Barnes, Julia

Published in the Mathematics Magazine from 2003 was an article called “A Julia Set That Is Everything.” The co-authors Julia Barnes and Lorelei Koss both have their Ph.D in Mathematics. Having had the same advisor in graduate school, the co-authors met as graduate students and have stayed in touch ever since.They have written a couple other articles together as well.

Julia Barnes grew up in Ocala, Florida and attended grade school there. She kind of always liked math and helped a lot of friends with their homework. She started officially tutoring in fourth grade. She always thought that she wanted to be a teacher when she grew up, specifically a math teacher. While in 4-H and leading workshops for younger kids, she developed a strong urge to go into education.

She then went on to earn her Bachelor of Science in Mathematics from the University of Central Florida in Orlando. Starting out a math education major, she planned on teaching high school. Preparing for her teaching career, she worked as a camp counselor at Camp Lutherock near Boone, NC. After completing almost all of the math requirements of a math education major, she switched to a mathematics major but still planned on teaching through lateral entry into the Florida public school system. But then early in her senior year, a professor took her aside and convinced her to go to graduate school. He believed she would be happier teaching college rather than high school.

So instead of student teaching, she applied to graduate schools. She graduated in 1990 with a BS in mathematics and it turned out the professor was right. While she still loved working with kids, she was meant to be at the college level. So continuing on to graduate school, she went for her Ph.D. at the University of North Carolina at Chapel Hill also in mathematics. She finished in 1996.

Since graduating, Dr. Barnes is a very involved member of the mathematical community. She is currently working on a book addressing tactile learning activities. She is the Associate Director for Project NExT—a professional development program for new university math faculty. It is a program of the Mathematical Association of America (MAA). She has also been in charge of coordinating a mathematical treasure hunt for the Southeast section of the MAA for almost a decade now. With the help of many volunteer faculty, they get around 90 student participants.

While not focusing completely in one area, Dr. Barnes likes to jump around to different areas of mathematics, depending on what seems interesting to her at the time. She has a written a wide variety of articles. Some of her articles are more a survey of topics, while others cover more research depth. She also has some articles that are teaching related. For her, the best part is working with a wide variety of people.

Most recently she has been working with a graduate school office mate named Beth (Drews) Schaubroeck who happens to be a Wartburg College graduate from 1993. Currently Dr. Schaubroeck is a civilian at the Air Force Academy. With Dr. Barnes specialty in complex dynamics and Dr. Schaubroeck’s specialty in complex analysis, they decided to collaborate—hoping to find some common ground. While leaning more towards the dynamics side, they were not able to generalize their work.

Yet they still presented their work at an MAA conference and a graduate student who was doing research in the area they had been dabbling in, had an idea on how to go further with their work. The three of them ended up collaborating on an article titled “Real and imaginary parts of polynomial iterates” published in the New York Journal of Mathematics. This led to the integration of another collaborator Elizabeth Russell, who was working at West Point at the time. Being in three different time zones between the four of them, they mostly did work or presentations at national meetings in subsets.

Dr. Barnes and her co-author Lorelei Koss have written three articles together, including “A Julia Set That Is Everything.” This and one other one, “Ergodic Theory Carnival” are survey articles. She is proud to say that the latter has been translated into Chinese. While she is unable to read any of the Chinese characters, she still can recognize the diagrams. As mentioned before, Dr. Koss and Dr. Barnes met in graduate school and have stayed in touch. All of their publications have been written through email since graduating.

Outside of mathematics, Dr. Barnes remains busy with other projects. For five years she lived in a residence hall on campus as a Faculty in Residence working to increase faculty to student interactions. She mostly worked with faculty to bring them into the residence halls for programs. For eight years, Dr. Barnes was a teacher in a program for gifted high school students in a program of earth science. It was a four week program where kids would stay on campus and conduct research in stream ecology. She taught the statistics part of it in the mornings, and then helped in collecting data every afternoon. This was one summer job she really enjoyed.

More personally, Dr. Barnes enjoys cooking, sewing, and forestry judging. Also, she was a high school youth leader at her church for five years. She is currently a Sunday School teacher. In addition, she has done a lot of home renovations with her father who is a retired building contractor. Together they have re-roofed her house, resided it, renovated the kitchen and bathroom as well as completely repainted the interior.

