Recent News
Letter from the Chair - 2016
May 31, 2016
As I begin my second term as chair of the Mathematics Department, I have some big news to share with you. Thanks to a generous donor, the College of Science and Mathematics has the opportunity to partner with the College of Agriculture, Food and Environmental Sciences on a new research and teaching building. This facility will support undergraduate mathematics research with 1,800 square feet of computational and collaboration space. Our students and faculty have needed this space for a long time.
Though much of the support for this privately-funded building is secured, the college still needs to raise $5 million. If you’re interested in supporting the building, you can contact me at jborzell@calpoly.edu, or contact Ruzena Brar, the college's director of advancement, at rkbrar@calpoly.edu or 805-756-6534.
On a smaller scale, last year I mentioned that the Mathematics Department lab in Building 38 was substantially upgraded with new equipment and furniture that meets the needs of our applied math and mathematics education groups. This summer, the upgrade will be completed with a long overdue refresh of carpet and paint.
In the fall, we welcomed a new tenure-track faculty member, Anthony Samuel, an expert in fractal geometry and analysis. Tony joins us from the Universität Bremen in Germany as an assistant professor. Also, Kara Eversman has been promoted to the scheduling role in the department after spending a year with us as our front office staff person. In this newsletter, you can learn more about each of them, as well as the students’ and faculty’s many achievements.
Also this year, the department went through the thorough and important quinquennial program review process. I am happy to report that the review team affirmed that we are a collegial department comprised of outstanding faculty, staff and students, and one that offers a high quality mathematics program that embodies the Learn by Doing and teacher-scholar models. The team’s report also provided innovative ideas for educating the next generation of mathematicians.
In closing, I’d like to thank those who have supported us through your donations and gifts. Your generosity provides critical support for the students, faculty and staff of the department. It is very much appreciated.
Please keep in touch and let us know what you’ve been up to. If you’re on campus, we’d love to see you at the department office.
Sincerely,
Joseph Borzellino
jborzell@calpoly.edu
Return to Newsletter
Summer 2015 Research
May 27, 2016
Danielle Champney with Chad Eckman, Alvaro Matias and Alex Cheng
Mathematics students Alvaro Matias, Chad Eckman and Alex Cheng worked with Danielle Champney on developing interdisciplinary science, technology, engineering and math (STEM) curriculum that could be adapted for multiple grades and age groups. The group focused on topics in mathematics, statistics, physics and engineering and developed several modules for implementation in middle school, high school and college courses.
Additionally, Eckman adapted one of these modules, which focuses on students' data-based decision making, and implemented it in a fifth grade classroom as part of his senior project in fall and winter. He and Champney are currently writing up the findings. Liberal studies student Colin Schaefer is building on these findings and implementing similar research strategies in another fifth grade classroom to further study how young students make data-driven decisions.
Paul Choboter with Caleb Miller, Skyer Young and Tuyen Pham
Modern weather prediction relies on the careful incorporation of observational data into numerical simulations to improve accuracy. The process of merging data with a simulation is called data assimilation. The mathematics of data assimilation is well-developed and draws from variational calculus, optimization, control theory and statistics.
Data assimilation is used in simulations of ocean circulation as well, but ocean data is difficult to collect in large quantities, especially near the coast. This project seeks to answer the question: with a limited amount of data to assimilate in a coastal ocean model, where are the optimal locations to collect that data? Realistic simulations were run in several configurations, with synthetic data measured from one simulation and assimilated into a second simulation. The Regional Ocean Modeling System was used to perform the simulations. Preliminary results were reported at the Mathematical Association of America fall 2015 meeting, and the research is ongoing.
Caixing Gu with Heidi Keas and Robert Lee
Caixing Gu and students Heidi Keas and Robert Lee worked on a project titled "The n-inverses of a matrix," which resulted in the submission of a manuscript with the same title in December 2015. The concept of a left n-inverse of a bounded linear operator on a complex Banach space was introduced recently. Previously, there have been results on products and tensor products of left n-inverses, and the representation of left n-inverses as the sum of left inverses and nilpotent operators was being discussed. In this paper, the group gave a spectral characterization of the left n-inverses of a finite (square) matrix. They also showed that a left n-inverse of a matrix T is the sum of the inverse of T and two nilpotent matrices.
