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mathm a t t e r sSummer 2012

June 6-9, 2012 on the Iowa State University campusa conference for High School and Community College Teachers of PreCalculus and Calculus

Pre-Calculusthree communities; one goal

Midwestern GrapH TheorY (MIGHTY) LIII Conference - September 21-22

Coming soon to Iowa State University

Plenary speakers are Persi Diaconis of Stanford (left) and Ron Graham of UC San Diego (right), authors of Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks.

Deadline for registration for MIGHTY 2012 is September 1, 2012. More information about the conference can be found at:

The conference is supported in part by the National Science Foundation, the National Security Agency and the Institute for Mathematics and its Applications.

www.math.iastate.edu/mighty2012

The American Mathematical Society (AMS) sponsors sectional meetings every fall and spring in each region.

We are excited about hosting the central region meeting on campus April 26-28, 2013.

AMS invited speakers

Kevin Costello (Northwestern) Marianne Csoynyei (U Chicago) Vladimir Markovic (CIT) Eitan Tadmor (U Maryland)

ISU keynote speakers

Penny Haxell (U Waterloo)Phillip Protter (Columbia)Bryan Shader (U Wyoming)Pauline van den Drissche (U Victoria)

A poster session/reception will kick off the event on Thursday evening.

There will be many special sessions in areas of departmental research strength such as mathematical biology, probability, numerical analysis, linear algebra, graph theory, analysis.

Fan Chung (UCSD) will give a Mathematics Department Colloquium talk on the preceding Thursday, kicking off an exciting weekend of graph theory in Ames.

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A word from our chair...Of the 24,045 undergraduates at Iowa State in Fall 2011

only 254 were officially mathematics majors, i.e., 1.1% of all undergraduates. The program has grown by 37% since 2009 compared to an 8.6% growth of undergraduates overall at ISU. But Mathematics is still a very small percentage. Similarly, of the 4,392 graduate students, 96 were in a mathematics graduate program (excluding our Master of School Mathematics program), i.e., 2.2%. Our graduate program has grown by 12% since 2009, as compared to a growth of 1.1% for all graduate programs on campus.

Looking at the change of enrollment in Mathematics courses on campus over the last year, we note an increase of 1,124 students taking a mathematics class in 2011/2012 (as compared to 2010/2011), for a total of 14,143. Comparing student credit hours we see an increase of 3,870, or 8.55%, since last year to 49,120; of these 48,004 were undergraduate student credit hours.

It is interesting to note that the fastest growing (established, i.e., with more than 100 students) undergraduate majors in the College of Liberal Arts and Sciences between Fall 2009 and 2011 were Statistics (by 55% or 39 students), Computer Science (by 50% or 49 students), and Mathematics (by 37% or 69 students). Also, the fastest growing graduate programs in LAS over the same time period were, among programs with at least 60 graduate students: Statistics, Mathematics, and Chemistry (in this order).

It hence appears that the number of students studying mathematics (and the mathematical sciences, in general) is increasing faster than the number of students taking mathematics courses, and this number is climbing faster than student enrollment at ISU. There are certainly several good reasons for this, one of them may be connected to the job market.

CareerCast is a web-based consulting company that ranks jobs annually based on criteria such as income, outlook, environmental factors, stress and physical demands. The “top 10” during the last two years were, for 2011: Software engineer, mathematician, actuary, statistician, computer system analyst; and for 2012: Software engineer, actuary, human resources manager, dental hygienist, financial planner – with mathematician and computer system analyst still in the top 10.

All these jobs, with the exception of human resources manager and dental hygienist, require substantial mathematical/statistical/quantitative skills. What CareerCast observed is the general tendency that higher level and higher paying jobs require additional quantitative skills on all levels: “In recent years, the job market has increasingly rewarded math whizzes at the expense of less technical professionals. Actuary, mathematician, and accountant have all ranked among the best jobs in America by offering a pleasant work environment, good salary and healthy job security. … Continuing a recent trend, a majority of the jobs that rank in the top 10 this year require proficiency in math, science or technology, and all of them require higher education or specialized training.”

It appears that additional mathematical and quantitative skills pay off at all levels: at the level of quantitative literacy, of STEM degrees, of undergraduate degrees in the mathematical sciences, and at the graduate level. Basically all vocations and even general citizenship now require quantitative literacy, if just to sort the meaningful from the hyped data in political advertising. Many non-STEM professions require additional mathematical/statistical training, such as business, economics, psychology and advising, education professions and others. And all STEM related professions require additional quantitative, structural

and modeling training, usually provided through colleges and universities. Teaching mathematics today at the high school or college level means teaching everybody for their future endeavors: college mathematics courses have become providers of essential skills and enablers of high demand careers across the board.

Jobs for mathematicians are often not advertised as ‘searching for a mathematician’, but mathematics majors may end up in a job with a title such as engineer or analyst or developer. Mathematicians (and statisticians) find employment in almost all sectors of industry, government, and NGOs. The departmental web site at www.math.iastate.edu/Undergrad/UGopps.html#career provides many links to detailed descriptions of mathematics careers available to undergraduates with a bachelor degree.

There is much anecdotal evidence for another benefit of a college education in mathematics as Christian Roettger, one of our lecturers, pointed out to me: “This is directly tied to job security in the following sense. Suppose you don't like your current job. It's a lot easier to quit and find something else if you are a mathematician than if you are specialized in one narrow area. Well, even as a mathematician, you can specialize in some area, but you have the training to start a new job in a totally different field and learn whatever specifics you need - as fast as many competitors who have an education narrowly tailored to this job.”

At the graduate level we have seen, over the last years, an increase in positions in government (NSA, EPA, NIST, CDC, NIH), industry (financial, computer, software, instrumentation, high tech), and NGOs (data consulting, analyst), and in teaching and instruction at 2-year and 4-year colleges and at universities, where the number of lecturer-type (non-tenure track) positions have grown much faster than classical faculty positions. It may well be that the number of research faculty positions at universities will continue its steady decline for quite some time.

I hope that this edition of Math Matters provides you with interesting information about the department: among other things, we continue our series on thoughts about mathematics with a contribution by Ryan Martin. As always, we hope for your feedback, with comments on our discussions and on where we are going. Please don’t hesitate to contact me at kliemann@iastate.edu.

With my best regards

Wolfgang Kliemann

Lewis Central High School math teacher Bill Agan and Wolfgang Kliemann talk about curriculum at the PreCalc conference held on campus in June.

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More than 100 mathematics educators, including 74 high school teachers and 8 community college instructors gathered on campus in June to attend the Pre-calculus: Three Communities; One Goal conference sponsored by the ISU Mathematics Department and the Center for Excellence in Undergraduate Mathematics Education.

The three day conference featured several sessions about pre-calculus in the state of Iowa, but also sessions on related issues such as calculus, placement, transitions from high school to community college to colleges, and new ideas for the classroom.

Heather Bolles shares information about sessions and resources with Hoover High School teacher Laura Brinks. Many of the sessions were of interest to Brinks, who was trying to determine which to attend.

Precalculus and Calculus coordination: background to and lessons from a workshop

‘College readiness’ has become a major catch phrase as states get ready to implement the new Common Core State Standards (CCSS) and associated assessments. In Iowa, all the CCSS mathematics standards are part of the Iowa Core Curriculum – Mathematics. And Iowa is part of the Smarter Balanced Assessment Consortium, together with 36 other states. The rest of the states have formed the Partnership for Assessment of Readiness for College and Careers (PARCC). Both CCSS assessment consortia currently are involved in an extensive discussion about their missions.

