Recommendation Letters

I write letters for a Graduate Program (Master or PhD) only to those who took a junior or senior (300- or 400- correspondingly) classes with me and received A or A+ (that is 85–100) at least in one of them. I am not writing any recommendation letters based on sophomore classes like MAT244 alone (I used but now I have too many letters to write and junior classes do not carry much weight). Note that

  1. I write only what I know first-hand. No external documents are needed.
  2. Please fill forms completely; in particular address: 
    University of Toronto, Department of Mathematics 
    40 St. George Str., Toronto, ON, M5S 2E4 
  3. Please do not send any updates or reminders: I consider requests from Graduate Schools in the order they come by email. 
  4. Please  ensure that I have at least 14 days to submit the  reference letter and try to make all of them coming in batch). 

Vaccinations: more transparency needed

The best site reflecting status of vaccinations in Canada is (IMHO) which relies on the data provided by the provincial governments. In particular, Ontario government provides Not clear, where they get information how many doses were delivered to the province.

And even more important for the provinces would be provide not just the total number of doses but by vaccine.

Also, Quebec provides data by the region, Ontario does not.

And city of Toronto provides no vaccination data at all!

Neither does Government of Canada.

Is it too much to ask to provide this information on the website, not just in TV presentations? We do not have time to watch them!

Return to in-person teaching

Accrding to University plans to return to in-person teaching at Fall of 2021.

However to do so, University must ensure that all instructors are not just vaccinated, but all professors 65+ (my pick) are fully vaccinated by BioNTech-Pfizer or Moderna vaccines which provide the best protection. Indeed, in contrast to many professions, instructors cannot teach classes (and some classes are really large) in masks and blackboard teaching of many disciplines (in particular, Mathematics) require full use of the large blackboard, and putting plexiglass shield in fromt of it would, most likely, prevent students from properly seeing what is on the blackboard.

To do this University must ensure that instructors are considered to be essential workers and the second doze of these vaccines is administrated at least 2 weeks before classes.

So far we have not heard anything from the administration.

Surviving COVID teaching. II

One of the challenges of online teaching was reorganization of the class structure. Traditionally large class consists of Lecture sections and also of Tutorial sections. In the large classes like MAT244 and MAT334 I have not allowed students to change Lecture section as it could lead to the excess of 300 at Zoom meeting (students got Zoom links only to Lecture sections they were enrolled), in the medium size class APM346 all students got Zoom links to all Lecture sections.

But Quizzes which traditionally are held during Tutorials in Tutorial sections (or sometimes during Lectures in Lecture sections) were reorginized: there were 3+1 Quiz sections in MAT244 and MAT334, and 2+1 Quiz sections in APM346: these sections coincided with the Lecture sections except the last one, held in the time convenient to overseas studemts (in China). And students could select their Quiz section and change it between Qjuizzes (technically through Group mechanism in Quercus).

Similarly, 2 Tests groups were created covering 2 time slots and the similar mechanism was invoked. Unfortunately we were not able to offer Deferred sittings. The reason is simple: in the previous years we had a main sitting, 2 alternative sittings and a deferred sitting which required 4 variants of each test (other classes were less accommodating). But with online testing we had 4 variants in each sitting to reduce cheating and making more was not feasible (too much work for already overloaded Class Coordinator).

With the Final Assessment we offered Deferred sitting.

As one can see this system was much more flexible than the traditional one and it was made outside of the traditional framework.

After COVID teaching

The very dark cloud of COVID had a silver lining––for University teaching. First of all, we are left with a lot of new materials. Sure,  after COVID, during in-person teaching I will use a blackboard rather than a data-projector; however these slides and test problems (with solutions) will be very useful axillary materials.

But we also may retain an online teaching in some degree. In MAT244 there are 4 Fall and 3 Spring lecture sections (during Fall of 2020, without room availability and size constrains we were able to have 3 lecture sections, getting rid of one really poorly scheduled section). In MAT334 there are 3 lecture sections at Fall and 2 at Spring, and in APM346 1 at Fall and 2 at Spring. Each of these classes can offer 1 lecture section (in year) for online teaching as more economical option for some students.

What about testing then? Should be it online? My answer is “no”. Instead we should use the same model as Princeton GRE and may be existing infrastructure as well: students go to one of the local Test centers (used together by many Canadian and American universities) and write tests proctored by the local staff. Then their papers will be scanned and uploaded to Crowdmark server. Under exceptional circumstances some students could be allowed to write tests at home but they must purchase a camera and pay for professional proctoring.

Surving COVID teaching

Teaching load during Fall of 2020 was crushing. I was a Class Coordinator of MAT244 “Introduction to ODE” with more almost 900 students originally (the largest Math class coordinated by Research Stream faculty) and MAT334 “Complex Variables” with almost 500 students originally (the 2nd largest Fall class coordinated by Research Stream faculty). Coordinating each such class is a very significant load, coordinating simultaneously 2 is an extremely significant load, and doing this in the first classes of online teaching was crushing.

