Recent News
Students Attend Professional Mathematics and Math Education Conferences
May 11, 2018
The future of mathematics education got a little brighter this year as teachers-to-be attended multiple professional events and workshops with their faculty mentors. Students also attended and presented at the regional Mathematical Association of America Conference.
California Mathematics Council North Conference
Future elementary school teachers Emily Tom, Sky Griffin and David Gutierrez attended the 2017 California Mathematics Council North Conference for mathematics teachers and educators. They were joined by Maria Ramirez and Hayley Cushing, future secondary mathematics teachers, whose travel was supported by the Noyce Scholarship NSF grant. The students — from math, liberal studies and the single subject mathematics credential — attended talks and participated in discussions about K-12 mathematics in our state.
Elsa Medina and Amélie Schinck-Mikel led a workshop titled Fun with Algebraic Thinking at the conference.
Noyce Scholars
Todd Grundemeier and Elsa Medina offered two three-day mathematics workshops for Noyce scholars during summer 2017. The workshops provide a support system and an opportunity for these future and current mathematics teachers to discuss issues in the teaching and learning of mathematics.
Fifty Noyce Scholars from Cal Poly and other universities attended. The workshop is funded by a National Science Foundation grant that provides $12,000 or $24,000 scholarships to future mathematics teachers who make a commitment to teach in a high needs school district. Participants also receive $800 for attending the summer workshops.
Research on Undergraduate Mathematics Education Conference
Julia Gladding and Nicole Linman attended the Research on Undergraduate Mathematics Education conference to supplement their summer research and senior project work on bridging topics that span the entire K-16 curriculum. Their focus is on developing strands within which student learning can be coherently supported from kindergarten through college.
Cal Poly Math Academy
The sixth annual Cal Poly Math Academy, directed by Elsa Medina and Amélie Schinck-Mikel, welcomed more than 40 Hispanic students from local high schools to campus last summer. For one week, students solved challenging mathematical problems through hands-on activities. The academy, which is supported by the College of Science and Mathematics, aims to inspire students to pursue careers in STEM fields and to see and enjoy the beauty of mathematics.
Golden Section of the Mathematical Association of America Conference
Students Tim Wetzel and Perrin Silveira and professors Jonathan Shapiro and Rebecca Bishop attended the annual meeting of the Golden Section of the Mathematical Association of America Conference held at CSU East Bay. The Golden Section includes Northern California, Northern Nevada and Hawaii.
Wetzel presented a poster on his research findings on two ways to reduce noise in data. His advisor on the project was Professor Paul Choboter.
Wetzel's Abstract
Data transforms are used to put data into a different format, in order to manipulate it in ways impossible to achieve in its original form. These types of transformations are commonly used to “denoise”, or reduce noise in, data. This report examines two types of data transforms — the Fast Fourier Transform (FFT) and the Discrete Wavelet Transform (DWT) — and analyzes which is more effective at improving distorted signals. In this report, two signals were tested:
- Signal 1: a 20-second song clip of ‘Gotta Go’ by The Incrementals synthetically dis- torted with noise generated by matlab’s rand() function
- Signal 2: a seismic signal of a Mw9.0 earthquake originating in Tohoku-Oki, Japan on March 11, 2011, which includes noise organically
Preliminary research indicated that FFT is more accurate when analyzing sound waves due to the periodic nature of the transform, and that DWT is more accurate when analyzing data composed of discrete, unlinked data points. FFT is described as the faster method in all instances. In this report’s experiments, this proved true. FFT was measurably faster for both signals, and measurably more accurate for the sound signal. While it was impossible to quantify accuracy against an original seismic signal by the nature of that type of data, DWT was qualitatively more accurate than FFT in this case.
Faculty Do It All: Publications, Grants, Awards, Talks and Workshops
May 11, 2018
Cal Poly faculty contributed to the field and profession of mathematics in many ways in 2017-18. Read on to learn about their accomplishments, which ranged from discoveries about orbifold structures to presentations on gender equity in STEM disciplines.
Publications
J. Borzellino and V. Brunsden. “On the inheritance of orbifold substructures.” Topology and its Applications, 232 (2017) 176-182, doi:10.1016/j.topol.2017.10.005.
