## My Research Monograph @ Springer-Verlag

##### Microlocal Analysis, Sharp Spectral Asymptotics and Applications

Volume I. Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymptotics

Volume II. Functional Methods and Eigenvalue Asymptotics

Volume III. Magnetic Schrödinger Operator 1

Volume IV. Magnetic Schrödinger Operator 2

Volume V. Applications to Quantum Theory and Miscellaneous Problems

## MAT244 @Fall 2019 Enrolment Issues

• Instructors cannot help you to get into class. At the moment nobody can: all Lecture Sections are full. Furthermore, LEC 0101, LEC 0201 and LEC 5101 are at their rooms capacities.
• Moreover, waiting lists are in total around 40 (as of August 1).
• LEC 5201 is limited by 120 and it’s room (LM 162) capacity is 154; so it may happen that this section will be expanded to its room capacity (decision is with the Dean’s Office).
• All other sections could be expanded only if moved to larger rooms. For day sections (LEC 0101 and LEC 0201) I consider this as highly improbable.
• For LEC 5101 I consider this as rather improbable, but let us wait to see.
• Will be the fifth lecture section created? I consider this as highly improbable.
• Basically you chances are mainly with someone dropping from the class. There is an important date (September 18) which is a deadline to drop the class without financial penalty and the deadline to use ACORN to get into class, choose Lecture and Tutorial section.
• If you really want to take this class now, I suggest not to be picky and chose whatever is available. Chances are that later (it is difficult to say when, but after September 18 for sure) I will be able to help you to adjust your sections.

Class Coordinator
(Victor Ivrii)

## Prerequisites and Corequisites

Recently I have taught three courses:

#### MAT244H1 – Introduction to Ordinary Differential Equations.

• Prerequisite:
• Calculus I: (MAT135H1 & MAT136H1)/ MAT137Y1 or Analysis II (MAT157Y1)
• Linear Algebra I: MAT223H1 or Algebra I: MAT240H1
• Corequisite:
• Calculus II (MAT235Y1/​ MAT237Y1) or Analysis II​ MAT257Y1

I believe that

• MAT135/MAT136 and MAT235Y1 are too weak and should be quashed and
• Linear Algebra II: MAT244H1 or Algebra II: MAT247H1 should be Recommended.

#### MAT334H1 – Complex variables

• Prerequisite:
• Calculus II: MAT235Y1/​ MAT237Y1/​ or /Analysis II: MAT257Y1
• Linear Algebra I: MAT223H1 or Algebra I:​ MAT240H1

I strongly believe that

• MAT235 is too weak and should be quashed, while
• Linear Algebra I/ Algebra I is not needed.

#### APM346H1 – Partial Differential Equations

• Prerequisite:
• Calculus II: MAT235Y1/​ MAT237Y1 or Analysis II: MAT257Y1,
• Ordinary Differential Equations: MAT244H1/​ MAT267H1

I very strongly believe that

• MAT235 is too weak and should be quashed, and
• Linear Algebra II: MAT244H1 or Algebra II: MAT247H1 should be added as a prerequisite, and
• Complex Variables: MAT334H1 or Complex Analysis I: MAT354H1 should be added as a corequisite.

I also very strongly believe that MAT334 and APM346 are excessive for economists etc and should be replaced by a single one semester class

Elements of the Complex Variables an d Partial Differential Equations

## Crowdmark: using and abusing. III. Misc

###### Extra pages

If multiproblem Test has Extra pages, they belong to the last Question in the Test. It creates a lot of problems when a student uses them for any other Question. Solution: place on these pages “fake questions”, empty and worth 0. Then they will be “in the public use”

Even better: divide each page in half, and place on each the fake questions. The last half-page may be reserved for the supervisor comments.

###### Clone/Edit evaluation

Fasilitator (Instructor) can clone evaluation made by Grader (TA) and then edit it as his/her own (thus appropriate them). It allows the Instructor to add/edit comments and marking signs without disabling comments made by TA.