Tony Mendes with Thomas Taylor, Brian Jones and Shelby Burnett
Tony Mendes worked with students Shelby Burnett, Brian Jones and Thomas Taylor to study the following problem posed by the late Herb Wilf. Let uk(n) be the number of permutations of 1, 2,…, n with no increasing subsequence of length k+1 and let yk(n) be the number of standard Young tableaux with n cells with bottom row at most k cells.
The problem was to find a sign reversing involution proof of the identity
when k is even.
Using the Robinson-Schenstead correspondence, we interpreted the problem as one involving red and blue paths drawn inside symmetric permutation matrices. (See attached figure for one of these matrices when n = 10.) The group hoped that this new interpretation could lead to new insights into the combinatorics of permutations. We were able to solve the problem in certain special cases, but a general solution to the problem remains elusive.
Erin Pearse with Jon Lindren and Zach Zhang
Erin Pearse worked with mathematics student Jonathan Lindgren and engineering student Zach Zhang on the problems of reconstruction of missing data and denoising data. The team is developing an algorithm that converts a dataset (for example, a collection of images) into a network of connected points and then exploits the intrinsic geometry of the network to “fix” damaged points using linear algebra.
Jonathan Shapiro with Buddy Galletti, Adam Mair and Christopher Hurley
Jonathan Shapiro worked with students Christopher Hurley, Adam Mair and Buddy Galletti. The group studied the numerical ranges of composition operators on the Hardy space. They examined the numerical ranges for composition operators whose symbols are automorphisms of the disk, paying particular attention to those whose symbols are elliptical automorphisms. They made several conjectures involving the continuity of the numerical range and the numerical radius. Some continuity results which showed that the numerical range of certain composition operators with elliptical automorphism as their symbols are not disks.
Other research groups were Dave Camp with Darren Marotta and Ben Brown and Stepan Paul with Michael Blakeman, Matthew Varble and Madeleine Jacques.
Return to Newsletter
Faculty Publications, Grants and Awards
May 26, 2016
Publications
V. Bonini, J.M. Espinar, and J. Qing, “Hypersurfaces in Hyperbolic Space with Horospherical Support Function,” Advances in Mathematics, 280 (2015) 506-548.
T.A. Grundmeier, “Developing the Problem Posing Abilities of Prospective Elementary and Middle School Teachers”. In (Eds.) J. Cai, N. Ellerton, and F.M. Singer, Mathematical Problem Posing: From Research to Effective Practice. Springer. (2015)
C. Gu, “The (m,q)-isometric weighted shifts on lpspaces,” Integral Equations Operator Theory, 82 (2015) 157-187.
C. Gu, “Functional calculus for m-isometries and related operators on Hilbert spaces and Banach spaces,” Acta Sci. Math. (Szged) 81 (2015) 605-641.
C. Gu, “Structures of left n-invertible operators and their applications,” Studia Mathematica, 226 (2015) no. 3, 189-211.
J.F. Hall and T.D. Todorov, “Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus,” Bulgarian Journal of Physics, 42 (2015) 99-127.
J. Kautzsch, M. Keßeböhmer, and T. Samuel, “On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps,” Ann. Henri Poincaré, 17 (2016) no. 1, 1424-0661.
B. Li, T. Sahlsten and T. Samuel, “Intermediate β-shifts of finite type,” Discrete Contin. Dyn. Syst., 36 (2016), no. 1, 323-344.
E. Pearse, S. Kombrink, and S. Winter, “Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable,” Mathematische Zeitschrift (2016) to appear.
E. Pearse and P.E.T. Jorgensen, “Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks,” Complex Analysis and Operator Theory (2016) to appear.
J. Remmel and A. Mendes, Counting with Symmetric Functions (Developments in Mathematics). Springer. (2015)
T.D. Todorov, “Steady-State Solutions in an Algebra of Generalized Functions: Lightning, Lightning Rods and Superconductivity,” Novi Sad Journal of Mathematics, 45 (2015), no. 1.
Awards
Todd Grundmeier received the University Distinguished Teaching Award.