The idea of college readiness in this context roughly is that high school students passing a comprehensive exam (at the end of 11th grade) with a certain score should be able to successfully take introductory college courses. In Mathematics, such a comprehensive

exam would cover CCSS topics such as those traditionally found in high school Algebra I and II, Geometry, and most of ‘college algebra’. The CCSS and related assessments basically do not cover trigonometry, analytical geometry, precalculus or calculus; but about one third of high school students entering college will have had a calculus course, and more than half will have had a precalculus course in high school.

The topics of ‘college algebra,’ precalculus and introductory calculus are taught in high schools, community colleges and colleges. Iowa State taught about 3,250 students in these courses in Fall 2011, or about 40% of our total teaching. Many students in these courses repeat a topic that they have seen before.

We see it as our responsibility to help students graduate from college, i.e., to provide them with the mathematical background they need to be successful. And numbers show that students who successfully complete their freshmen year in college are very likely to graduate. So a good part of our instructional effort is directed to first-year students, and most of these students take ‘college algebra,’ precalculus and introductory calculus. This shows that collaboration and coordination among high schools, community colleges and colleges regarding this range of courses is crucial for students’ successful transitions.

The workshop on “Pre-Calculus:

Three Communities; One Goal” was the first attempt at careful coordination of ‘common’ courses. It showed that we need to develop an understanding of ‘what is precalculus’ and ‘how can we design precalculus courses so that students can transition without too much friction among the different types of institutions’. We will create a state-wide advisory board to accompany our precalculus redesign at Iowa State. And we hope that this board will help us answer these key questions (to some extent) over the next year. The idea would be to come up with a list of 10-20 core topics that a student must know well if they expect to succeed in calculus. These topics could be the core of a precalculus class at any school, but the core would be small enough to allow for other topics as desired. The Mathematics Transition Guide (www.math.iastate.edu/pdfs/MathTransitionGuide.pdf) has such a list that may have to be updated. Of course, learning mathematics is not primarily learning about a list of topics, but about mathematical practices, which are rightfully emphasized in the CCSS and at the workshop.

Another important transition issue came up again and again at the workshop: Which mathematics courses should students take in high school, at a community college, at a Regents’ institution? In particular, which students should be accelerated in high school? Studies show that

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ISU Department of Mathematics conference organizers Heather Bolles, Adrian Jenkins, Elgin Johnston, Gail Johnston, Wolfgang Kliemann and Chris Schultz designed the schedule with a good deal of time for discussions and exchanges of information among conference participants. Many of the participants remarked that they found these opportunities to talk with other educators of immense value, and urged that similar conferences be organized in the near future.

High school and community college teachers accounted for 82 of the participants. Each of these teachers received a grant for meals and housing, and a stipend. Many of the participants also will receive license renewal credit through the Area Education Agencies.

In addition to sessions for teachers, there was one day of sessions for high school counselors. The counselors discussed placement, the importance of taking four years of mathematics in high school, and issues about transition. Strategies for working with students when they “hit the wall” were shared as well as an introduction to MyMathLab, the program used for online learning. Wolfgang Kliemann joined the counselors to discuss all aspects of ISU’s mathematics program and underscore why the ISU Math Department cares.

Marilyn Carlson (ASU) Developing Precalculus Level Students’ Mathematical Meanings and Practices; former AMA president David Bressoud (Macalester College) Calculus in High School: Too Much of a Good Thing?; Eric Hart (The American University of Dubai), Megan Blalock (UNI), and Judith Spitzli (IDOE) Additional High School Standards in Iowa Core Mathematics; and Eric Schulz (Walla Walla CC) Engaging visualizations for precalculus and calculus. Other sessions offered teachers new ideas for teaching pre-calculus and calculus, introduced the new ALEKS placement assessment, and discussed the content and purpose of our pre-calculus courses. For a complete listing of programs and resources, visit:

www.math.iastate.edu/Events/2012PreCalculus/Program.pdfwww.math.iastate.edu/Events/2012PreCalculus/resources.html

Keynote speakers added value to the conference, including:

taking challenging mathematics courses throughout high school is strongly correlated with a high probability of earning a college degree (www2.ed.gov/rschstat/research/pubs/toolboxrevisit/toolbox.pdf). This means that high schools should have interesting senior-level mathematics courses in their repertoire, such as precalculus. But parents, teachers, and administrators should also make sure that students are accelerated in mathematics only if they have a very competent grasp of all basic mathematics courses: superficial ‘sampling’ from a few advanced courses does not lead to understanding mathematics (see Chris Schultz’ article in the Spring 2012 Newsletter of the Iowa Talented and Gifted Association, p. 14-15 at http://iowatag.org/DOCUMENTS/2012SpringIssue.pdf). More importantly, students who were accelerated without sufficient basics will need to take introductory level courses in college that cover again the same topics as their ‘accelerated’ high school courses, without gain in time. These students often face strong difficulties passing these college courses. Some of these issues were summarized in David Bressoud’s talk at the workshop (www.macalester.edu/~bressoud/talks/2012/Iowa-APCalc.pdf). In particular, a joint March 2012 statement from the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) emphasizes that ‘students who enroll in a calculus course in secondary school should have demonstrated mastery of algebra, geometry, trigonometry, and coordinate geometry’.

Of course, the workshop brought many more insights for participants. An electronic alias list has been established so that discussions may continue beyond the conference. And we are thinking about encouraging another workshop of this kind within a year or so to continue the collaborations that began during this week.

Participants listen to Wolfgang Kliemann talk about preparing students for career opportunties available in mathematical fields.

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H. Tracy Hall, visiting scholar with Brigham Young University, came to campus in October to offer the first public presentaton of proof of Maehara’s 20-year-old conjecture.

This particular presentation was a few years in the making.

An AIM workshop focused on minimum rank back in 2006 organized by Leslile Hogben, Richard Brualdi and Bryan Shader introduced a number of problems, including the Delta conjecture.

Maehara’s Delta conjecture appeared in L. Lovasz, M. Saks and A. Schrijver. Orthogonal representations and connectivity of graphs. Linear Algebra and its Applications

114/115: 439--454, 1989.

Workshop attendee Wayne Barrett took the problems back to BYU where colleague Tracy Hall found them facinating; his interest led Hogben to invite him to participate in AIM SQuaRE, a small research group the met over the next three years. Visits to ISU to work on similar research followed, and in 2009 Hall spent two weeks on campus as a research visitor.

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“It’s a thing that nonmathematicians don’t realize,” observed eclectic Princeton mathematician John Conway. “Mathematics is actually an aesthetic subject almost entirely.” Symmetry is often easy to see and appreciate in a visual field, such as geometry. The ancient Greeks were captivated by mathematics in general and by geometry in particular. Archimedes, the legendary mathematician from the city-state of Syracuse had, after a great deal of effort, computed the volume of a sphere, given the radius. He further observed that, if a cylinder circumscribes a sphere, then the ratio of their volumes (and of their surface areas) is 3:2. He was so astounded by this result that, despite the many remarkable discoveries he had made throughout his life, Archimedes insisted the image of a cylinder circumscribing a sphere should be inscribed on the stone marking his grave.

