Tag Archives: 2019

Generalized Cohen Iterations

Set Theory Seminar (RESCHEDULED from April 12)
CUNY Graduate Center, Room 6417
Friday, May 17, 10:00-11:45am
Jonas Reitz, CUNY
Generalized Cohen Iterations

Adding Cohen subsets to each of a class of cardinals in turn is a common construction in set theory, and underlies many fundamental results. The construction comes in two basic flavors, products (as in Easton’s Theorem on the powers of regular cardinals) and iterations (forcing the GCH). These flavors are apparently quite similar, forcing at stage kappa to add subsets via the Cohen partial order Add(kappa,lambda). They differ only in the universe over which Add(kappa,lambda) is defined – in the case of products the ground model poset is used at each stage, whereas in typical iterations the poset is taken from the partial extension up to kappa. In this talk I will consider an alternative, in which we allow Add(kappa,lambda) to be defined over an arbitrary inner model (lying between the ground model and the extension up to kappa) at each stage. These generalized Cohen iterations are ZFC-preserving, although neither the proof for products nor for traditional iterations transfers directly. They allow constructions such as class iterations of class products of Cohen forcing, with applications including new work with Kameryn Williams on iterating the Mantle.



Opening Gateways: Supporting Success in STEM through Success in Gateway Mathematics

CUNY CUE Conference 2019
May 10, 2019
New York City College of Technology’s new Academic Complex, 285 Jay Street

Presenters:  Jonas Reitz, Charlie Edwards, Laura Ghezzi, Andrew Parker

Abstract: “Opening Gateways to Completion: Open Digital Pedagogies for Student Success in STEM” is a 5 year collaborative grant between the New York City College of Technology and the Borough of Manhattan Community College funded through the Department of Education’s Developing Hispanic-Serving Institutions (Title V) program.  The project supports student success in mathematics courses that serve as gateways to STEM disciplines, courses that often act as barriers to progress and completion in these disciplines. Cohorts of full-time and part-time faculty from both campuses take part in an intensive professional development seminar, where they are exposed to active learning strategies, open digital pedagogies, multiplayer and flipped classroom techniques, games in the classroom, WeBWorK, Desmos and much more.

An ecosystem of high-quality OERs support the pedagogy of our participants. WeBWorK, an open source alternative to expensive and proprietary online homework systems, serves as a platform for the development of problems and problem sets aligned with the curriculum, with customized feedback and error-recognition.  At City Tech, additional development has bridged WeBWorK and the OpenLab: students seeking help on WeBWorK are directed to an OpenLab community space where they can ask and answer questions. Classroom activities and STEM applications developed by our participants, and a curated collection of resources such as online videos, round out our OER ecosystem.

Join us to learn more about our professional development model and see first hand some of the exciting OERs, activities and STEM applications developed and utilized by our participants for Algebra and Precalculus courses.

WeBWorK on the OpenLab:  Leveraging City Tech’s open digital platform to create a community space for homework help

Venue: Mathematics Association of America (MAA)
Metro New York Section, 2019 Annual Meeting
New York City College of Technology, May 4, 2019

Presenters:  Andrew Parker, Charlie Edwards, Jonas Reitz

Abstract: WeBWorK, an open-source online homework system supported by the MAA and the NSF, provides a platform for students to practice and engage with their mathematics studies.   WeBWorK offers a number of advantages over traditional pencil-and-paper homework, including instant, customized feedback and error-recognition. But how do we help students when they get stuck? At City Tech a team of faculty and developers has worked to bridge WeBWorK and the OpenLab, our open digital platform for teaching, learning and collaboration.  Students seeking help on a WeBWorK problem are directed to an OpenLab community space where they can review answers to previous questions about their problem or ask their own. By moving the conversations around homework help into a public space we increase transparency, reducing the repetitious explanations that can occur in one-on-one support models, such as email, where many students can ask very similar questions, each requiring a near-identical response from the instructor.

Want to bring this technology to your own institution? We will discuss how you can set up your own OpenLab, free, through Commons in a Box OpenLab, and our planned release of the WeBWorK OpenLab bridge.

Join us to learn more and see the project in action.