Kate Riley received the Most Supportive Professor award from Cal Poly’s Society of Women Engineers.
Grants
Tony Samuel received a grant from Deutsche Forschungsgemeinschaft - Sachbeihilfe in Germany titled Diffusion on Irregular Sets. He will work with Marc Keßeböhmer and Malte Koch. Along with Erin Pearse and John Rock of Cal Poly Pomona, Samuel also received a grant from the National Science Foundation to host the Summer School on Fractal Geometry and Complex Dimensions.
Stan Yoshinobu received a grant from the National Science Foundation for a five-year project to increase the nation’s capacity for inquiry-based, or active, learning in college mathematics courses. This project will expand faculty workshop offerings by training regional workshop leaders. The goals of the project are to offer 12 week-long workshops, and several short workshops to recruit faculty and departments interested in research-based, active-learning teaching methods.
Presentations
In summer 2015, students Colin Schaefer and Alex Cheng traveled with Danielle Champney to Austin, Texas, to present at the Legacy of R. L. Moore and Inquiry-Based Learning (IBL) Conference. The trio presented the talk "Stories of Empowerment: the IBL experience for non-math majors in an upper division math course." The students shared their IBL experiences in both interviews and a student panel.
Todor Todorov presented a talk titled “Large Steady-State Solutions of Ordinary Differential Equations in an Algebra of Generalized Functions” at the International Conference on Generalized Functions. Todorov also presented the talk “A Ring of Fermat Reals with Invertible Infinitesimals” at the Workshop on Generalized Functions and Non-Standard Analysis, organized by the University of Vienna.
Workshops
In fall 2015, Danielle Champney co-taught a course on project-based learning for future teachers with mechanical engineering professor John Chen. The projects focused on wheelchair accessibility. Students designed wheelchairs and built scale models using the engineering equipment and labs. Cal Poly math alumnus and local teacher Ben Woodford (B.S., Mathematics, 2012; Single Subject Credential, Mathematics, 2014) assisted with the students' projects and shared his experiences using project-based learning to teach high school math.
Elsa Medina and Todd Grundmeier led two summer workshops for 50 Noyce scholars from the western U.S. Summer 2015 was the eighth Cal Poly summer workshop for Noyce scholars and focused on functions. Activities were developed around “Putting Essential Understanding of Functions into Practice” published by the National Council of Teachers of Mathematics (NCTM), and “Using Research to Improve Instruction: 2014,” also published by NCTM. During the workshop, participants engaged in problem-solving activities and discussions and attended scholarly presentations.
In June, Tony Samuel, Erin Pearse and John Rock from Cal Poly Pomona will host an international group of mathematicians will gather to teach and lecture on fractal geometry and complex dimensions. The conference will emphasize student participation. On the first day, students will be introduced to the fundamental concepts of fractal geometry — noninteger dimension, self-similarity, etc. There will also be three mini-courses taught throughout the summer school and a variety of more specialized talks, discussions and open problem sessions.
Return to Newsletter
Cal Poly Fares Well at Putnam, Modeling Competitions
May 26, 2016
Putnam Competition
The Cal Poly team — which consisted of Brian Jones, Christopher Hurley and Michael Blakeman — placed 84 out of 554 participating institutions at the annual William Lowell Putnam Mathematical Competition. Other Cal Poly students competed as individuals. This year’s contest was a difficult one, even by the standards of the Putnam Competition. The median score was 0 out of 120.
The best individual scores at Cal Poly were from Michael Boulos with a score of 12 points for a ranking of 504.5 out of 4,275 competitors followed by Michael Blakeman and Alex Radermacher with 11 points each. The six-hour exam consists of 12 problems solved in two three-hour sittings, no calculators allowed.
Mathematical Contest in Modeling
Four Cal Poly teams competed against more than 7,400 international teams from 13 countries in this year's Mathematical Contest in Modeling. The teams earned two Meritorious Awards, given to teams in the top eight percent; one Honorable Mention, given to the top 44 percent, and one Successful Participant. Only 35 teams, or 0.05 percent, placed above Meritorious Award.