Modern mathematics has its own beautiful results, including the remarkable Euler’s identity: e^iπ+1=0. This simple equation uses arguably the 5 most important constants in mathematics – 0,1,e,π,i – and 3 basic operations – addition, multiplication and exponentiation – each exactly once. Benjamin Peirce, a 19th century mathematician, after demonstrating a proof of it said, “[T]hat is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore, we know it must be the truth.”

Even after a theorem has been proven, mathematicians often look for a proof that is simpler, that requires fewer assumptions, in short, more beautiful. The four-color theorem can be stated in an elegant and simple manner: If a two-dimensional plane is separated into contiguous regions, then those regions can be colored with four colors so that no two regions that share a boundary receive the same color. In common terms, the countries on a map can be colored with four colors so that no two adjacent countries get the same color.

The formal statement is more subtle; for instance, two regions don’t share a boundary if they only share corners. Nonetheless, it is a simple enough statement to have captivated mathematicians since it was first

conjectured in 1852. The first proof was provided by Appel and Haken in 1976. However, the proof was too long to check by hand (requiring the verification of 1,936 configurations) and required a computer. The proof was simplified by Robertson, Sanders, Seymour and Thomas in 1996, but even their 633 configurations still had to be checked by computer.

So, although the four-color theorem has been proved, a short simple proof is still on the wish list of many mathematicians. Short, elegant proofs are treasures in mathematics. The great 20th century Hungarian mathematician Paul Erdős spoke of a “book”, which he said was located in heaven, in which God has written down the most beautiful proofs. “You don’t have to believe in God,” he said, “but you should believe in The Book.” Erdős was fond of proclaiming that a short, beautiful proof was a “Proof from The Book.” Some of these were collected in an earthbound paper version.

Mathematicians are intrigued by concepts in which seemingly unrelated ideas can be tied together. Such an example in graph theory is the family known as the Moore graphs. Simply, a degree d Moore graph is one in which every vertex has d neighbors, every vertex can be reached by every other by at most 2 steps and there are exactly 1+d^2 vertices, which is the most possible, given the previous restrictions. The question is, how many Moore graphs exist?

Moore graphs are quite rare. Lázsló Babai and Peter Frankl cite a result of Hoffman and Singleton in their chapter “Beauty is rare” in an unfinished manuscript entitled Linear Algebraic Methods in Combinatorics. The Hoffman-Singleton theorem shows exactly how rare a Moore graph can be: There is the 5-cycle (d=2), the Petersen graph (d=3, pictured), the Hoffman-Singleton graph (d=7) and there is the possibility that a graph or graphs on 3,250 vertices (d=57) exist. But there can be no others!

Not only is the proof of the Hoffman-Singleton theorem an elegant use of basic linear algebra and factorization of polynomials, but it leaves an intriguing open problem: It is not known whether a Moore graph on 3,250 vertices exists.

Randomness is another notion that highlights the beauty of mathematics, although it wouldn’t seem so. In colloquial speech, the word “random” is often used to mean “arbitrary”. In mathematics, however, randomness is a beautiful concept. For instance, the outcome of a single coin flip can seem arbitrary, the number of heads in 10,000 coin flips is much more predictable. Combinatorialists are often very pleased when they discover that a given phenomenon can be compared to a random one. The notion of “pseudo-random” is many and varied depending on the context, but the idea is intuitive: A pseudo-random object is one that has similar properties to an “ average’’ one.

In a proof of an important number theory result in the 1970s, Hungarian mathematician Endre Szemerédi developed a tool used in graph theory and combinatorics to solve some of the most intractable problems regarding arithmetic progressions and graphs. Szemerédi’s “regularity lemma” – the main idea used in his proof – became one of the most remarkable results in discrete mathematics and has been used to prove a dizzying array of results. In it, he shows that every graph, no matter how arbitrary, can be explained in terms of pseudorandomness. For this work, Szemerédi won the 2012 Abel prize, a prestigious honor awarded by the Norwegian government and worth approximately one million US dollars.

Beauty is, indeed, rare. But the search for symmetry, simplicity and subtlety has always been a thread in human history and is most certainly a foundation stone for mathematics.

At its core, mathematics is a quest for beauty, for order, for symmetry.

By associate professor Ryan Martin. Martin’s research interests lie in extremal and probabilistic combinatorics and graph theory.

Learn more about Martin at http://orion.math.iastate.edu/rymartin/

Figure 1: The Petersen Graph, the Moore graph where d=3

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domains in Cn with positive real part. She also studies connections between function theoretic properties of these functions and operator theory by finding characterizations of such classes of functions in terms of operator-valued Herglotz kernels and via von Neuman type inequalities.

Kristopher Lee (PhD, math, Clarkson University) A graduate teaching assistant, Lee’s research interests are in the fields of algebra, analysis, and point-set

topology. He is particularly interested in the study of algebras of complex-valued, continuous functions, which combines ideas from these fields. His work has focused on analyzing mappings between algebras and investigating the interaction between the structure of the algebra with the topological structure of the underlying domain of the functions.

Elijah Stines (PhD, math, ISU) Stines served as lead teaching assistant at ISU, where he is currently working on developing categories, over which, certain varieties of

algebras with quasi-orders are monadic. In addition, he has been investigating the group of divisibility of pseudo-valuation domains and begun working on some ways to find the smallest variety generated by fields.

Paul Tokorcheck (PhD, math, UC-Santa Cruz). An instructor, Tokorcheck’s research interests include Groups of Lie type, in particular the exceptional group G 2 constructed

over a local field, as well as associated topics including non-associative algebras, representation theory, and the theory of Bruhat-Tits buildings.

Welcoming new faces...Jessica Conway (PhD, applied math, Northwestern) Conway, who held a postdoctoral fellowship at the University of British Columbia, is interested in using mathematics to

gain insight into physical/biological systems. Recently she used a stochastic approach to a within-host disease problem: investigating mechanisms for viral persistence in treated HIV+ patients, developing a numerical method to extract from a branching process model the evolving probability distributions over time of viral/cellular species to improve understanding of HIV dynamics and eradication timing.

Songting Luo (PhD, math, UC-Irvine) As a visiting assistant professor with Michigan State University, Luo’s research focus was on numerical methods for partial differential

equations with applications, especially on (1) multiscale and multiphysics modeling and computation of nano optical responses, nano optics; (2) computational high frequency wave propagation, geometrical optics and beyond; and (3) Hamilton-Jacobi equations with applications, homogenization.

Timothy McNicholl (PhD, math, The George Washington University) As an associate professor at Lamar University, McNicholl’s research interests included theory of computation, complex analysis, computable analysis, Green’s function for

unbounded domains, conformal mapping of multiply connected domains, Dirichlet problems for multiply connected domains, computation of boundary extensions of

Paul Barloon (Masters, math, University of Northern Iowa). most recently served as adjunct instructor for Des Moines Area Community College.

Jean Krusi (Masters, Cornell) teaches in the Ames Community School District. Her research interests include classroom discourse.

Miriam Castillo-Gil (PhD, math, University of Florida) A graduate teaching assistant, Castillo-Gill is currently studying classes of holomorphic functions on

conformal maps, multi-resolution cellular automata and computational pursuit-evasion games.

James Rossmanith (PhD, applied math, University of Washington) As an assistant professor at UW-Madison, Rossmanith’s research focus is on numerical methods for

nonlinear hyperbolic PDEs. In particular, he works on high-order shock-capturing methods, including wave propagation, discontinuous Galerkin, and residual distribution schemes, for PDEs that arise in application areas such as plasma physics, gas kinetic theory, and relativistic fluid dynamics.