F. Dreher, M. Keßeböhmer, A. Mosbach, T. Samuel and M. Steffens. “Regularity of aperiodic minimal subshifts.” Bulletin of Mathematical Sciences. (2017) 1-22.
C. Gu, H. Heidi and R. Lee. “The n-inverses of a matrix, Functional Analysis.” Approximation and Computation. 31 (2017) 3801-3813.
C. Gu, I.S. Huang, D. Kang and W. Y. Lee. “Normal singular Cauchy integral operators with operator-valued symbols.” J. Math. Anal. Appl. 447 (2017) 289-308.
C. Gu and D. Kang. “Rank of truncated Toepltiz operators.” Complex Analysis and Operator Theory. 11 (2017) 825-842.
C. Gu, S. Luo and X. Jie. “Reducing subspaces on the Dirichlet space and Riemann surfaces.” Complex Manifold. 4 (2017) 84-119.
C. Gu and S. Paul. “Tensor splitting properties of n-inverse pairs of operators.” Studia. Math. 238 (2017) 17-36.
M. C. Kafatos and G. C. Kato. “Sheaf theoretic formulation for consciousness and qualia and relationship to the idealism of non-dual philosophies.” Progress in Biophysics and Molecular Biology. 131 (2017) 242-250.
G. C. Kato and K. Nishimura. “An integrated brain function.” Scientific J. Cogn. Sci. 1(2)(2017) 39-42.
L. Patton, E. Militzer, I. M. Spitkovsky and M. C. Tsai. “Numerical ranges of 4-by-4 nilpotent matrices: flat portions on the boundary.” Oper. Theory Adv. Appl. 259 (2017) 561-591.
Grants and Awards
The Cal Poly Math Club honored Emily Hamilton as the 2016-17 Outstanding Faculty Member of the Year.
Tony Mendes received the Cal Poly University Distinguished Teaching Award.
Tony Samuel received the 2018 Cal Poly Terrance Harris Excellence in Mentorship Award. He also, along with principle investigator J. Walto, secured funding from LMS Research in Pairs – Scheme 4 (41715) for the project titled, “Cohomology of generalised Grigorchuk words” for travel costs for investigators to carry out research visits to the University of Durham.
Joyce Lin and principle investigator Steven Poelzing from the Virginia Tech Carilion Research Institute were awarded a four-year, $2 million grant from the National Institutes of Health to study the role of size and space between cells in determining the risk of sudden cardiac death and possible therapeutic targets to modulate the health of heart patients.
Invited Talks
Danielle Champney gave an invited talk at the AMS Meeting in Riverside titled “Transforming Our Classrooms into Calculus Communities, and the Role of Productive Failure.”
Goro Kato traveled to universities in Kyoto, Osaka, Shizuoka, Waseda, Josai and Jochi, Japan, giving a series of talks on “The diagonal and triangle derived categories of N-complexes” and “Quantum physics and t-topos.”
Joyce Lin served as a speaker for the Gender Equity Center Women in STEM panel, along with Lauren Rueda from EcoVox, Kimberly Walter from Newton Construction & Management and Bushra Anjum from Amazon. Students from all STEM fields at Cal Poly were invited to ask questions about challenges and advantages to being a woman in a male-dominated field.
Linda Patton gave invited talks at the International Linear Algebra Society in Ames, Iowa, on “Numerical Ranges with Rotational Symmetry,” and at the Joint Mathematics Meetings in San Diego on “Pick Interpolation on the Boundary of the Bidisk.”
Tony Samuel gave two talks, “Regularity of aperiodic minimal subshifts” at Durham Universityin the U.K. and “A meander through the space of intermediate β-transformations” at the Fractal Geometry and Dynamics research program in the Mittag-Leffler Institut, Sweden. Samuel also organized two conferences: the Bremen - Cal Poly - Lübeck One Day Meeting on Dynamics, Geometry and Stochasticsm; and Thermodynamic Formalism - Applications to Geometry and Number Theory [In memory of B. O. Stratmann (1957 - 2015)].
Workshops and Conferences
Dave Camp participated in a joint meeting between ReCoVER and Past Earth Network that took place at Dartington Hall, Devon, U.K.. The meeting looked at a hierarchy of nonlinear models of past climate and will consider how global oscillations of climate variables are created (forced or internal) and may be "paced" by astronomical or other forcing. This adds to our understanding of how the climate system in general responds to forcing, which is relevant for projected future climate change.