Return to Newsletter
Cal Poly Program Could Help Reduce Math Anxiety, Close Gender Gap with NSF Funding
Oct 8, 2015
SAN LUIS OBISPO — Thanks to a $3 million grant from the National Science Foundation, Cal Poly’s Academy of Inquiry Based Learning will lead an effort to increase active learning in college math classes across the nation, with research support from the University of Colorado, Boulder’s Evaluation and Ethnography Research unit.
Active learning — also known as inquiry-based learning (IBL) — has been shown to reduce math anxiety and close the gender achievement gap in math classes.
IBL is a student-centered approach that is significantly different from traditional lecture-based math classes. Students are given problems and tasks that lead them through an exploration of mathematical strategies and skills. With instructor guidance, students form their own understanding of mathematical concepts rather than focusing on finding answers. The system allows students to learn from their failures and recognize trial and error as an integral part of the learning process.
Stan Yoshinobu
“You need to actively engage students so that they construct their own understanding and ask their own questions, so they become better thinkers,” said Stan Yoshinobu, director of Cal Poly’s Academy for Inquiry Based Learning and one of the project’s leaders. “This approach is confirmed by brain research about how people learn.”
Research has shown that IBL reduces math anxiety by focusing on the process of doing mathematics rather than just memorization. This benefits all student populations, including women and minority groups. IBL also mitigates the gender gap currently found in math and science classes. In IBL courses, men and women earn similar grades and continue taking math courses at the same rate.
“We can start addressing some serious social issues by changing how we teach,” Yoshinobu said. “We can make a practical impact.”
Because IBL is so different, professors who want to use it in their class need training. “When you teach through inquiry, you have to adapt to your students in real time and help them get over their obstacles,” Yoshinobu said.
Currently, there is a shortage of trainers, and a limited number of faculty members nationwide have access to IBL workshops each year. This grant aims to triple the number of workshop leaders and add variety to the types of workshops that can be offered to better meet the needs of math instructors.
“As math professors, we can do our regular job in a different way and make a difference in students’ lives. The purpose of this project is to increase the number of people doing that,” Yoshinobu said.
Return to Newsletter
Cal Poly and Santa Maria School District Receive $1.8 Million Math Education Grant
Apr 10, 2015
Kate Riley
SAN LUIS OBISPO — Cal Poly and the Santa Maria-Bonita School District received a $1.8 million California Mathematics and Science Partnership grant from the state Department of Education for a program to improve elementary and middle school student achievement in mathematics.
With this funding, Cal Poly will offer a three-year mathematics development program for local teachers called Central Coast STEM Institutes. The program will help teachers develop a curriculum that links mathematics to the real world.
"What we're trying to do is adapt the Cal Poly model of Learn by Doing into mathematics units for third- through eighth-grade teachers," said Kate Riley, a mathematics professor at Cal Poly who will lead the program.
Over the course of three years, 76 teachers from the district will receive substantial instruction in mathematics content and best teaching practices. They will partner with Cal Poly education and mathematics faculty members to construct curriculum modules — a group of lessons that include a hands-on activity — for example, creating scale architectural models to understand ratios and proportions. The curriculum modules will also align with the new Common Core State Standards.
"Applying mathematics in other contexts, such as simple engineering projects, helps students gain a conceptual understanding. It helps them relate math to the real world," Riley said. "In the 21st century, students need to move beyond ‘add, subtract, multiply and divide’ and into the application of mathematics."
A number of Cal Poly engineering faculty will be co-instructors, guiding teachers as they develop projects to take back to their classrooms. Central Coast community members who work in the engineering industry will also participate.
"Central Coast STEM Institutes will have a huge positive impact on our district," said Olivia Bolaños, director of curriculum and instruction for the Santa Maria-Bonita School District. "With the Common Core State Standards still being relatively new, our third- through eighth-grade teachers have this wonderful opportunity to learn how to teach differently and give our students the 21st century skills and engineering practices they need to be college and career ready."
Through an online platform, teachers who participate in the program will be able to share the curriculum they develop with their colleagues in the district and teachers throughout the state. The program also includes a peer evaluation and improvement process that will allow teachers to collaboratively improve the curriculum over time.
"We think this model will create and sustain positive change in the district and hopefully statewide," Riley said.