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Meet Erin Pauly, undergraduate mathematics major (who also minors in economics)

How did you choose mathematics as a major? In my search for a major, I vacillated between many different options - English, Physics, Music, Mathematics, Linguistics, even History. I enjoyed so many different subjects, it was difficult for me to choose just one. In the end, though, I chose the major that could apply to more future careers than any other, the major that I felt could hold my attention and passion - Mathematics.

To me, mathematics is one of the few things in life that is constant, yet there are infinitely many possibilities with it. It describes almost everything in the known world, and all of science is rooted in math. It is also one of the few universal languages. These facts intrigue me and drive me to keep learning more.

What do you want to do after you graduate? After I graduate, I plan on obtaining a job in Actuarial Science. I have taken one actuarial exam already, Exam 1/P, and plan on taking Exam 2/FM this August. Additionally, I interned with Nationwide in the Farm Pricing Department last summer and am interning with Nationwide again this summer, but in the Reserving Department. I'm well on my way to becoming a true actuary, but I will continue to be a student even upon graduation, as I have to study and take exams as I progress through one of the two actuarial associations - Casualty Actuarial Society (CAS) or Society of Actuaries (SOA).

Describe organizations/activities in which you have been involved. I have been primarily involved in two groups during my college career. One is Women in Science and Engineering (WiSE). WiSE helps women in STEM fields be heard in their classes, lives, and careers, and, subsequently, be successful in all three, as well. The other group is ISU GROOVE Drumline Club. It is primarily active

in the spring semester - we practice all semester for our final show at VEISHEA. It is a great way to keep music in my life without all the pressure of performances.

Within WiSE, as I said, I was a first year peer mentor. I worked with a group of freshmen women in the STEM fields as they journeyed through their first year here at Iowa State. I helped them with homework, talked them through any personal problems they had, connected them with resources, and made sure that they had every chance to succeed.

The biggest thing WiSE does to help women be "heard" is to try and instill confidence in themselves and their choices. It can be hard for women in STEM fields, as they are often underrepresented. We therefore offer free tutoring, job shadowing, internships, and the preparation necessary for all of this - study halls with the peer mentors, resume workshops, and one-on-one meetings. We offer these things to help STEM women grow as people so they may be taken seriously as professionals in their classes and future careers.

Describe volunteer activities in which you have been involved. I have volunteered at the middle school, high school and Department of Energy Science Bowl hosted here at Iowa State. I have alsocollected non-perishable items through Alpha Lambda Delta/Phi Eta Sigma's trick-or-canning event, as well as at the annual Charity Skate.

Tell me just a little bit about you as a person. I am a quiet, independent person who would much prefer reading a book over attending a party.

I am always trying to expand my base of knowledge so I can better myself and help others.

What do you do for fun and relaxation? I love to read, especially the fantasy genre, although I've been trying to get through a comprehensive list of literary classics. It's rare that I am without a book - I often actually have two. I also enjoy baking and playing video games, especially RPG's.

What is the most important thing in the world to you? Knowledge coupled with wisdom; knowledge is the result of learning whereas wisdom is having the judgment to apply that knowledge in the correct manner.

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Graduate study of mathematics at Iowa State University

Arriving at a research topic

Michelle Lastrina recalls being first exposed to her doctoral research topic, graph theory, as an undergraduate participating in REU (Research Experience for Undergraduates).

“Participating in an REU was my first experience with doing mathematical research and it was one of the main reasons I decided to pursue graduate school in mathematics,” Lastrina revealed. “I was drawn to graph theory because it is a very accessible topic, and I understand many of the main results with ease. It is also very visual and I get to draw lots of pretty pictures!”

A question posed by UNC professor Mark Lemmers concerning a possible variation of the basis pursuit technique developed in the compressed sensing literature inspired my work (Dominic Kramer).

Most challenging aspect of the doctoral journey

Mathematical research in general can often be challenging when you spend great deal of time working on

a problem, only to find that you've come to a dead end or someone else has solved the same problem you've been struggling with. The last year of my journey had an added challenge because my major professor was in another country. While this changed our working relationship, it was a wonderful opportunity to begin working more independently and start collaborations with others (M. Lastrina).

Discovering (in my first year of grad school) that study habits that are effective as an undergraduate might not be adequate for graduate school. In particular, it’s not enough just to do the assigned problems; you have to go above and beyond (T. Peters).

The role major professors play

Dr. Weber was instrumental in helping me understand frame theory, compressed sensing, wavelets, and optimization theory. I really appreciate all of the expert advice he has given me with understanding current methods, exploring new techniques, writing proposals, and giving presentations (D. Kramer).

Dr. Axenovich helped me find the problems I worked on for my dissertation, as well as worked with and helped me with the contents of my dissertation. Her vast knowledge served as a wonderful resource (M. Lastrina).

Dr. Hogben is an outstanding mentor. She is genuinely concerned about the success of her students, and I am very privileged to have worked with her. She helped me complete my degree in a timely manner, and design a program of study that reflects my career goals. Even though currently advising a handful of graduate students, she made time to meet with me on a regular basis (T. Peters).

Role graduate student community plays in personl mathematical development

The graduate students in the Math Department played the role of collaborators and supporters throughout my mathematical development (M. Lastrina).

We have a very welcoming and inclusive group of graduate students in the math department, which makes for a collaborative and productive work environment (T. Peters).

How teaching fits into overall experience

I really enjoyed being able to teach a wide variety of courses ranging from College Algebra to Differential Equations. Teaching has given me a wonderful opportunity to help others understand mathematics, and it has helped me to develop my communication, presentation, and organization skills (D. Kramer).

My experience teaching shaped the way I myself learn. Being able to explain concepts in a clear and concise way changed the way I read and understood research papers (C. Vidden).

We asked graduating PhD candidates to reflect on their study at Iowa State University. Here is a sampling of what they had to say:

Sixteen candidates defended their research during the past year, among them Sukjung Hwang (at left), Dominic Kramer, Michelle Lastrina and Travis Peters (next page).

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Advice for incoming students

While learning established theories or exploring your own techniques, always be aware of how the topic at hand relates to the bigger picture of mathematics as a whole (D. Kramer).

Stay in touch more with other graduate students' research; Go to conferences as much as you can; Shake as many hands as you can; Push your advisor to spend more time with you; Evaluate yourself and your progress frequently; Have as much fun as you can have in your social life (A. Ozer).

What you found most rewarding about working with your candidates

Experiencing Ozkan’s true passion for mathematics. For him, it is not enough to find a solution to a problem; the aesthetics and methodology are important. In his thesis work, Ozkan elegantly combined several methodologies and produced results that are applicable to a class of systems- not only his specific problem (S. Hansen).

The constant pushing of each other’s boundaries in our perception of how far we can go and how much Sijia and I can achieve in our projects (A. Matzavinos).

Witnessing the tenacity in Tracy’s problem-solving and her intellectual curiousity. A voracious reader, she is able to track down and connect obscure results (R. Martin).

Dominic's boundless energy, creativity. He worked very hard on solving problems, and made fantastic progress (E. Weber).

Approaching the task of major professor

I meet with a student regularly to discuss problems, narrow the research

project, discuss proofs, examine the mathematical profession and consider career strategies (M. Axenovich)

I start with a simple problem that allows the student to learn the theory. After reading enough literature it is possible to start working on something more complex. In Ozkan’s case, he found interesting new results even for the simple problem (S. Hansen).