While there is not much information on Dr. Koss, it is known through correspondence with Dr. Barnes that they have remained good friends since graduate school. Dr. Koss’s undergraduate degree in mathematics was accomplished at Columbia University in 1989. Her master’s and Ph.D. were attained at the University of North Carolina in 1992 and 1998, respectively. She is currently employed at Dickinson University as a Professor of Mathematics and has been there ever since finishing her Ph.D. Her personal work focuses on ergodic theory and complex dynamical systems with special attention to parametrized dynamics of meromorphic functions.

Bibliography

Barnes, Julia. "Re: Biographical Request." Message to the author. 7 Oct. 2013. E-mail.

Barnes, Julia. "Re: Biographical Request." Message to the author. 9 Oct. 2013. E-mail.

Faculty. Dickinson U, 2013. Web. 6 Nov. 2013. http://www.dickinson.edu/academics/Faculty/

Wilczek, Frank

Frank Wilczek Biography

If you were to picture a crazy scientist, Frank Anthony Wilczek would certainly fit the part. On the 15th of May in 1951, the soon to be genius was born in Mineola, New York. It became apparent to his parents that he was going to excel in mathematics. Curiosity is what fueled him at a young age to take on mathematics. He asked himself questions such as, “How many ways can one exchange coins to get the necessary amount?” He found interest in huge numbers as well. Wilczek wanted to get large numbers in very few steps. He said big numbers made him feel “powerful” (Frank Wilczek - Biographical).

Prior to college, Frank attended high school in Queens at public school 186, Martin Van Buren High School. It was there that he received his diploma. With many desired questions left unanswered he decided to attend the University of Chicago where he would study mathematics. The cognitive processes of the brain always fascinated Wilczek, but he decided that brain science wasn’t for him because those questions couldn’t be answered with mathematics. Physics was never on the frontier of his goals until his last semester at the University of Chicago. Wilczek was inspired and became interested in physics by his passionate physics professor, Peter Freund. Freund’s class was about symmetry and group theory. He was inspired; he saw the connections of mathematics. It was as if he found his calling. He loved the freedom of mathematics, but his technical ability with numbers and analytics could finally be applied to something with a little less freedom, physics. He graduated from the University of Chicago with his Bachelor of Science in Mathematics in 1970 and decided to further his academic career by traveling to Princeton, New Jersey.

His mathematics career continued at Princeton with physics remaining in the back of his mind at all times. Symmetry and its deep connection to physics became very apparent to him; specifically, the gauge theory of electroweak interactions, and the scaling symmetry in Wilson's theory of phase transitions (Frank Wilczek - Biographical). It was then that he realized that his training as a mathematician would turn him into a physicist by trade. He started to work extensively with David Gross, a professor at Princeton University. By the time Frank was 21 years old he helped define the properties of color gluons (MIT Department of Physics). Perhaps the most important part of his career occurred while in collaboration with Gross and Hugh D. Politzer on the basic theory of quantum chromodynamics. Their work led them to the discovery of asymptotic freedom, which is a property of some gauge theories. It states that bonds between particles become asymptotically weaker as energy increases and distance decreases (Asymptotic Freedom). Together, their work in from 1971-1973 in quantum chromodynamics led them to the Nobel Prize in Physics in 2004. He attained his Master of Arts in Mathematics from Princeton in 1972, and eventually his Ph.D. in physics in 1974. Princeton then offered him a teaching position until 1981.

Besides the Nobel Prize in Physics, he has received several other prestigious awards. Wilczek won the J. J. Sakurai Prize in 1986 for his work to better understand the strong interaction between quarks. In 1994 he won the Dirac Medal. Every four years the Royal Netherlands Academy of Arts and Sciences awards the Lorentz Medal for important contributions to theoretical physics. Frank won the Lorentz Medal in 2002.

Professor Wilczek now holds the title Herman Feshback Professor of Physics at the Massachusetts Institute of Technology. He is currently researching areas in physics including: applications of asymptotic freedom, or “pure” particle physics, how particle physics can apply to cosmology, and the quantum theory of black holes (MIT Department of Physics). Frank is an avid reader, and the research will end only when he ceases to be.  