Linda Patton participated in a workshop “Crouziex’s conjecture” at the American Institute of Mathematics in San Jose from July 31-August 4, 2017.
In Memoriam: Professor Emeritus Jean (Jeannie) Marie McDill
May 11, 2018
The Cal Poly Mathematics Department lost a treasured friend and colleague on Dec. 8, 2017, when Professor Emeritus Jean Marie McDill passed away. Jeanie received her bachelor’s in physics from the University of Texas. She earned her doctorate in mathematics from the University of Florida in 1971, writing her dissertation in category theory under advisor George Strecker. She taught in the Cal Poly Mathematics Department from 1973 until her retirement in 2001; she also taught part-time in the Faculty Early Retirement Program until 2006.
Jeanie was a strong proponent of visualizing mathematical concepts, and she had many creative ideas for such illustrations. Starting in the early ‘90’s, Jeanie worked with other early adopters of instructional technology to create Interactive Differential Equations, a set of tools for visualizing phenomena involving differential equations; she made visualization tools for business calculus as well. She coauthored a well-received textbook “Differential Equations and Linear Algebra” with Jerry Farlow, James Hall and Beverly West.
Locally, Jeanie was one of several faculty who developed and used the computer lab in 38-135 for active learning projects with software. After retiring, Jeanie continued to participate in special sessions involving the Community of Ordinary Differential Equations Educators at the Joint Mathematics Meetings.
In addition to differential equations, Jeanie frequently taught graduate topology and the history of mathematics. One memorable year, her history of math class featured a Newton vs. Leibniz “trial” in which students played the roles of attorneys and witnesses to illustrate the controversy over who really discovered calculus.
Jeanie was one of the first women to teach in the Cal Poly Mathematics Department; she was probably the first tenure-track female faculty member in pure mathematics. She was a wonderful mentor and supporter for female faculty who were hired after her. In addition to providing serious advice, she taught us how to maintain equanimity while frequently losing keys, purses and other important items.
Along with her accomplishments in mathematics and teaching, Jeanie was a founding member of the San Luis Obispo Folk Music Society. She loved reading mysteries and science fiction. Especially after retirement, she traveled to exotic places all over the world with her family and many friends. Her adventures included swimming with whales off the coast of Africa, riding a camel in Egypt, and visiting the Galapagos Islands. Jeanie is survived by her daughter Kathleen McDill, son-in-law Karl Bilawski, grandsons Erik and Ian, and brother Richard Willmore, as well as many extended family members and close friends. Former students and colleagues can send messages or memories to Kathleen at jeanies.memorial@gmail.com.
Kato, Todorov to Retire in June 2018
May 11, 2018
Goro Kato
Goro Kato was born in 1948 in Kariya, Japan, where the founder and first president of Toyota, Mr. Sakichi Toyota, was born and raised. He came to the United States as a graduate student on a Rotary International Foundation Fellowship in June 1972. He earned his doctorate at the University Rochester, in New York with advisor Saul Lubkin who proved Weil’s conjectures (except the Weil-Riemann hypothesis). Kato came to Cal Poly in June 1981 as an assistant professor.
He has given 75 talks, lectures, workshops and seminars at international conferences in Italy, Belgium, the U.K., Romania, Holland, Sweden, Germany, Japan and the U.S., including presentations for the European Science Foundation supported Advanced Lecture Series. He has published forty papers and six books.
Kato has been invited to the Institute for Advanced Study — one of the world’s leading centers for basic research, located in Princeton, New Jersey — seven times. His first invitation was arranged by Professor R. Langlands in 1986, with subsequent invitations arranged by Professor P. Deligne.
His areas of study are p-adic cohomology and its zeta invariants (See The Heart of Cohomology published by Springer, 2006), the theory of D-modules (See Fundamentals of Algebraic Microlocal Analysis, coauthor: Daniele Struppa, published by Chapman & Hall / CRC, 1999), temporal topos in theoretical physics (See Elements of Temporal Topos, published by Abramis Academic, Arima Publishing, 2013), and cohomological algebra. He recently finished the manuscript for his memoir, “Being Here” to be published by Iwanami-Shoten, Tokyo, in 2018 or 2019.