Each student has different strengths and interests. It's important to see what kinds of problems and techniques will motivate the student. These research projects may follow the student their entire careers, so they should have a good one (R. Martin)

Most exciting or enriching about being a major professor

The opportunity to work with a student on a project in depth for several years. During that time both the student and the professor learn a lot (M. Axonovich).

It is always rewarding to expand mathematical horizons of students. Sometimes it goes both ways, and my students expand my horizons (S. Hansen)!

I like the interaction with students, the ability to hash out ideas, and the unique perspective and knowledge that a student brings to the problem (R. Martin).

Seeing students develop their own mathematical personality (J.D.H. Smith).

Serving as a major professor is one of the most important dimensions of academic life. It is exciting to teach an individual all that I know about my discipline and academic life…but I am also learning a lot from my advisee as well (S. Song).

Carrying on the mathematical legacy (E. Weber).

Challenges of being a major professor

When things go wrong. Now and then after a lot work on a problem, we either find that it is easily solvable by another method or maybe we made a mistake somewhere and have created many pages of garbage. In this case

We also asked faculty members currently serving as major professors to reflect on their experiences mentoring candidates. Some of their thoughts:

11

The graduate programs in Mathematics and in Applied Mathematics have grown over the last years to about 90 graduate students in 2011-12.

“This is a consequence,” explains Department chair Wolfgang Kliemann, “of continuing interest of the job market in graduates with advanced degrees in the mathematical sciences, of the attractiveness of these jobs to the group of mathematically talented college graduates, and of the financial health of the Department of Mathematics at Iowa State that is able to offer a good number of assistantships to interested students.”

Cliff Bergman, director of graduate education, agrees. “Certainly the “tech boom” of the last 15 years has made a career in the mathematical sciences seem more glamorous,” he said. “Also, in recent studies the mathematics profession has ranked quite high in terms of salary, stress level and working conditions.”

But Bergman also believes a significant factor in our success has been our growing reputation as a great place to study. “ISU Math has long been known for its nurturing environment,” notes Bergman. “As the background of undergraduate math majors becomes more diverse, this quality attracts the attention of an increasing number of students.”

The Department has graduated 10 PhD students per year over the last five years, and this number is expected to increase to about 12 over the next years.

The academic year 2011-12 set a record in PhD students with 16: Since the first mathematics PhD at Iowa State in 1933 (Ernest Anderson wrote a thesis on “Statics of special types of homogeneous elastic slabs with variable thickness” under the direction of Dio Lewis Holl), the department had graduated 12 PhD students in 1993, and 11 in 1968, 1969, 2009 and 2011.

“Also remarkable is that of these 16 PhD students, 15 had job offers before they graduated, or within a few weeks of graduation,” noted Kliemann. The other one will accept an offer as temporary instructor at ISU. “In a still very tight job market the placement rate of 94% is complementary of our efforts and of the reputation of the PhD education in our department,” he added.

Growth is not without challenge. According to Bergman, we have reached a point at which the size of the graduate program is putting stress on our research faculty (not to mention the physical facility). “In order to preserve the learning environment that we value, our short-term plan is to improve the quality of our incoming students, rather than increase the quantity,” he cautions.

you salvage what is useful and move on. It is part of the research process (S. Hansen).

Providing interesting and challenging problems. We have some very bright graduate students and personally I pay great attention to identifying research quetsions that fit the student’s interest and also engage them in research pertaining to large, difficult problems (A Matzavinos).

Balancing letting students try whatever they need to with making sure that they actually get something done. When they are trying to figure out their research path, I try not to let my ideas influence their decision, but

Universal Algebraby Clifford BergmanCRC Press

Starting with the most basic notions, Bergman’s new textbook introduces key elements needed to read and understand current

research in this field. Based on his two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics.

Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.

sometimes I find it crucial to point them in a particular direction (G. Lieberman).

Matching the advisee's experiences, competence, and goals to an appropriate sequence of coursework, independent studies, research projects and assistantship while meeting the time-to-degree completion are challenging at times (S. Song).

Having a research-active core of graduate students

There is a natural cycle to teaching and learning. We do research, but in describing it to students, we refine our

own ideas. Students bring fresh ideas to the research and we do, indeed, learn from each other (R. Martin).

Graduate students play a significant role in increasing the visibility of the department via participating in conferences, giving talks in their home undergraduate institutions, and of course continuing the profession in research or teaching institutions (M. Axenovich).

Students that write papers and go to conferences bring recognition to the research being conducted in our department (S. Hansen).

Anything else

Working with students is very rewarding. The dynamics involved in collaborating on solving a problem and developing a student's research program is always a worthwhile adventure (R. Martin.)

Administrators Kliemann and Bergman reflect on graduate study

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Take graduate mathematics student Kevin Palmowski, undergraduate mathematics major Kristin Gaffney, and graduate non-mathematics student Laura Ekstrand and put them all in the same classroom and you have a representation of what applied linear algebra looked like last fall.

As resources become more limited, we look for ways to provide more class options for junior/senior mathematics majors. One strategy the university offers is dual listing of a class on both the graduate and undergraduate level.

When we offered applied linear algebra in this dual format on an experimental basis last fall, 16 students finished the course.

Professor Leslie Hogben led the group, comprised of about equal numbers of graduate students enrolled at the graduate level, graduate students (from other areas) enrolled as undergraduates, and undergraduates enrolled as undergraduates.

Hogben delivered one set of lectures; all students used the same text; assignments were made according to level (UG/grad).

As an undergraduate, Kristin Gaffney was slightly skeptical about taking the graduate level course that her differential equations tutor told her about. “I did enjoy Math 317, and like working with matrices and linear algebra to solve equations, however, and decided to give it a go,” she recalls.

The class opened with a two-week review of Math 317 and built from there.

“Sometimes homework was difficult or the class time was fast paced since it was a graduate-level lecture, but after seeing Dr. Hogben during office hours, I always learned and had a better understanding of the material,” Gaffney said. “Classmates were more helpful toward the end of class, so I wish I had made a study group with some of the graduate level classmates early on. I liked that Dr. Hogben showed us the applications in real world situations and described in detail 'what was under the hood' of things like picture encoding

and matrix data.”Laura Ekstrand (PhD student in

mechanical engineering) didn’t have the background in formal proofs and calculus necessary to take the class as a graduate student, so she enrolled for the undergraduate level and used the credit as an elective in her program. “While

it was challenging, I appreciated being able to listen to graduate-level content, finding it both interesting and potentially useful to my research,” she reported. “Knowledge gained in this class made the algorithms I encountered this spring in computational perception much easier to

understand.”“Moreover,” Ekstrand continued,

“Math 407X cemented the more basic linear algebra concepts in my brain. This is very useful for me because I use computer graphics for my research, and the whole of computer graphics relies heavily upon linear algebra.”

Kevin Palmowski loved the course. “As a first-year grad student in applied math, 507 was a great way to get a lot of the advanced linear algebra background I need without the stress of taking the core-sequence Linear Algebra course.”

Palmowski noted that Hogben successfully assembled and delivered content that was relevant to graduate students in mathematics and related applied areas, while keeping her lectures at a level that was accessible to advanced undergrads.

“And,” he said, “I thought that the homework assignments were designed well. The 407 problems had to be completed by everyone, and on every every assignment Dr. Hogben threw in two or three ‘more interesting’ extra problems for the 507 students to work on.”