Works Cited

“Asymptotic Freedom”. Wikipedia.com. 22 Sept 2013. Web. 11 Oct 2013. http://en.wikipedia.org/wiki/Asymptotic_freedom

"Frank Wilczek - Biographical". Nobelprize.org. Nobel Media AB 2013. Web. 14 Oct 2013. http://www.nobelprize.org/nobel_prizes/physics/laureates/2004/wilczek-bio.html

“Frank Wilczek”. Wikipedia.com. 10 Oct 2013. Web. 11 Oct. 2013. http://en.wikipedia.org/wiki/Frank_Wilczek

Wilczek, Frank. MIT Department of Physics. Massachusetts Institute of Technology, 31 July. 2013. Web. 12 Oct. 2013. http://web.mit.edu/physics/people/faculty/wilczek_frank.html

Barker, Andrew

The Career of a Mathematician:  Like a Sine Curve without the Consistency

            What does it mean to be a mathematician?  It’s a question that comes up often in class and one that we can’t quite pinpoint but only describe values pertaining to the individual.  I believe the question is difficult to answer because just like the many fields of mathematics, mathematicians are just as diverse.  Sure we all have a basic understanding of quite a few mathematical fields, but after that a mathematician is defined by his/her research, publication, discoveries and/or theories.  One man who is making his mark in numerical analysis and other closely related fields is Andrew T. Barker.  Dr. Barker just got into his 30’s, but has published and presented dozens of pieces of his research findings.  He’s truly a valuable component to the mathematical community because he doesn’t just solve problems, but he solves problems better.  Not bad for a guy who was a self-proclaimed “ok” math student in high school.      

            Dr. Barker attended public school in Virginia and Oregon and went on to attend Wheaton College in Illinois.  He was originally a computer science major, but then shifted his focus just a bit to mathematics.  “…something about the calculus classes and teachers at Wheaton made me fall in love with the subject and switch majors” said Barker and he has been studying and excelling at math ever since. (A.T. Barker, personal communication Nov. 1 2013).

            After his undergraduate studies, Dr. Barker went on to complete his Ph. D. in Applied Mathematics.  His main research interests were in numerical analysis and parallel computations, with an applicable focus in simulation of blood flow in human arteries.  So what does all this mean to the non-mathematical society?  “Basically lots of people have ideas for numerical techniques they think will be fast or efficient or accurate, and I write the code to test them and see how they work in practice” (A.T. Barker, personal communication Nov. 1 2013).

            Dr. Barker went on to take a postdoctoral position at Louisiana State University from 2009 to 2012, teaching classes in both Mathematics and Computer Science.  He now works for a research institute named Max Planck Institute for Dynamics of Complex Technical Systems based in Magdeburg, Germany.  The company primarily works with chemical and bioengineering research and analysis (2013), making this career choice for Dr. Barker a rather obvious one.

            Dr. Barker has went on to publish many works in the field of mathematics, including one in The College Mathematics Journal entitled Evolution Stability in the Traveler’s Dilemma.  In the article, Barker discusses the game The Traveler’s Dilemma (closely related to The Prisoner’s Dilemma), a game that is based on two people placing a value on their lost suitcase between $2 and $100.  There are a lot of variables that go into who gets how much for their suitcase, but essentially the value of your suitcase depends on the other person’s placed value on their suitcase; if both passengers but the same value on their suitcase they get that amount. However, if passenger A places a lower value on his/her suitcase, the difference is taken from passenger’s B value and given to passenger A.  The game itself is easier then it sounds, but also more difficult in a strategic and analysis stand point.  Many studies including Dr. Barkers have concluded that irrational strategies produce better “profit” for the “passengers” and therefore analytically better than rational strategies and traditional game theory (Barker 2009).

            Some of Dr. Barkers other published works include, but are not limited to:  engineering application and analysis, non-symmetric system strategies and parallel method application for a variety of sciences dating back to his days at Wheaton College as an undergraduate (Barker 2012).

            While attending Wheaton College, Dr. Barker met his future wife Linda and is now the proud father of two daughters, Abigail and Amanda.  In his spare time, Dr. Barker enjoys reading, hiking and drinking coffee.  He and his family currently reside in Germany where his job is located.  He ahs future mathematical aspirations in economic analysis; using mathematics to better understand economic inequality, what it exactly entails, how to better measure it and where it comes from (A.T. Barker, personal communication Nov. 1 2013).

                  Unlike the U.S. economy, the immediate future looks bright for one Andrew T. Barker.  The “ok” grade-school math student is certainly doing better than ok in mathematics today.  With 18 articles published in the last 5 years, while spending most of that time as a Ph.D. student or a postdoc. Professor, Dr. Barker is making more than just sine and cosine waves in the world of analysis and overall problem solving.  With his advancements in application and analytical research and his loving family by his side, maybe our economic system isn’t as bad of situation as it looks with Dr. Barker taking some interest in the situation.

