Papers by Petra Bonfert-taylor
Using data to improve programming instruction
DeLFI, 2018
Annales Academiae Scientiarum Fennicae. Mathematica, 2000
We explore in this paper whether certain fundamental properties of the action of Kleinian groups ... more We explore in this paper whether certain fundamental properties of the action of Kleinian groups on the Riemann sphere extend to the action of discrete convergence groups on R 2. A Jørgensen inequality for discrete K-quasiconformal groups is developed, and it is shown that such an inequality depends naturally on the quasiconformal dilatation K. Furthermore, it is established that no such inequality can hold for general discrete convergence groups. In the discontinuous case a universal constraint on discreteness is formulated for both quasiconformal and general convergence groups.
Journal of the Optical Society of America, Feb 17, 2012
This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography.... more This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography. It is demonstrated that, given a fixed imaging geometry, one cannot-relative to standard techniques such as Tikhonov regularization and truncated singular value decomposition-improve the spatial resolution of the optical reconstructions via increasing the node density of the mesh considered for modeling light transport. Using techniques from linear algebra, it is shown that, as one increases the number of nodes beyond the number of measurements, information is lost by the forward model. It is demonstrated that this information cannot be recovered using various common reconstruction techniques. Evidence is provided showing that this phenomenon is related to the smoothing properties of the elliptic forward model that is used in the diffusion approximation to light transport in tissue. This argues for reconstruction techniques that are sensitive to boundaries, such as L 1-reconstruction and the use of priors, as well as the natural approach of building a measurement geometry that reflects the desired image resolution.
2018 ASEE Annual Conference & Exposition Proceedings, Sep 10, 2020
Teaching C Programming Interactively at Scale Using Taskgrader
This demo paper introduces a tool and a method to provide a barriers-free, rich, interactive lear... more This demo paper introduces a tool and a method to provide a barriers-free, rich, interactive learning experience for students of all levels of preparation in programming courses. Taskgrader is an open-source autograding tool providing instant feedback in large-scale online programming classes. This in-browser tool offers extensive feedback to student code submissions right within any LMS and pass data back to the gradebook.
Journal of Geometric Analysis, Sep 1, 2005
We provide new bounds on the exponent of convergence of a planar discrete quasiconformal group in... more We provide new bounds on the exponent of convergence of a planar discrete quasiconformal group in terms of the associated dilatation and the Hausdorff dimension of its conical limit set. In doing so, we use these bounds to realize a theorem of C. Bishop and P. Jones as an asymptotic limit in the dilatation.
The Exponent of covergence and a theorem of astala
Indiana University Mathematics Journal, 2002
We provide bounds on the exponent of convergence of a planar discrete quasiconformal group in ter... more We provide bounds on the exponent of convergence of a planar discrete quasiconformal group in terms of the associated dilatation and (a) the Hausdorff dimension of its conical limit set, or (b) the exponent of convergence of an underlying Kleinian group.
Proceedings of the American Mathematical Society, Nov 30, 2000
We study Fuchsian quasiconformal groups with small dilatation. For this class of groups we establ... more We study Fuchsian quasiconformal groups with small dilatation. For this class of groups we establish a Jørgensen-type inequality in all dimensions. We show discreteness persists to the limit under algebraic convergence and that such groups are discrete if and only if every two generator subgroup is discrete.
Journal of Geometric Analysis, Nov 16, 2010
The exponent of convergence of a non-elementary discrete group of hyperbolic isometries measures ... more The exponent of convergence of a non-elementary discrete group of hyperbolic isometries measures the Hausdorff dimension of the conical limit set. In passing to a non-trivial regular cover the resulting limit sets are point-wise equal though the exponent of convergence of the cover uniformization may be strictly less than the exponent of convergence of the base. We show in this paper that, for closed hyperbolic surfaces, the previously established lower bound of one half on the exponent of convergence of "small" regular covers is sharp but is not attained. We also consider "large" (non-regular) covers. Here large and small are descriptive of the size of the exponent of convergence. We show that a Kleinian group that uniformizes a manifold homeomorphic to a surface fibering over a circle contains a Schottky subgroup whose exponent of convergence is arbitrarily close to two.