## Crowdmark: using and abusing. II. Owner

Owner (of the test) is a person, who prepares the test, uploads it to Crowdmark, imports and add students, invites Graders (TAs) and Facilitators (instructors) to grade, can see and do everything…

The biggest shortcoming of Crowdmark out-of-the-box is that everybody gets the same test. If the owner wants more than one variant, Crowdmark recommends “make several assessments”. This is inconvenient, especially if we want adjacent booklets to be different.

Why we need several variants? Tests often have early and/or late sittings.

Quizzes are written during regular lectures or tutorials, so different sections should get different variants (at least, if written at different times. Further, while Tests and Exams are usually conducted in the special rooms with the individual tables for each student or, at least, students are sitted with sufficient spacing, Quizzes usually are written in the normal lecture or tutorial settings, with students, sitting side by side and are especially prone to cheating. But it looks like cheating happens even in the Test and Exam settings.

So, we want to have under an umbrella of the same quiz or test for Crowdmark server have several different assesments, and they may be arranged in different ways:

Example 1: We want booklets 1–100 to be Assesment A, 101–200 to be Assesment B.

Example 2: We want booklets with the number $\equiv 1 \pmod 5$ to be Assesment A, $\equiv 2 \pmod 5$ to be Assesment B, $\equiv 3 \pmod 5$ to be Assesment C, $\equiv 4 \pmod 5$ to be Assesment D,
$\equiv 0 \pmod 5$ to be Assesment E.

Example 3: Combined

So we need to “cheat” Crowdmark Server. We upload either an empty booklet, or a booklet containing only common elements of all variants. Then, say, we get a big pdf file, containing, say 200 booklets of 4 pages each (for Quiz). Each front page contains the form to be filled by a student (we use beta-version with the server-side OCR) and each page has a unique QR-code and its textual reflection.

After this we use this 800 page booklet (call it “dummy.pdf”) as a background for LaTeX file.

###### Sample Quiz 1

See Sample Quiz. You need to modify it for your purposes, in particular, redefine problems, and booklets, and the number of pages in the booklet and the number of booklets.

###### Sample Quiz-1a

See Sample Quiz 1a. You need to modify it for your purposes, in particular, redefine problems, and booklets, and the number of pages in the booklet and the number of booklets.

This is a latest and greatest version of the real Quiz.

###### Sample Quiz 2

This is again a LaTeX file but designed to help barbarians who do not use LaTeX. Say, there is Q.pdf which is produced by MSW or other JunkWriter and consists of 5 versions of the same 4-pages Quiz stacked one after another, and dummy.pdf obtained from Crowdmark.
Then This Sample Quiz takes Q.pdf and overprints it by pages 1–20 of dummy.pdf, then adds Q.pdf again and overprints it by pages 21–40 of dummy.pdf etc.

## Crowdmark: Using and abusing. I . Grader

Crowdmark is a system of online grading students papers, which allows to do it in a more civilized way than the usual paper grading. It is useful for a large class, and especially useful when there are few graders.

I am not going to explain the obvious, but there are less known features.

###### The grader can put into comment
1.  a LaTeX code (surrounded by dollar signs) and it will be parsed (there are plenty limitations and some quirks too; also it is a rather known feature)
2.  an emoji
3. url like http://www.math.toronto.edu and it will become a clickable link
4. image link <img src=”http://www.math.toronto.edu/cms/MathSite/images/math_logo_white.svg” > </img> and image appears
###### The grader cannot paste into comment
1. formatted (font, size, bold/italic/underlined… ) or colored text;
2. graphics

To be continued with real hacks!–for owner (who prepares test)

###### Library
1. Library of comments is not just an archive of the comments used, it is an integral part of the commenting process. Editing comment in the Library changes all instances of this comment on different booklets.
2. Comments may be shared with other graders.
###### Cheating
1. Unfortunately in the large classes cheating is now widespread. It was not so 20 years ago, but then I stopped giving homeworks which are graded (too much sharing) and now Quizzes go the same way.
2. With Crowdmark cheaters are much more exposed: by default Crowdmark  graders grade booklets in the order of their numbers. Meanwhile, students with adjacent or close booklet numbers seat close to one another and sharing happens between neighbours. This means that the grader can easily spot too close similarities.
3. However, I do not want to catch cheaters, I want to prevent cheating and the best way to do it is to give multiversion quizzes and tests. I am discussing how to do it in my next post.