Today is The Day We Fight Back against mass surveillance by the NSA.
Mathematicians, do your part and don’t go to work for the NSA. If they don’t have our talent, then they won’t be able to do as much mass surveillance.
Don’t let the USA become more of a police state than it already is!
The first day of class for the spring semester went great! I’m teaching two sections of math for liberal arts. We’ll be covering geometry, set theory, logic, counting theory, probability, and statistics. The course is primarily intended for students with weak mathematical backgrounds who do not intend to major in the sciences or math.
At the end of class in one of the sections, two of the students told me they were excited for the class, and one said that I gave the best introduction of all her professors that day.
The cap on my classes was 100 students each, but I ended up with twenty-some in one section and thirty-some in the other section. So we have this big classroom with a microphone and TV screens so students at the back can see, and I just have everyone sit towards the front teach it like a regular class. The smaller class size will sure make things easier when it comes to grading, and while I will be missing out on the skill-building opportunity of teaching a bigger class, I prefer having a smaller class.
I’ve divided the tests and homework problems into easy, medium, and hard problems. It’s possible to get passing grades answering just the easy and medium problems on the homework and just the easy problems on the test. But to get an A, one has to answer the hard problems, which are substantially more involved and require more critical thinking. That way, I hope that every student can be challenged at their own level.
I got a lot of my teaching preparation done for the whole semester over winter break, as well as almost all of my academic job applications for the current hiring cycle, so I don’t think I’ll feel like I’m scrambling to keep up all semester, as I did last semester.
I gave a talk for the Florida Atlantic University math colloquium last Friday, October 25. The abstract is below. Markus Schmidmeier, the colloquium organizer, told me today that a record number of his students attended this talk as compared to other colloquium talks, and that they told him they enjoyed the talk. It was a fun talk to give, very high-level with no proofs, an overview of set theory to encourage students to learn about it more deeply later. I touched on the ZFC axioms, forcing, inner models, and large cardinals.
Abstract: The ZFC axioms are the basic axioms underlying almost work in contemporary mathematics. Set theorists refer to the universe of all sets as V. The sets of V, as a whole, satisfy the ZFC axioms. But is this the only universe of sets? Are there other universes of sets that also satisfy the ZFC axioms? In fact, there are. I will discuss these universes of sets and how set theorists build them. I will also discuss how a statement can be true in one universe of sets but false in another. In this case, we say that the statement is independent of ZFC.
I am planning to attend the MAMLS conference at Rutgers next weekend. I’ll look forward to seeing many of my friends and colleagues there.
I am teaching two sections of Calculus 2 this fall. It’s my first time teaching calc 2. I am trying to incorporate some suggestions in my teaching given to me by various colleagues, including Joel Hamkins and Bill Kalies. These suggestions include staying standing up as much as possible, marking participation points for every time that students participate in class, and encouraging more student participation in working out the examples, even at the cost of being able to go over fewer examples per class session. Bill Kalies is the official Master Teacher in the FAU math department, so I have been working with him to develop my teaching, and I invited him to sit in on my class a month or so into the semester.
The classrooms that I’m teaching in are very nice; they are in the business school building, which received funding from Office Depot. They feature whiteboards and opaque projectors (i.e. a digital video camera hooked up to a projector). Although I have a personal aesthetic preference for chalkboards, the whiteboards are nice, because they allow me to use different colors more easily — colored chalk is hard to erase. It’s also my first time teaching with whiteboards. Maybe by the end of the semester, I’ll prefer them over chalkboards. The opaque projectors are helpful, but they take a while to warm up, so I’m not sure how much I’ll use them.
The sections are about 35 students each, the same size as the sections that I taught at City College.
There are four total sections of Calc 2 at the main FAU campus this semester, and the other two sections are being taught by another Visiting Assistant Professor. He and I are planning to meet up irregularly to discuss teaching-related issues.