arXiv (Cornell University), Jan 15, 2014
Blending and Flipping: A Blended View of Pedagogical Innovation at Wesleyan
In this session we will describe our experiences with flipped classrooms and blended learning at ... more In this session we will describe our experiences with flipped classrooms and blended learning at Wesleyan University from three perspectives: instructor, instructional technology support, and the administration. We will focus on three math courses: 1) A flipped major-level course using recorded lectures created with a Livescribe Smartpen and pre- and post-class Moodle assignments; 2) A flipped sophomore-level course in which students prepared for class by jointly annotating PDF documents and taking Moodle quizzes, and 3) a blended advanced course that used Coursera video lectures originally created for a Wesleyan MOOC and which some students attended remotely (but synchronously). Petra Bonfert-Taylor will share pedagogical insights she gained from her experiences with pre- and post-class online activities, in-class activities, and engaging remote students in collaborative class activities. Jeffrey Goetz will discuss lessons learned in supporting these courses, particularly concerning the software platforms involved (Moodle, Watchitoo\u27s Class Interact, and Coursera). Karen Anderson will discuss some of the bigger-picture administrative issues brought to light by these courses and how Wesleyan addressed them
Transactions of the American Mathematical Society, Oct 2, 2002
We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates th... more We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing so we define new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension. We find these invariants help to expose and explain the discrepancy between the conformal and quasiconformal setting of Patterson-Sullivan theory.
Michigan Mathematical Journal, Oct 1, 2001
Computational Methods and Function Theory, Mar 29, 2014
Exotic quasi-conformally homogeneous surfaces
Bulletin of The London Mathematical Society, Oct 12, 2010
Conformal geometry and dynamics, Dec 8, 2008
In this paper we explore the ambient quasiconformal homogeneity of planar domains and their bound... more In this paper we explore the ambient quasiconformal homogeneity of planar domains and their boundaries. We show that the quasiconformal homogeneity of a domain D and its boundary E implies that the pair (D, E) is in fact quasiconformally bi-homogeneous. We also give a geometric and topological characterization of the quasiconformal homogeneity of D or E under the assumption that E is a Cantor set captured by a quasicircle. A collection of examples is provided to demonstrate that certain assumptions are the weakest possible.
Designing a unique revision loop updating courses simultaneously on different MOOC platforms
2023 IEEE Learning with MOOCS (LWMOOCS)
Annales Academiae Scientiarum Fennicae. Mathematica, 2000
We explore in this paper whether certain fundamental properties of the action of Kleinian groups ... more We explore in this paper whether certain fundamental properties of the action of Kleinian groups on the Riemann sphere extend to the action of discrete convergence groups on R 2. A Jørgensen inequality for discrete K-quasiconformal groups is developed, and it is shown that such an inequality depends naturally on the quasiconformal dilatation K. Furthermore, it is established that no such inequality can hold for general discrete convergence groups. In the discontinuous case a universal constraint on discreteness is formulated for both quasiconformal and general convergence groups.
Blending and Flipping: A Blended View of Pedagogical Innovation at Wesleyan
In this session we will describe our experiences with flipped classrooms and blended learning at ... more In this session we will describe our experiences with flipped classrooms and blended learning at Wesleyan University from three perspectives: instructor, instructional technology support, and the administration. We will focus on three math courses: 1) A flipped major-level course using recorded lectures created with a Livescribe Smartpen and pre- and post-class Moodle assignments; 2) A flipped sophomore-level course in which students prepared for class by jointly annotating PDF documents and taking Moodle quizzes, and 3) a blended advanced course that used Coursera video lectures originally created for a Wesleyan MOOC and which some students attended remotely (but synchronously). Petra Bonfert-Taylor will share pedagogical insights she gained from her experiences with pre- and post-class online activities, in-class activities, and engaging remote students in collaborative class activities. Jeffrey Goetz will discuss lessons learned in supporting these courses, particularly concerning the software platforms involved (Moodle, Watchitoo\u27s Class Interact, and Coursera). Karen Anderson will discuss some of the bigger-picture administrative issues brought to light by these courses and how Wesleyan addressed them
Geometriae Dedicata, 2004
We show that a discrete, quasiconformal group preserving H n has the property that its exponent o... more We show that a discrete, quasiconformal group preserving H n has the property that its exponent of convergence and the Hausdorff dimension of its limit set detect the existence of a non-empty regular set on the sphere at infinity to H n. This generalizes a result due separately to Sullivan and Tukia, in which it is further assumed that the group act isometrically on H n , i.e. is a Kleinian group. From this generalization we are able to extract geometric information about infinite-index subgroups within certain of these groups.
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Papers by Petra Bonfert-taylor