Todor Todorov
Todor D. Todorov earned his doctorate in mathematical (theoretical) physics from the University of Sofia and the Bulgarian Academy of Sciences in 1982 under Christo Yankov Christov, a professor of the University of Sofia and Academician of the Bulgarian Academy of Sciences, a prominent theoretical physicist and one of the founders of mathematical physics in Bulgaria.
Todorov emigrated to the U.S. in 1988 as a political immigrant from then communist Bulgaria and has been a U.S. citizen since 1994.
After earning his doctorate, Todorov held the following permanent and visiting positions: research fellow at the Bulgarian Academy of Sciences in Sofia, Bulgaria; visiting research fellow at the International Institute for Theoretical Physics at Trieste, Italy; visiting professor at the International School for Advanced Studies (SISSA) at Trieste; visiting professor at the University of California, Santa Barbara and since 1990, a lecturer and then a professor of mathematics at Cal Poly.
His favorite course to teach was Math 248, Methods of Proof. He was the advisor for two master theses in mathematics and numerous senior projects and produced several joint articles with students.
Todorov published almost forty articles in different mathematical journals. Most of his research, beginning with his dissertation, is on the application of non-standard analysis (modern theory of infinitesimals) to the Colombeau theory of generalized functions and the problem of multiplication of Schwartz distributions. He also has published articles on the compactification of ordered topological spaces, solvability of linear partial differential equations with smooth coefficients, standard and non-standard asymptotic analysis, Laplace transform, and teaching calculus, in particular, how to teach limits using infinitesimals.
After retiring, Todorov plans to work on a research monograph tentatively titled “An Axiomatic Approach to the Colombeau Theory of Generalized Functions” and enjoy life as much as possible in both California and Europe.
Letter from the Chair - 2017
Jun 13, 2017
It’s been a big year for the College of Science and Mathematics. You may have heard that Bill (Biochemistry, ’72) and Linda Frost recently made a historic gift of $110 million to the college. We’re very grateful to the Frosts for their generosity.
This gift will directly impact the Mathematics Department in a number of ways. It includes money for scholarships to attract the most academically talented high school students. Math students are eligible for these scholarships, which offer $20,000 a year for four years. Currently, there are four of these Frost Scholars in the department.
Summer research students will also benefit from the gift. You can read about the accomplishments of our summer research students in this newsletter.
This gift also includes the previously announced $20 million for the new Science and Agriculture Teaching and Research Complex, which will provide approximately 2,000 square feet of dedicated computational and collaboration space for student-faculty research in multiple disciplines, including mathematics. The building is scheduled to open in the 2021-22 academic year.
From what I’ve seen of preliminary design plans, this new building will be one of the most impressive on campus. Located across from the Baker Center in the open space between the English and Science North buildings, it will incorporate many of the latest innovations in architectural design.
The total cost for the science and mathematics facilities in the building is $25 million, and the college still needs to raise $2 million. In addition to providing needed funding, your donation to this building project will demonstrate to the Frosts that mathematics alumni are dedicated to Cal Poly. If you’re interested in supporting the building, you can read more information online, contact me, or contact the college.
We’re grateful for all the different ways our alumni give back to Cal Poly. In January, we were excited to host alumnus Don Gibson (Mathematics, ’80). As a student, Don competed as a Putnam Exam team member, was a member of Kappa Mu Epsilon, completed two internships with IBM, and was named Outstanding Graduating Senior for the School of Science and Mathematics. After graduating from Cal Poly, Don worked for Hewlett-Packard until his retirement in January 2011. At HP, Don worked in many capacities, which included conducting hundreds of interviews for technical positions. Don spoke to a packed room of math majors about his experience as a recruiter and passed on advice for students confronting job interviews for the first time. It was a pleasure to meet Don, as well as a wonderful experience for our students to connect with him and benefit from his expertise.
In closing, I’d like to once again thank those who have supported us through donations and gifts. We are grateful for the critical support you provide through your generosity. Your continued interest in helping the department meet its goals is very much appreciated by our students, faculty and staff.