This post is being cross-posted on both my teaching and research blogs, since it lies somewhere in between. Katie Brodhead and I will be teaching a logic course/seminar this semester at FAU. The seminar will be meeting Mondays, Wednesdays, and Thursdays from 3-4PM in the math lounge, room SE 215, beginning on Wednesday, September 4. I will generally be presenting on Mondays and Wednesdays, teaching an introductory course on large cardinals. The suggested prerequisite for my course is a graduate course or an advanced undergraduate course on logic. Katie will generally be presenting on Thursdays, teaching an introductory course on algorithmic randomness. The two courses are independent in terms of the content, but the participants will heavily overlap. Everybody reading this blog is welcome to attend my course. I would assume that Katie would say the same for hers, although you could contact her to be certain.
This paper appears in the Archive for Mathematical Logic. It has been published first online here http://link.springer.com/article/10.1007/s00153-014-0410-y and will soon appear in print.
This is an adaptation of many of the results from the second chapter of my dissertation into a journal article. You can read the preprint here.
Abstract
I analyze the hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal. Many of these cardinals are defined by modifying the definition of a high-jump cardinal. A high-jump cardinal is defined as the critical point of an elementary embedding $j: V \to M$ such that $M$ is closed under sequences of length equal to $\sup\{j(f)(\kappa) \ |\ f: \kappa \to \kappa \}$. Some of the other cardinals analyzed include the super-high-jump cardinals, almost-high-jump cardinals, Shelah-for-supercompactness cardinals, Woodin-for-supercompactness cardinals, Vopenka cardinals, hypercompact cardinals, and enhanced supercompact cardinals. I organize these cardinals in terms of consistency strength and implicational strength. I also analyze the superstrong cardinals, which are weaker than supercompact cardinals but are related to high-jump cardinals. Two of my most important results are as follows.
– Vopenka cardinals are the same as Woodin-for-supercompactness cardinals.
– There are no excessively hypercompact cardinals.
Furthermore, I prove some results relating high-jump cardinals to forcing, as well as analyzing Laver functions for super-high-jump cardinals.
UPDATE (2/25/15):
Kentaro Sato wrote to me recently and informed me that he has proved the result on the equivalence of Woodin-for-supercompactness cardinals and Vopenka cardinals in his paper,
Kentaro Sato
Double helix in large large cardinals and iteration of elementary embeddings
Annals of Pure and Applied Logic
Volume 146, Issues 2–3, May 2007, Pages 199–236
What I call Woodin-for-supercompactness, he calls 0-W-huge in Def. A.1. In Cor. A.7, he shows this to be equivalent to what he calls 1-W-strong, which is also called 2-fold Woodin in Def. 9.1. In Cor. 10.6, he shows that 2-fold Woodin and 1-fold Vopenka are equivalent, with an even stronger statement, Thm. 10.5, the equivalence on the filter level.
I was not aware that Sato had proven this fact at the time that I wrote my paper.
My own modest contribution regarding the equivalence was to provide a different proof using a different theoretical framework, and to highlight the result using a different vocabulary.
I have accepted a Visiting Assistant Professor position at Florida Atlantic University for the 2013-2014 academic year. I just dropped off the signed contract at a UPS shipping location this morning. I am looking forward to working on research with Bob Lubarsky, who was very helpful in setting me up with the job. I will be teaching two undergraduate courses per semester, most likely in calculus, and also likely teaching independent studies in set theory to graduate students. I’m super-excited about the opportunity to teach graduate students. I really feel like my career is moving in a nice direction.
Florida Atlantic is a public university located in Boca Raton, about an hour north of Miami.
I recently found a video of my classroom teaching from my time at City College. It shows the first half of a college algebra class, in which I pass back homework, go over homework problems, collect homework, and teach a lesson about solving equations with radical expressions. You can view it here as a streaming video. Feel free to offer suggestions and feedback on my teaching style.
A year a half ago, I wrote a research statement as part of an application for the Dissertation Year Fellowship at the Graduate Center. The application materials asked me to make my research accessible to a nonspecialist, so I attempted to do that. I later changed the application drastically, upon receiving advice from an insider that even though I was supposedly supposed to make the research accessible, that was not what they were actually looking for. Now, I present an essay adapted from that research statement on my research blog. It shows how my current research interest in big numbers stems from ideas that interested me even as a young child. It’s a few pages long, so I am posting it as a pdf file in order not to hide earlier blog posts with its length. Click here to read it.