Yes, I saved each week about 6–8 hours for commuting but I spent at least 20 hours each week preparing slides; I was not invigilating Tests or Final Exam but I wrote 8 variants of each (for two sittings) and extra 4 variants of the Final Exam (now–Final Assessment) for Deferred Sitting and this increase in variants also consumed far more time and efforts. And administrating those on Crowdmark took also a hight toll.

While making slides was the most time and efforts consuming, preparing and editing other materials required also some time. I had no other choice as at least 20% of students were in China.

Sure, there were Summer classes before Fall but they were taught by Graduate students and teaching staff, and I salute them as a first responders, but they left no materials.

I had several screw-ups with online tests and quizzes (everyone had–we started with zero experience; now I know pitfalls and how to avoid them) and I spent a lot of efforts to fix them.

Agreeing to coordinate 2 large classes I knew that it would not be easy, but I underestimated the load. Still I do not regret this decision: leaving one class to be coordinated by postdocs who were mostly other instructors would be unfair and bad for everyone. My experience with those classes (before COVID) and technical expertise would not be used in the full degree.

This semester my load is much easier: I am teaching and coordinating only one class APM346 “Partial Differential Equations” which has in 2 sections less than 300 students. I have much more experience. And I have my Online Textbook. However even this requires reformatting textbook text into slides (and this requires time since Online Textbook and Slide presentation are completely different medias with rather different requirements). And I am upgrading my Textbook in the process!

Significant help came from few most experienced TAs (who were instructors in Summer classes) and from teaching support staff of the Department.

Evil Clicktons and Incompetent Developers

More and more educational platforms include equation editors, and some even claim to support LaTeX. But is such a message always true? Indeed, in some types of Canvas and Piazza pages, you can not only insert an equation by clicking on the corresponding button, but also switch from the “Clicktonian language” to “LaTeXian”. However, let’s see what happens next.

If I decide to correct the equation, it turns out that it is only saved as graphics, not as code, and fix = retype. WTH? !! This is not a support, but a tripping! A statement of support for LaTeX indicates either dishonesty or incompetence, but rather both.

No dual mode delivery

In MAT 244 and MAT 334 (Fall) and APM 346 (Spring) of 2920/21 there will be only online classes and no “dual mode”. Why?

All mathematical classes, and MAT 244 “Introduction to Ordinary Differential Equations”, MAT 334 “Complex Variables” and, especially, APM 346 “Partial Differential Equations” have a lot of formulas. Which means, in person classes, that they should be written on the blackboard (which is the common practice, and it is the best) or projected on the screen as a slideshow (which is a rather standard practice in seminar and conference talks).

In the dual mode it means that while some number of students are in the lecture hall, the rest are watching it as a broadcast. The normal ratio was planned to be 1:5–1:7.

And this online majority gets a raw deal! If the blackboard is small, the result is not too bad but if it is a large stacked blackboard, then without a professional technician on-site formulas on the blackboard are poorly readable or not readable at all.

On the other hand,  pdf slideshow in the lecture hall defies in-person teaching, at least, in mathematics. Further, pdf slideshow from the screen in the lecture hall is definitely worse than one directly broadcasted from the computer in Zoom.

Plus these students have no interactivity, while in Zoom Lecture there is a rather limited interactivity. The same is true for Tutorials, but in Zoom Tutorial TA can provide more interactivity (since the class is much smaller).

Instructor  can send slideshow to both the screen in the lecture hall and Zoom but it  leads to a double workload during the lecture and to the worse experience in Zoom learning, than in pure Zoom meeting.

Conclusion: while the dual mode delivery is reasonable for some classes but definitely not for mathematical classes.

At the moment APM 346 (Spring) is scheduled as a dual mode, but it will be fixed, so

LEC 0101 + LEC 9101 → LEC 0101 (online),

LEC 0201 + LEC 9201 → LEC 0201 (online),

TUT 0X0Y + TUT 9X0Y → TUT 0X0Y (online),

TUT 5X0Y + TUT 6X0Y → TUT 5X0Y (online).

My Talk at Geometry & Dynamics Seminar (Tel-Aviv University, May 27, 2020)

Heavy atoms and molecules: Thomas-Fermi and Scott approximations

The purpose of this talk is to discuss the rigorous mathematical results:

  • Thomas-Fermi approximation to the ground state energy, excessive
    positive and negative charges, and ionization energy (old results).
  • Thomas-Fermi and Scott approximations to the ground state density (new results).


Student Teaching Evaluations

Very interesting article from MAA:

These evaluations positively correlate with the student’s achievements in the current course, but negatively correlate with student’s achievements in the follow-on related courses.

Students of less experienced instructors who do not possess terminal degrees perform better in the contemporaneous course being taught, but perform worse in the follow-on related courses.