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
Publications, Grants and Awards 2016-17
Jun 6, 2017
Publications
A. Bertram and R. Easton. "The tropical Nullstellensatz for congruences." Advances in Mathematics. 308 (2016) 36-82, DOI 10.1016/j.aim.2016.12.004.
J. Borzellino and V. Brunsden. “On the notions of suborbifold and orbifold embedding.” Algebraic & Geometric Topology. 15 (5)(2015) 2789-2803.
E. Brussel, K. McKinnie and E. Tengan. “Cyclic length in the tame Brauer group of the function field of a p-adic curve.” American Journal of Mathematics. 138(2)(2016) 251-286.
C. Gu. “Algebraic properties of Cauchy singular integral operators on the unit circle.” Taiwanese Journal of Mathematics. 20 (1) (2016) 161-189.
C. Gu. “Reducing subspaces of weighted shifts with operator weights.” Bulletin of the Korean Mathematical Society. 53 (5) (2016) 1471-1481.
C. Gu, M. Chō and W. Y. Lee. “Elementary properties of infinity - isometries on a Hilbert space.” Linear Algebra and its Applications. 511 (2016) 378-402.
C. Gu, I.S. Huang, D. Kang and W. Y. Lee. “Normal singular Cauchy integral operators with operator-valued symbols.” Journal of Mathematical Analysis and Applications. 447 (1) (2017) 289-308.
E. Hamilton. “Double coset separability of abelian subgroups of hyperbolic n-orbifold groups.” Proceedings of the American Mathematical Society. 144(6) (2016) 2327–2336.
G. Kato. “Topos Theoretic Approach to Space and Time.” Space, Time and the Limits of Human Understanding. Springer, 2017.
J. Liese, B. Miceli and J. Remmel. “Connection coefficients between generalized rising and falling factorial bases.” Annals of Combinatorics. 19(2)(2015) 337-361.
A. Mendes and M. Romero. “A note on the kth tensor product of the defining representation.” Journal of Combinatorics. 7(4)(2016) 715-724.
B. Richert. “A proof of Evans’ convexity conjecture.” Communications in Algebra. 43(8)(2015) 3275-3281.
K. Falk, T. Jäger, M. Keßeböhmer, J. Rademacher and T. Samuel, ed. Diffusion on Fractals and Non-linear Dynamics: Discrete and Continuous Dynamical Systems Series S. 10 (2017).
R. Veeraraghavan, J. Lin, J. P. Keener, R. G. Gourdie and S. Poelzing. “Potassium Channels in the Cx43 Gap Junction Perinexus Modulate Ephaptic Coupling: An Experimental and Modeling Study.” Pflüger's Archiv - European Journal of Physiology. Aug 11 (2016) 1651-1661.
Invited Talks
Tony Samuel gave two invited talks at the University of Bremen: “Continuity of entropy in one-dimensional Lorenz maps” and “Quasicrystals, Jarník sets and spectral metrics.” Samuel will conduct research at the Mittag Leffler Institute in Swededn in fall 2017.
Joe Borzellino traveled to Krakow, Poland, in fall 2016 to work with collaborator Tomek Rybicki of AGH University of Science and Technology and, while in Poland, attended the 50th Session of the Seminar Sophus Lie at the Mathematical Research and Science Center in Będlewo.
Joyce Lin traveled to Atlanta, Ga., for the Joint Mathematics Meetings in January 2017 to give an invited talk in the American Mathematical Society Special Session on Mathematics in Physiology and Medicine. Undergraduates Sidney Arthofer, Jeffrey Lee, Jojo Brooker, Nolan Schock, Kevin Sum and Caroline Yovanovich also attended.
Grants
Joyce Lin received a joint National Science Foundation-National Institutes of Health grant to study ephaptic effects — a form of communication within the nervous system — in cardiac tissue. She will collaborate with Steven Poelzing at Virginia Tech’s Carilion Research Institute.
Awards
Kappa Alpha Theta, a women’s fraternity founded in 1870, named Danielle Champney one of ten Outstanding Faculty Award recipients following the 2015-16 school year.