Similarly, Gaffney found mixing with graduate students and other majors a

great experience. “Not only do you get to see the true value of the material, but the level is challenging but possible, which makes a good preparatory class for future graduate students. Classes are smaller and grad students can help teach material to undergrads, valuable to both sides,” she said.

Palmowski agreed, saying, “It is a good opportunity for undergrads who are considering graduate school to get a taste of the experience, sans the related stressors and heavy workload.”

Projects took the place of exams, which was nice for Gaffney, since some of the proofs were very specific, detailed and, at times difficult to follow. “I loved having a project to work on, and getting familiar with Wolfram Mathematica during the course of my project, Gaffney explained. “It was a good experience and worth the time and effort.”

“Although as an undergraduate I may have needed additional time or practice to stay on the level of graduate students, the class also helped me with time management and task management.”

Gaffney appreciated listening to the graduate presentations. “They were intriguing and it was obvious of the importance to understand the Math you are trying to 'teach' and apply,” she said. “I feel like I learned more in this class than any other class because of the teaching/learning relationship amongst peers and an obvious real world connection.”

Math 407/507X will be will be offered again in Fall 2012.

Dual listing course benefits students

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Master of School Mathematics

The Master of School Mathematics (MSM) program emphasized topics in statistics during Summer 2011. Amy Froelich taught the six-credit Stat 410X, Statistical Methods for Mathematics Teachers, by means of Adobe Connect software to more than twenty teachers across Iowa. Meeting for two and a half hours every day for seven weeks, teachers collected data, performed statistical analyses on multiple data sets, implemented statistical software as well as graphing calculators in the analyses, and participated in small group discussions of the processes and interpretations. One memorable experiment, based on the article “Trashball: A Logistic Regression Classroom Activity” published in the Journal of Statistics Education, engaged teachers as they attempted to toss a ball into a trash can from various distances. Teachers’ successful tosses into the trash can were noted and used in the fitting and interpreting logistic regression models.

Most of these teachers also participated in the one-credit mathematics education seminar which focused on assessment and teaching diverse groups of students, in addition to statistics and probability.

Four teachers successfully wrote and defended their creative components since Spring 2011. Rachel Giesmann examined the topic, “Testing For Randomness: How Do You Prove What Should Happen When Anything Can Happen.” Aaron Ratliff investigated, “Graphical Representations of Complex Zeros.” Clint Gentry explored, “Tetrahedrons Connecting Triangle Theorems to Three-Dimensional Space.” Jody Tomjack wrote, “Algebra II, Computer Science, and Cryptography: A Curriculum Proposal.” Several more teachers are currently working on creative components with plans to complete the program within the next few months.

Financial mathematics helps prepare students for exam

This spring graduate assistant Geoffrey Tims led 35 students through an independent study designed to help them prepare to take the actuarial exam. Topics included interest theory, time value of money, annuities, loans, bonds, general cash flows and portfolios and immunization. Beyond simply understanding these areas, Tims emphasized the mathematics behind them.

The experience was received so well by students that consideration is being given to offering it in the future.

The initiative of interested students in other departments is increasing Math Plus options. Math + Bioinformatics and Math + Materials Engineering now allow students with strengths in those fields of application to add second majors in Mathematics by including in their programs a few more relevant upper level mathematics courses.

Spring 2011 saw 35 Math Plus graduates, and this spring the total was near 50.

This steady increase in mathematics will likely allow us to repopulate some undergraduate courses such as Introductory Combinatorics and Topology that had recently been on hold. Both are used extensively throughout mathematics.

Math Plus growing

Janson Professorship in MathematicsClifford Bergman is the new Janson

Professor of Mathematics at Iowa State University. He was selected by the Dean of the College of Liberal Arts and Sciences from an exceptionally strong field of applicants.

Bergman, who received his Ph.D. from U.C. Berkeley, has been an outstanding teacher and scholar in the Department of Mathematics for about 30 years. He won the ISU teaching award in 1989, and in 2004 was selected as a Master Teacher by the College of Liberal Arts & Sciences. He has taught thousands of undergraduate students over the years, and received outstanding evaluations by his students. However, he has also been influential on the graduate level: in 1997, in response to a need in the Department of Electrical and Computer Engineering, he developed a course in cryptology (CrpE/Math 533). This course, which he taught for many years, is taken by graduate students in engineering, mathematics, and other areas, as well as by many students around the world

through its web component. In 2011 Bergman authored a graduate text in universal algebra, which has become the reference in this area, which is currently being used at several universities.

Currently the Graduate Coordinator in the Department, Bergman plans to use some of the Janson funds to support a training program for new graduate teaching assistants, which includes recording and reviewing sample lectures and other directed classroom activities. Also on the drawing board is a lecture series on the role of the mathematical sciences in the nonacademic world. The goal of the series is to inform high school and college students about exciting career opportunities and encourage them to consider mathematics and statistics for their undergraduate major.

The professorship was established by alumnus and Governor of Iowa State, Barbara Janson, in support of a research mathematician with a commitment to undergraduate education.

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Graduate program talent, numbers

The graduate programs in Mathematics and Applied Mathematics are finishing up a banner year. This year's graduating class may be the largest ever in the history of the department. It also may be the most talented. Several of our students are moving on to positions that should be the envy of everyone in the mathematical community.

It is also a class of substantial breadth. The large cohort of students in graph theory, under the direction of Profs. Axenovich, Martin, and Willson, will surely cement Iowa State's reputation as a growing center in combinatorics. Several members of the stochastics group have landed research positions in both academia and industry. Students in algebra and

Mathematics/Statistics Graduate Career Day held in September. L-R: Wolfgang Kliemann, Dale Zimmerman (UI), Jeff Anderson (UW-Stout), Cliff Bergman, Leslie Hogben, Andrei Lyashenko (QRM), Cynthia Clark (NASS), Elgin Johnston, Alicia Carriquiry.numerics round out the group.

As one class leaves, another enters. We have what looks to be a very strong group of students joining the program in the Fall. Several newcomers have been awarded AGEP (Alliance for Graduate Education and the Professoriate) fellowships. One will receive the Diane Brandt Fellowship for Women in STEM. For the second year in a row, more than half of our new students will be women. We continue to attract applicants from better and better schools and this, in turn, makes our graduate program stronger and stronger.

Our big event of the year was the fall Career Day. On September 24, several distinguished ISU alumni returned to campus to tell the Math and Stat students about career opportunities in

the mathematical sciences. Our very own Jeff Anderson (Ph.D. Applied Mathematics, 1989), now Dean of the College of Science, Technology, Engineering and Mathematics at the UW-Stout talked about the job market at 4-year colleges. Former postdoc Andrei Lyashenko, head of Quantitative Research at Quantitative Risk Management Inc., discussed the allure and the pitfalls of a career in finance. Finally, Paul Hertzel (MS. Mathematics, 1991) described life at Iowa community colleges. There were also presentations by several graduates of the ISU Statistics Department. All in all, a very successful--and tiring--day for all concerned.

In recent years, our graduate students have taken more and more opportunities to attend conferences, present posters, and participate in workshops in the mathematical sciences. This year was no exception. ISU is becoming known for the large contingent that attends the Central Sectional meeting of the American Mathematical Society. Organized by Stephen Willson, three busloads of budding mathematicians made the trip to Lincoln, Nebraska in October. We also had groups attend workshops at the Fields Institute in Toronto, The Mathematical Biosciences Institute in Columbus, The Northwestern Probability Workshop in Evanston, and a workshop in Cancun. Much of this travel was subsidized by the Mathematics Department, partly with funds donated by our generous supporters.

