue working with your Camp faculty mentor in the academic year, you could use the topic in MA490Senior Seminar, you could request a for-credit future directed study on the research question, or (for only the most advanced projects) you could apply to write an honors thesis or enroll in a BSI (Butler Summer Institute) research project. The MRC could also help you realize if graduate school in mathematics might interest you.  

The Camp and its Participants: The Camp will take place from Monday, August 10 to Monday, August 17.  (Students can arrive on campus to check into their fall Residence Hall rooms between 8:30 and 10 AM on Monday the 10th. They will have to check out on the 17th but can leave their stuff.)  The "Butler Research Faculty" will direct the camp; they include (as pictured) Drs. Wahl, Sharma, Wilson, Johnston, Mummert, and Webster.  The University lets you move for free into your residence hall early (during Camp), and the Department provides work areas in Jordan Hall.  It also provides breakfast and lunch in the Math Lab each day, and off-campus dinners are provided nearly every night, as faculty mentors and students dine together.
Each MRC day will be filled with mathematics: presented by the faculty; worked on individually with faculty members; worked on by you in your own individual research, reading materials and formulating questions; and worked on in "research proof sessions."  Each day starts at 9 AM and continues with research activities until 5 PM-you'd simply be responsible for participating in each event.  Each night provides a chance to share an evening meal, relax, and enjoy one another's company.   The last day has a super cool poster session, where you can show off your work.  In this way, you can expect animmersion experiencein research mathematics-a blast!

Application Process: It's easy to enroll.  Just come by and work with Mrs. Duerksen to turn in the short enrollment form.  Of course any of us would be delighted to talk with you beforehand.  We expect all interested students will be able to participate-limited resources are the only constraints (then requiring selection based on levels of commitment, seniority, experience, and grades).  Come on and join us-let's

Application Process:It's easy to enroll.  Just come by and work with Mrs. Duerksen to turn in the short enrollment form.  Of course any of us would be delighted to talk with you beforehand.  We expect all interested students will be able to participate-limited resources are the only constraints (then requiring selection based on levels of commitment, seniority, experience, and grades).  Come on and join us-let's discover some math!

 MAA Bowling Event

The MAA student club invited the professors in the department to go bowling on a Friday afternoon.  A great time was had by all!

The Department Fall Picnic 2014

The department hosted the annual student/faculty picnic for all mathematics and actuarial science majors at Professor Duane Leatherman's residence in Resco "D" Unit on Thursday, September 11, 4:00-6:00 pm.

http://blue.butler.edu/~dleather/fir/unitD/events14/mathdinner.html

Celebration of the Mind in honor of Martin Gardner's 100th birthday

The celebration of Martin Gardner's 100th birthday (born October 21, 1914) took place on October 21, 2014 in Jordan Hall 238 from 2:30-4:00 p.m.

Dr. Judi Morrel's honors class presented magic tricks with mathematical foundations, and Professor Jeremiah P. Farrell contributed a new magic trick to this fun event. Gardner's birthday is celebrated world-wide.  Martin Gardner was highly respected for his contributions to the world of mathematics and science through his many Scientific American articles about puzzles, tricks, and other astounding mathematical ideas.  He wrote many books which are still enjoyed today.

Research Conference in Korea, July 2014 - Dr. Mummert

Dr. Mummert attended a conference in Gyeongju, Korea from Aug 23-26, which brought together over 60 research mathematicians (ranging from graduate students to acknowledged experts in the field) to discuss topics in holomorphic dynamics in one and several complex variables. Dr. Mummert presented a poster entitled "A Path Lifting Algorithm for the Julia Set of a Complex Henon Map."  For more information about the conference check out the website athttp://www.math.sunysb.edu/koreadyn/.

Korea trip summer 2014 signs                  Korea trip summer 2014            korea trip 3

Past Mathematics and Actuarial Science Colloquium Speakers

Special Colloquium Presentation

Allan Rossman, Ph. D., presented "Choosing the Best: Decision Making under Uncertainty" on Friday, October 31, 2014, 2:00-3:00 pm, Jordan Hall 238.