Mathematical Competition Results 2016-17
Jun 6, 2017
Cal Poly Fares Well at Putnam Exam
The 2016 Cal Poly Putnam Exam team of Zach Cooperband, Michael Boulos and Perry Roeder placed 70th out of 568 teams and was coached by Lawrence Sze. Cal Poly was the highest ranking team in the CSU. The team’s high score came from Zach Cooperband, who earned a score of 29, which gave him a ranking of 460.5 out of 4,164 participants. He was one of only two students in the CSU in the top 500. Michael Boulos and Sam Lindbloom-Airey scored 11 points each, Perry Roeder earned 9 points, and Nore Vellandi finished with 8 points. View the complete results online. Congratulations to the team and Coach Sze!
Mathematical Contest in Modeling Team Finishes in Top 10 Percent
In January, six three-student teams competed in the Mathematical Contest in Modeling. The top Cal Poly team of Sidney Arthofer, Caroline Yovanovich and Aron Daw earned the rank of Meritorious, which is awarded to the top 10 percent of teams. Three Cal Poly teams achieved Honorable Mention, awarded to the top 50 percent of teams, and two teams were designated Successful Participants. The highly competitive field included 8,843 teams, only three percent of which were from the U.S. Congratulations to all the student competitors!
Students Learn by Doing Summer Research
Jun 5, 2017
Morgan Sherman with Jason Chew and Aron Daw
The Rate of Convergence of the Kähler-Ricci Flow on the Complex Torus
The Rate of Convergence of the Kähler-Ricci Flow on the Complex TorusThe Kähler-Ricci flow is a flow of metrics on a complex manifold that satisfies a PDE which is a nonlinear analog of the heat equation. A solution is a flow of metrics which will tend to smooth out the irregularities in the curvature on the manifold. In our summer project we numerically approximated solutions to the PDE on the complex torus (which, for a given metric, will look like a deformed doughnut) in order to investigate the rate at which the metric converges to the flat metric. Our aim was to compare the rate of convergence with conjectured bounds and our results were consistent with these conjectures.
To tackle this project, the students first acquainted themselves with the notion of a complex manifold, which is, roughly speaking, a smooth geometrical space that can be described by coordinates consisting of complex numbers (a natural example is the complex plane itself). Then we were able to formulate the PDE of interest to us in the case of a torus (which can be realized as a complex manifold). We learned various techniques for numerically approximating the solution to a PDE, and, with extensive coding in MatLab, were able to generate a great deal of concrete examples of tori who were originally deformed due to an irregular curvature but would 'flow' in time toward a more smoothly dispersed curvature.
Caixing Gu with Eunwoo Choi and Luan Dinh
Higher Order Isometries on Finite Dimensional Banach Spaces
An isometry is a linear map that preserves the norm. Isometries on the finite dimensional inner product space are orthogonal matrices or unitary matrices. There are relatively few isometries if the norm of the finite dimensional vector space does not come from an inner product. In this project, we study a generalization of isometries — high order isometries. Numerical and symbolic experiments discovered many higher order isometries when the norm is closely related to an inner product norm. We would like to prove these numerical results in a future project.
Linda Patton with Mollie Zechlin and Jing-Tian Isabella Ye
Mollie Zechlin and JingTian Isabella Ye worked with Professor Linda Patton to study unitary invariants for 4 by 4 matrices. There is a known list of 20 traces involving a matrix A and its conjugate transpose A*. Equality of these 20 traces for two matrices A and B is necessary and sufficient for the matrices to be unitarily similar. Our group made the additional assumption that the matrices are nilpotent. This assumption implies some of the traces are automatically zero so they can be eliminated from the list when checking unitary similarity. Our conjecture was that some of the other traces might be redundant in the nilpotent case. Although we were unable to definitively determine that, we did create examples showing that most of the traces could not be eliminated from the list.
Joyce Lin with Jeffrey Lee
Studying the Effects of Anisotropy on Action Potential Propagation in Cardiac Tissue
Jeffrey Lee worked with Joyce Lin to study the speed of action potentials, not simply along the surface of the heart, but also in the depth of the heart tissue. When an electrical signal passes through heart tissue, the muscles contract and allow blood to pump through the body. This electrical signal is called an action potential (AP). The speed of the AP has been studied as an indicator of arrhythmia — abnormal heart beats — and heart failure. We have excellent simulations of the AP, but given the complexities of the cardiac cells, this is only computationally feasible in a tissue sheet. How does this extend to a full three-dimensional heart? We were not able to complete this project during the summer, though Jeffrey found some interesting trends.