Dominic Kramer presents a poster at the Central Section Meeting of AMS.

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A sampling of 2011-12 colloquia 2012-13 Faculty Professional Development Assignments

Two faculty members have FPDA during the 2012-13 school year: Jonathan D. H. Smith and Fritz Keinert.

Smith will focus on advanced algebra, education and research in Ames, Warsaw and Denver. His work will address

two goals: (1) the need for review of the way advanced algebra is taught at both undergraduate and graduate levels. As core content evolves, new methods and applications must be found that parallel student preparation, skill sets and interests, and (2) the advancement of two emerging fields of algebra addressing some of the key issues that arise as science attempts to cope with an increasingly involved and interconnected world: approximate symmetry and complex systems.

Keinert will spend spring semester at the Universita de Bologna in Italy focusing on new and continuing research projects in compressed sensing. In

particular, Keinert will work to develop new algorithms for CS of video sequences, where correlation between successive frames can be used to eliminate data errors and further reduce the number of measurements.

Anita Layton (Duke) A mathematical model of the myogenic response of the rat afferent arteriole

Nic Lanchier (Arizona State) Two-strategy games on the lattice

Yuan Lou (Ohio State) Evolution of dispersal

Benton Duncan (NDSU) Operator algebras and topological dynamics

Bin Zhang (Sichuan U) Cone multiple zeta values, Shintani multiple zeta values and their double subdivision

Jianqiang Zhao (Eckerd College) Non-standard relations of multiple polylog values at roots of unity

Chihoon Lee (Colorado State) Some stability properties of a reflected fractional Brownian motion on the positive orthant

Michelle Cirillo (University of Delaware) Powerful and productive mathematics discourse

Jon Peterson (Purdue) Traps, slowdowns, and bridges of one-dimensional random walks in a random environment

GSO adds new graduate student clusters

Members of the Mathematics Graduate Student Organization are working to form clusters modeled after the extremely successful Edge program for women led by Leslie Hogben.

Clusters are designed to support first year students by giving them a forum to voice concerns and ask questions. The monthly dinner meetings are aimed at aiding students’ transition to graduate school.

First-years will be paired with senior graduate student mentors, who will participate in the same cluster to which the first-year is assigned as a means of strengthening their relationship.

Plans include a teaching cluster, which may organize an in-house teaching conference, an industry and government cluster, and a general interest cluster where undecided students can consider various career paths.

Fibonacci meets Erdos-Ko-Rado (Steve Butler)

Minimum Rank of Symmetric Matrices described by a Graph (Leslie Hogben)

What's Wrong with Voting? (Mark Hunacek)

Pappus, Desargues, and Cross Products (Roger Maddux)

The Mathematics of Secrecy: An Introduction to Public-key Cryptography (Cliff Bergman)

The Small World Problem: Six Degrees of Graph Theory (Ryan Martin)

Exponential Dominating Numbers (Michael Young)

UG Math Club programs

David Radford (University of Illinois at Chicago) Kaplansky's ten Hopf algebra conjectures

David Bressoud (Macalaster) Characteristics of successful programs in college calculus: Preliminary findings

Lu Wang (Johns Hopkins) Rigidity of self-shrinkers of mean curvature flow

Chao Zhu (UW-Milwaukee) On optimal harvesting problems in random environments

Todd Moore (Kansas State University) What calculus do students learn after calculus?

Holly Swisher (Oregon State University) An extension of a proof of the Ramanujan congruences for multipartitions

Mahamadi Warma (University of Puerto Rico-Rio Piedras) Dirichlet and Neumann boundary conditions for the p-laplace operator: What is in between?

Lexing Ying (U Texas - Austin) The fast multipole methods and its extensions

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You may designate the amount of your contribution to one or more of these established funds:

Dio Lewis Holl Chair in Applied Mathematics Fund (2700481) to recruit and retain the brightest and best faculty members. Janson Professorship in Mathematics (2702279) to support a research mathematician with a commitment to undergraduate education.Dr. Richard Sprague Memorial Fund (2701594) to furnish space and provide resource materials for upper level math majors.Marian Daniells Scholarship Fund (0711566) for outstanding undergraduate math majors.Robert & Marion (Betty) Lambert Award Fund (1900008) to support and reward teaching and research excellence by a graduate student.Mathematics Graduate Student Scholarship Endowment (1900058) to support graduate study.Dio Lewis Holl Award Fund (1909241) for an outstanding junior and an outstanding senior math major.Herta & H.T. David Scholarship in Mathematics Fund (2700486) for an undergraduate math major with financial need and challenging family background.Fred Wright Mathematics Endowed Scholarship Fund (2702071) for an undergraduate student that shows exemplary skills in extracurricular activities.Mathematics Department Development Fund (2700704) to support the efforts of the Math Department.Mathematics Department Scholarship Fund (1900057) to support math majors.Mathematics Department Lectureship Fund (1922512) to finance lectures in mathematics at ISU by mathematicians who are not members of the ISU faculty and awards to graduate students.

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Sharon McKimpsonBruce MericleRana MikkelsonDonald & Marcia MillerOrville & Miriam MillerR. Dennis MinerEverett MooreMarvin & Margaret MundtAnn Gray NoblettJanice NyhusRobert & Cheryl OotenTimothy PenningsDonald PetersonMary PetrickAlan PoormanMatthew & Debra RegennitterAndrew RegenscheidThomas & Sandra RobinsonThomas & Maryn RoggeEdgar RutterDaniel Sarasio MeyerRobert SchmidtJerry & Marjorie SedlacekRobert & Lynda ShiveSherwin SkarKeith SmithSuzanne SmithCheryl StensbyPamela SwanJames ThoreenAmanda TossbergRichard & Gayle Ver SteegCharles VernonC. Mel VickWilliam WagnerJames WalkerJoan WelchEsther WilliamsJean WilliamsonDuane WinklerLonny WinrichBret Wortman

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Dio Lewis Holl AwardTyler Chenhall (Senior)Hao Yuan (Junior)

Elmer Billman Scholarship in MathematicsBenjamin ShellerEmily RickenbachQianrong Wu

Marian Daniells ScholarshipStephen Berg Rebecca EhlersHuan LuErin PaulyXiyuan SunRoy Tinguely

Fred Wright Mathematics Endowed ScholarshipChristopher CoxAlec FilakDiego Hernando Useche Reyes

Alan Heckenbach AwardChelsea HoldridgeBettina Khanthongdy

Gertrude Herr Adamson AwardTyler ChenhallKevin MossNathan Rehfuss

Outstanding Problem SolversTyler ChenhallKevin MossChunlei Yuan

Iowa Collegiate Mathematics CompetitionFirst place: Tyler Chenhall, Kevin Moss & Nathan Rehfuss.Third place: Matt Krambeer, Benjamin Sheller & Hao Yuan

ISU Putnam teamTyler Chenhall, Kevin Moss, and Nathan Rehfuss finished 35th in this year’s competition, with 4,440 students from 572 colleges/universities in the US and Canada competing. Individually, Chenhall ranked 102nd among all competitors while Moss ranked 276th.