Works cited

A.T. Barker (personal communication, November 1, 2013).

Barker, A.T. (2009).  Evolutionary Stability in the Traveler’s Dilemma.  The College Mathematics Journal, 40(1), 33-38. 

Barker, A.T. (2012).  Andrew T. Barker.  Bio. Website. Retrieved October 30, 2013, from https://www.math.lsu.edu/~andrewb/.

(2013). The Max-Planck Institute:  Research.  Max Planck Institute for Dynamics of Complex Technical Systems.  Retrieved October 30, 2013, from http://www.en.mpi-magdeburg.mpg.de/institute/presentation.en.html.  

    

Gallian, Joseph

Joseph A. Gallian

Adam  J. Kucera

Intro

Born to the parents of a glass factory foreman and a waitress in small town Pennsylvania in 1942, Joseph Gallian  (commonly called Joe)  was never a person meant to go to college. However, after working for three years in a  glass factory,  Joe  enrolled in college.   After successfully completing his undergraduate and doctoral degrees, Joe  moved on to  find a position teaching. After sending applications all across the country, Joe eventually landed at the University of Duluth.  From here he has built one of the most prestigious undergraduate mathematics research opportunities in the country as well as contributing greatly to the mathematical community in the form of mentoring.  Joe  currently lives and works as the chair of the mathematics department in Duluth,  Minnesota.   He is continuing to mentor some of the best mathematically minded undergraduate students in the country.

Early  Life

Joe Gallian describes himself as a class clown throughout his childhood. He often did poorly in most of his classes, but generally excelled in the course that he liked (mainly mathematics) [3].  Although  he barely graduated high school, Gallian  says that  he had a fantastic high school math education. He credits all of his success in high school to a product of his generation. He says:

“My math teachers were outstanding . . . my generation had the great advantage that there weren’t many opportunities for women except in teaching and nursing. . . . That  meant that people like me had the benefit of women who might have joined [other] professions becoming great teachers” ([3]).

Throughout his high school career he often hung out with the neighborhood kids. After

high school, however, most of his friends went on to college. This option was never much of a thought for Gallian,  however, because his father had already secured him a position at the local glass factory that he worked at.  After working for three years, however, he was called to go into the factory and be a ’breaker’. This job required the worker to stand under a large sheet of glass as it was stretched and then break it off at a scored location. This job payed extra, but there was often injuries.  After being trained on a newer machine, Gallian  told himself that he was going to be OK  with breaking. The next day, however, he was no longer in training and seniority dictated that he work on the oldest, and most dangerous machine. After breaking for three hours on his own, Gallian  experienced the worst thing that  could

happen to a breaker, the glass exploded.  The glass shattered, leaving Gallian  holding one piece, the other in free fall like a large guillotine. Luckily,  Gallian  was not seriously injured during this accident, but he realized just how dangerous breaking was.  He called over the foreman and recalls the following exchange:

. . . I called the foreman over and said, ”I’m  leaving–I’m going home. He said, ”You mean you're not even finishing your shift?”;  and I said, ”I'm  going home.”  He said, ”If  you walk off, you lose your job.  Do you realize this?”  And I said, ”I’m  going home and”–here’s the exact quote–’I’m not a married guy; I want all my parts.  I don’t want to lose any fingers or kneecaps–I want all my parts!”  It  was kind of morbid.  Say  someone lost a kneecap; the rst thing he would do is figure out how much he’d get.  You got paid if you got injured; an eyeball might be worth $5000, a finger $1500. They  had a formula.  I said, ”I  don’t want any $5000 or $1500. I want all my parts”  ([3])

Coming home four hours earlier than planned, Gallian’s father immediately knew some- thing was wrong.  He immediately became incredibly angry.   His father had never had a job outside of the factory,  and in that  time no connections almost always meant no job. In an attempt to diffuse the situation, Gallian  threw out the only thing he could think of,

”how ’bout if I go to college?” [3]. The result surprised even Gallian.  His father immediately calmed down and called the factory to say that he wasn’t going to be coming in the following day.  The next day Gallian and his father drove up to Slippery Rock College, where three of his best friends were in their 4th year. With only just graduating high school, Gallian wasn’t sure if they would admit him.  However, after sharing his experiences  in the glass factory, the admissions person surprised him.  They let him in on probation [3].