Erin Pearse and Joyce Lin with Jon Lindgren
In the spirit of Learn By Doing, Jon Lindgren has been working with Erin Pearse and Joyce Lin to develop pedagogical materials using a 3D printer. These manipulatives are designed to enhance student learning in the calculus sequences and other upper level courses, providing hands-on visuals for abstract concepts.
Paul Choboter and Joyce Lin with Sidney Arthofer and Caleb Miller
Nonlinear internal waves, a well-established feature of the coastal ocean, play an important role in various physical and biological processes, including vertical mixing. In our summer project, graduate student Caleb Miller and undergraduate student Sidney Arthofer worked with Paul Choboter and Joyce Lin and physics Professor Ryan Walter to explain the ability of a fully nonlinear mathematical model — the Dubreil-Jacotin-Long equation — to describe field observations with a strong background shear current. This interdisciplinary study utilizes mathematical techniques, numerical simulations, and field observations to answer important questions about internal wave characteristics and water column stability. This research was extended through the 2016-17 academic year, with undergraduate Jeffrey Lee joining the research group.
Danielle Champney with Lacey Christophersen, Kathryn Voltmer, Brian Keating and Andrew Crosby
Math students Andrew Crosby, Brian Keating, Lacey Christopherson and Kathryn Voltmer spent the summer working closely with Danielle Champney studying data on the assessment of several unique classroom systems from fifth grade through college. Crosby and Keating also worked with alumnus Ben Woodford (B.S., Mathematics, ’12; Single Subject Credential, Mathematics, ’14) on designing curriculum on Growth Mindset for the New Tech High School teacher professional development program. Christophersen and Voltmer spent additional time thinking deeply about student engagement in fifth grade math. The team produced several papers and posters in progress based on the summer research.
Jeffrey Liese with Jordan Brooker, Alfredo Ramirez and Kevin de Szendeffy
Professor Jeffrey Liese worked with students Jordan (Jojo) Brooker, Alfredo Ramirez and Kevin de Szendeffy studying the asymptotics of minimally overlapping permutations. A permutation p is said to be minimally overlapping if there no integer k>1 such that the first k integers of p are in the same relative order as the last k. Previous work included finding a bound on the probability that a random n-permutation is minimally overlapping as n tends to infinity.
This summer, the students worked on obtaining some exact results with the ultimate goal of precisely determining the aforementioned probability. Although this probability still remains unknown, the group was able to produce some partial results. In particular, they provided some explicit formulas for the number of permutations that overlap in certain specific ways. Perhaps future work on studying other types of overlaps could yield enough information to characterize the asymptotics of minimally overlapping permutations.
Zachary Cooperband also participated in summer research advised by Dave Camp.
Engaging the World of Mathematics
Jun 5, 2017
Inquiry-Based Learning
Professors Danielle Champney, Todd Grundmeier, Dylan Retsek and Stan Yoshinobu are collaborating on a $2.8 million National Science Foundation-funded project to expand the professional development capacity of the mathematics profession. This five-year project is in its second year, and during the summer of 2017 they will organize three Inquiry-Based Learning workshops in collaboration with 15 other facilitators across the nation.
Robot Mentors
In June 2016, students from Da Vinci High School in Hawthorne, Calif., visited Cal Poly to showcase robots that they designed and built in response to a problem designed by Cal Poly math students Curtis Li and Alvaro Matias, engineering students Lucas Dodd and Vitto Monteverdi, and faculty advisor Danielle Champney. The Cal Poly team designed a two-month long project to build a robot that could rescue a trapped faculty member in the engineering quad by navigating several obstacles by remote control.
The Cal Poly team also served as mentors for the high school students for the duration of the project along with math student Brian Keating, and helped the high school students troubleshoot their mathematics, physics and engineering questions. During the academic year, the project expanded to grades 9-12. Math students Hayley Cushing, Maria Ramirez and Nick Rubio; engineering students Kara Hewson and Gloria Whang; and physics student Max Yarbrough mentored the high school students.