Phi Beta Kappa initiatesSeniors:Brent Aronson

Graduate

Undergraduate

J. J. L. Hinrichsen Pure Mathematics AwardCraig Erickson

The Aggie Ho Teaching AwardDominic KramerTracy McKay Chad Vidden

continued next page

Long wins Ruth I. Michler Memorial Prize

Associate professor Ling Long received the Ruth I. Michler Memorial Prize for 2012-13 from the Association for Women in Mathematics and Cornell University.

The Michler Prize grants a mid-career woman in academia a residential fellowship in the Cornell University mathematics department without teaching obligations. This pioneering venture was established through a very generous donation from the Michler family and the efforts of many people at

AWM and Cornell.Ling Long was selected to receive the

Michler Prize because of her wide range of mathematical talents. In 1997 she earned a B.Sc. from Tsinghua University, Beijing, China, majoring in mathematics with a minor in computer science and engineering. Long received her Ph.D. in mathematics from the Pennsylvania State University (PSU) in 2002. She studied modularity of elliptic surfaces under the direction of Wen-Ching Winnie Li from PSU and Noriko Yui from Queen’s University.

Before coming to the Iowa State University in 2003, where she is currently an associate professor in the Department of Mathematics, Long spent a year as a postdoctoral fellow at the Institute for Advanced Studies.

Long’s research involves modular

forms for finite index subgroups of the modular group. These groups play an important role in Grothendieck’s program of dessins d’enfants (children’s drawings). Her work is partially funded by the National Science Foundation

At Cornell, Long plans to work with Ravi Ramakishna on Galois representations attached to noncongruence modular forms based on the pioneering work of Anthony Scholl and her joint work with Oliver Atkin, Winnie Li, and Tong Liu. The Langlands philosophy predicts that the L-functions of these Galois representations should be expressible in terms of L-functions of automorphic forms. Such a connection has far-reaching impacts on the arithmetic of modular forms. Long also looks forward to potential collaborations with other faculty members at Cornell.

Honors & AwardsStephen BergKelley MarkhamJustin MasseyBenjamin MulaosmanovicNathan RehfussLingwei ZhaoElizabeth Ann Whitehead

Juniors:Tyler ChenhallYao FangMatthew KrambeerErin Pauly

Edward Allen Awardee: Tyler Chenhall

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Faculty and Staff

Clint Gentry, Tetrahedrons connecting to triangle theorems to three-dimensional space (Justin Peters)

Rachel Giesmann, Testing for randomness: How do you prove what should be when anything can happen (Amy Froelich)

Aaron Ratliff, Graphical representations of complex zeroese (Irvin Hentzel)

Jody Tomjack, Algebra II, computer science and cryptography: A curriculum proposal (Cliff Bergman)

Lauren Hermann, Stream ciphers and the 1/p generator (Cliff Bergman)

Paul Hertz, Two kinds of approximate symmetry (Jonathan D. H. Smith)

Jeremy Knutson, A survey of the use of cellular automata-like models for simulating a population of biological cellsitle (Michael Smiley)

Wenjun Qin, Discrete Ornstein-Uhlenbeck process in a stationary dynamic environment (Alexandar Roitershtein & Arka Ghosh)

Arianne Ross, Positive semidefinite zero forcing (Leslie Hogben)

Volodymyr Sukhoy, A geometric buildup algorithm for the molecular distance geometry problemle (Zhijun Wu)

Ruth I. Michler Memorial PrizeLing Long

Vinograde Graduate Advising AwardLeslie Hogben (photo below)

LAS Merit Excellence AwardEllen Olson

Promotions effective August 2012 Maria Axenovich to full professorJun Pan to senior lecturer

Master of Science

Master of School Mathematics

Doctor of Philosophy

Devin Bickner, On normal networks (Stephen Willson)

Jyy-I Hong, Coalescence in Bellman-Harris and multi-type branching processes (Krishna Athreya)

2011-12 GraduatesSukjung Hwang, Holder regularity of solutions of generalized p-Laplacian type arabolic equations (Gary Lieberman)

Anchalee Khemphet, The Jacobson radical of semicrossed products of the disk algebra (Justin Peters)

Dominic Kramer, Basis identification through convex optimization (Eric Weber)

Michelle Lastrina, List-coloring and sum-list coloring problems on graphs (Maria Axenovich)

Sijia Liu, Novel data clustering methods and applications (Tasos Matzavinos)

Tracy McKay, The edit distance function for graphs: An exploration of the case of forbidden induced K 2, t and other questions (Ryan Martin)

Oktay Olmez, On highly regular digraphs (Sung Yell Song)

A. Ozkan Ozer, Exact boundary controllability and feedback stabilization for a multilayer Rao-Nakra beam (Scott Hansen)

Travis Peters, Positive semidefinite maximum nullity and zero forcing number (Leslie Hogben)

Reza Rastegar, Topics in self-interacting random walks (Alex Roitershtein & Arka Ghosh)

Jason Smith, Induced saturation number (Ryan Martin)

Elijah Stines, Abelian qo-groups and atomic pseudo-valuation domains (Jonathan D. H. Smith)

Chad Vidden, The direct discontinuous Galerkin method with symmetric structure for diffusion problems (Jue Yan)

Andrew Ylvisaker, A formalization of logic in diagonal-free cylindric algebras (Roger Maddux)

Alberta Wolfe Research FellowshipJing Wang

Lambert Award for Excellence in Applied Mathematics Chad Vidden

Lambert Teaching Award Reza Rastegar

Lambert Graduate Assistantship Hui YuChi-Jen Wang

ISU Teaching Excellence AwardSukjung HwangRyan JohnsonOktay OlmezTravis PetersJason SmithElijah StinesNathan Warnberg

ISU Research Excellence AwardOktay Olmez

Departmental Research Excellence AwardTracy McKayElijah Stines

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Math Matters is published once a year by the Department of Mathematics at Iowa State University. Vol. 6, Issue 1. (c) July 2012Editor: Sue Ellen Tuttletuttle@iastate.edu 515-294-8680

Send address corrections to: Records Department ISU Foundation 2505 Elwood Drive Ames, IA 50010-8644or: recordsstaff@foundation.iastate.edu

Iowa State University does not discriminate on the basis of race, color, age, religion, national origin, sexual orientation, gender identity, sex, marital status, disability, or status as a U.S. veteran. Inquiries can be directed to the Director of Equal Opportunity and Diversity, 3210 Beardshear Hall, (515) 294-7612.

Department of Mathematics396 Carver HallAmes, Iowa 50011-2064

2011-12 Faculty professional development assignmentPaul Sacks was on Faculty Professional Development Assignment for the 2011-12 academic year. The time between September and December of 2011 was spent at several locations in Europe attending conferences and participating in research programs. In September he presented a lecture at the Chemnitz Symposium on Inverse Problems, at the Chemnitz University of Technology in Germany. After that he spent two weeks in Izmir, Turkey giving several lectures and collaborating on research on inverse problems in elasticity with Professor Valery Yakhno in the Electrical and Electronics Engineering department of Dokuz Eylul University. Later in October he attended and presented a lecture at the International Conference on Scientific Computing in Santa Margherita di Pula, Italy. Finally he spent two months as a Visiting Fellow at the Isaac Newton Institute of the University of Cambridge in England, taking part in the Special Program on Inverse Problems which was hosted by the Institute from July to

December of 2011, and giving a lecture in the concluding workshop of the program. During this time period, Sacks also visited Durham University and presented a lecture there.

Sacks with Turkish host Valery Yakhno on a weekend excursion to the archeological site of Ephesus.

Group shot of workshop at Isaac Newton Institute in Cambridge.