Dr. Rossman presented a classic probability problem known as the "Secretary Problem" which illustrates the utility of probabilistic thinking when making decisions under uncertainty.  The problem is easy to state: Your task is to hire a new employee for your company.  You know how many candidates have applied, you interview them one-at-a-time in random order, and you can rank the candidates after you have interviewed them.  But the rules are that you have to decide immediately whether or not to hire a candidate (i.e., you can't invite one back later), and you must hire THE best candidate (i.e., if you hire the second best one, you have failed).  We will devise a clever strategy for choosing the best candidate and will explore how (surprisingly) well the strategy performs with both small and large numbers of candidates.  We will also consider a gambling application and ponder whether the optimal strategy is relevant to finding your soul-mate in life!

Allan Rossman is Professor and Chair of the Statistics Department at Cal Poly - San Luis Obispo and previously taught in the Department of Mathematics and Computer Science at Dickinson College.  His Ph.D. is in Statistics, from Carnegie Mellon University.  He is co-author with Beth Chance of the Workshop Statistics series and Investigating Statistical Concepts, Applications, and Methods, both of which adopt an active learning approach to learning introductory statistics.  He was Program Chair for the 2007 Joint Statistical Meetings and President of the International Association for Statistical Education from 2007-2009.  He served as Chief Reader for the Advanced Placement program in Statistics from 2009 - 2014.  He is a Fellow of the American Statistical Association and was one of the recipients of the Mathematical Association of America's Haimo Award for Distinguished College or University Teaching of Mathematics in 2010.

J. James Woods guest speaker

William Dunhamwilliam dunham
"Your Humble Servant, Is. Newton"

Almost fifty years ago, Cambridge University Press published the correspondence of Isaac Newton, a seven-volume, 3000-page collection of letters that provide insight into this great, if difficult, genius. Dunham will share his favorite examples of Newton as correspondent.  From his earliest known letter in 1661 (where he scolded a friend for being drunk), through exchanges with Leibniz, Locke, and others, to documents from his days at the Mint in London, these writings give glimpses of Newton at his best … and his worst.  He will end by discussing Newton's most-quoted line about standing on the shoulders of giants and describe how his search for its place of origin led him, improbably, to a library in Philadelphia.

William Dunham, a historian of mathematics, is retired after 22 years as the Koehler Professor of Mathematics at Muhlenberg College.  As a visiting professor at Harvard University, he taught a semester course on the mathematics of Leonhard Euler at Harvard University in both 2008 and 2013, and he also held a visiting appointment at Princeton University in the spring of 2014. He is currently a visit at the University of Pennsylvania and serves as the MAA's George Pólya Lecturer.

 

 

J. James Woods Lecture Series

Skylar Tibbits

A 4D Future

Wednesday, Feb. 18, 2015 - 7:30 p.m., Reilly Room

Tibbits3D printing has grown in sophistication since the late 1970s. TED Fellow Skylar Tibbits is shaping the next development, which he calls 4D printing: where the fourth dimension is time. This emerging technology will allow us to print objects that then reshape themselves or self-assemble over time. Think: a printed cube that folds before your eyes, or a printed pipe able to sense the need to expand or contract.

In this keynote, Tibbits explains how we are now able to program nearly everything-from bits of DNA, proteins, cells, and proto-cells; to products, architecture, and infrastructure. Programmability and computing are becoming ubiquitous across scales and disciplines. Tibbits shows us how soon these small-scale technologies will translate into solutions for large-scale applications-and what it means for your industry.

MAA Scavenger Hunt 2015 was cancelled because of bad weather

Each year, Butler University's Mathematics Association of America (MAA) chapter hosts an MAA Scavenger Hunt on campus for local high school students to attend. This event offers students the chance to utilize mathematical concepts they have learned in the classroom in a fun way. Past participants have enjoyed the hunt, and we look forward to hosting it again this year! The scavenger hunt will be held on February 21, 2015. Registration will be limited to the first twelve teams to register on a first-serve basis.  Each school is allowed to bring up to two teams consisting of three participants.