All Things Noyce
Noyce Workshop
Todd Grundmeier and Elsa Medina offered two three-day mathematics workshops for 47 Noyce Scholars during summer 2016. The workshop is designed to provide a support system for these future and current mathematics teachers and an opportunity for them to discuss the teaching and learning of mathematics. The workshop is funded by a National Science Foundation grant that provides $12,000 or $24,000 scholarships to future mathematics teachers who make a commitment to teach in a high needs school district. Noyce Scholars also receive $800 for attending the summer workshops.
Noyce Summit
Elsa Medina and Noyce Scholar Ben Woodford (B.S., Mathematics, ’12; Single Subject Credential, Mathematics, ’14) presented the results of National Science Foundation-funded work by Medina and Todd Grundmeier in a presentation titled "A Model for Continued Support for Math Scholars" at the 2016 Noyce Summit in Washington, D.C. Woodford was selected from a nationwide pool to be part of a panel presentation at the conference and represented Cal Poly's Math Noyce program.
Noyce Conference
Elsa Medina, Amelie Schinck-Mikel and undergraduates Maria Ramirez and Hayley Cushing gave a presentation titled "Using the Fold-and-Cut Theorem to Engage Students in Mathematics" at the Western Regional Noyce Conference held in Fresno, Calif.
Future Teachers Attend Conferences
Math students Roxanne Windover, Julia Gladding and Maria Ramirez attended the 2016 December California Mathematics Council North conference for math teachers and educators.
Elsa Medina, Danielle Champney and four students who are preparing to become mathematics teachers attended the annual California Mathematics Council Conference held in Pacific Grove, Calif.
Math Academy
The fifth annual Cal Poly Math Academy, directed by Elsa Medina and Amelie Schinck-Mikel, welcomed more than 40 Hispanic students from local high schools to campus this summer. For one week, students solved challenging mathematics problems through hands-on activities. Students also had the opportunity to explore the campus, heard from a campus police officer about forensic science, asked questions of members of the Society of Hispanic Professional Engineers, and toured the agricultural facilities. The academy, which is supported by the College of Science and Mathematics, aims to inspire students to pursue careers in science, technology, engineering and mathematics (STEM) fields and to recognize and enjoy the beauty of mathematics.
Middle School Science Bowl
The Central Coast Middle School Science Bowl was held at Cal Poly on Saturday, February 25th. The Regional Science Bowl competition is an annual, fast-paced, question-and-answer contest in which students answer questions about Earth, physical, life, and general sciences, and math. Eighteen teams from eight middle schools participated.
Although Science Bowl tournaments have been taking place on the Central Coast for several years, this is the first time that this competition was held at Cal Poly. The competition was organized by Paul Choboter (Mathematics), Jenny Cruz (CESAME) and Jason Diodati (Templeton High School).
The event was generously supported by CESAME, and local community sponsors included IQMS in Paso Robles, MindBody in San Luis Obispo and RSH Construction in San Luis Obispo. The members of the winning team from St. John's Lutheran School in Bakersfield, Calif., received all-expenses paid trips to Washington, D.C., to participate in the National Science Bowl. The U.S. Department of Energy, Office of Science, manages the National Science Bowl and sponsors the finals competition.
Simple Group Sends Large Cohort to Graduate School
Jun 3, 2016
Thanks to funding from a generous donor, a group of math and math-interested majors met weekly during 2014-15 and 2015-16 for in-depth, on-going discussions of mathematics-related subjects. The Simple Group — named after an enigmatic mathematical object — also hosted well-known guest speakers and held group GRE study sessions.
Though diving deeper into mathematics is the group’s main purpose — discussion topics included the nature of pi and Heegner numbers — it proved a great springboard for graduate school. Five students will attend prestigious doctoral programs at the University of Illinois at Chicago; University of Colorado, Boulder; UC Santa Barbara; UC Santa Cruz and UC Davis.
These successful graduate school applications are due in part to group study efforts on the Mathematics GRE exam, which significantly streamlined the problem-solving process. The fall GRE scores were among the highest ever recorded by Cal Poly math students, reaching as high as the top 10 percentile. This may be one of the most significant and long-lasting benefits of the Simple Group meetings because the department now has good ideas about how to prepare our majors for the exam.
The group is seeking funding to continue in the 2016-17 school year. For more information contact Joe Borzellino, department chair, at jborzell@calpoly.edu or 805-756-2206.