The college didn’t have any dorm space, but through an advantageous connection forged by his mother, his landed in an off campus house with two senior math majors. This math majors, it turned out, encourage Gallian  to become interested in higher mathematics.  Not because they were very good at it, but because they were very bad. Gallian,  in an attempt to understand what they were talking about,  picked up an algebraic book and not only understood it,  but  began tutoring his housemates.  After several semesters  of exploring upper level mathematics,  learning how to  study, and getting  married, Gallian began to look into life after getting his undergraduate. At  the time Gallian  was at school, the only professions for a person interested in math was an education degree. During his sophomore year, however, Slippery Rock offered a liberal arts degree. Under the tutelage of a favorite teacher, he switched to a liberal arts degree in mathematics.  This worked out in Gallian’s favor and he applied to several different universities  in pursuit of a doctorate in math.

He was first accepted into the university at Kansas.   He excelled in that  program and soon became interested in infinite group theory.   After his first master’s thesis adviser left Kansas for Michigan State,  he wrote his master’s thesis with one of his colleagues working in the same area.  However, one day his new adviser came in and announced that  he was also leaving for Michigan State.  Knowing that he wanted to work in infinite group theory, he decided to apply elsewhere and ended up at Notre Dame [3].

After  having his adviser at  Norte Dame leave for New Zealand,  Gallian  published his thesis with an adviser who gave him a good problem, but little support.  This worked out, in large part, to be in Gallian’s  favor.  “He  gave me almost no help beyond giving me the problem, but that worked to my advantage, because when I eventually got to Duluth,  there was nobody to work with. But I was already used to working on my own” ([3])

Mentoring

In June  of 1972, Gallian  was still working at Notre Dame after two unsuccessful years of looking for a different position. However, a position in Duluth opened up when the original hire backed out.  The university called Gallian and two others up to campus for an interview. During  the  interview, among many other topics,  a  discussion about senior mathematics projects for undergraduates came up. When asked about if there were any tractable problems in finite group theory for undergraduates, Gallian replied that there was lots of them. After being selected for the faculty position at Duluth,  Gallian  devoted a lot of time and energy and time into the student projects. This was a precursor to his great work with the Research Experience for Undergraduates (REU)  program  [3].

The summer of 1976 was the first year that Gallian started recruiting talent from across the country.   This came in the form of a program called an Undergraduate Research Participation program (URP). This program was more of a literature search than research, but Gallian  applied anyway and received the grant.   The  largest benefit of this program for Gallian  and the future Duluth  REU   program was the exposure that  Duluth  received by recruiting talent from MIT, Princeton, and Harvard  [4].

Every year since 1977, with the exception of one, there has been a ten-week REU  program in mathematics at  the University of Minnesota Duluth.   Through 2012, the program has seen 194 students (not counting multiplicity) and produced over 190 papers that have been published in professional-level  journals.  The ma jority of these papers have been in graph theory, number theory, and field theory  [2].

The vast amount of success at the Duluth  REU  is often cited as the reason to attempt an REU  at Duluth.  Gallian,  however, has found a different meaning. “. . . you can still get a lot out of an REU  experience even if you don’t have anything on paper to show for it.  . . . if they go through the research process and learn something, that’s a success” ([4])

Gallian  is not only known for his amazing work with the REU  program at Duluth,  he is also the author of several survey papers in the field of abstract algebra. The survey papers on a specific topic that Gallian has written has been cited over 500 times via Google Scholar [1]. In his own words:

I liken my surveys to what someone who loves football and knows a lot about football but does not have the physical capacity to play in the NFL. So instead, he becomes a coach.  He still contributes to the sport by helping others become better players, but he doesn’t have to be a player himself. ([1])

Conclusion

Undergraduate mathematics education is the driving force behind much of the innovation and progress in higher level mathematics. Gallian,  in the respect, is an esteemed conductor. He has built an REU  program from the ground up that has been internationally recognized for its ability to foster amazing undergraduate mathematics research. Gallian is truly a role model for undergraduate  professors in the way he gives good problems to great students and allows them to build their own solutions. “I’m  not a whiz kid.  I’m not an incredibly strong mathematician, but my talents match up with what strong students don’t have.”  ([4])

References

[1]  Joseph Gallian.  private communication, 2013.

[2]  Joseph Gallian.  The vita of joseph gallian, aug 2013.

[3]  Deanna Haunsperger.  A  break for mathematics:  An  interview with joe gallian.   The

College Mathematics  Journal, 39:174–189, 2008.

[4]  Sara  Robinson.   In  the mix at  model reu:  Creative  mentor, talented students, hand- matched problems, jul 2005.