I will send the passcode via email to all students in the class

This is a

In the time of a pandemic, the class is online, and the students will have to learn doing their presentations in

- You prepare your slides writing everything on paper in advance. That is what you want people to see during your presentation. You scan these slides -- probably just take pictures with your phone. You may make a slide show, or, if you are a bit lazy and not overly computer-savvy, you create a folder on your computer with these pictures (simply as jpg-files).

During your presentation, you share your computer screen, show the slides one after one, and and use the cursor as a pointer.

- One may create a slide show for a presentation using special software such as
*latex beamer*or*powerpoint.*

For instructions on LaTeX beamer class, see, for instance, one, two, three, and, possibly, tons of other web-sites.

I know little about Microsoft Powerpoint and other proprietary presentation making software, while those who use that may achieve quite impressive outcome.

There are many other technologies one may benefit from. I do not discourage to experiment with any technologies while I certainly do not require to do that.

The usage of advanced technology may enhance the presentation, while for those who are not especially computer-savvy and good in presenting math, the amount of effort invested does not yield an adequate increase of the presentation quality

- attending regularly and participating in class discussions,
- presenting solutions to homework assignments at least four times during the semester (oral presentations),
- taking the mathematics department assessment exam that will be administered during the semester in this class

by Jiří Matoušek

Student Mathematical Library, Volume 53, published by American Mathematical Society,

- To start with, during the first several classes, every student gives a short (approximately 15 minutes) general presentation

*"Why have I chosen Mathematical major, and what is it good for?"*

- After that, every student gives a presentation (approximately 20 minutes) about a field of mathematics on their choice.

That may be:

- Algebra; possibly a smaller subfield such as commutative algebra, category theory, etc would be a better choice
- Geometry; possibly a smaller subfield such as differential geometry, algebraic geometry, etc would be a better choice
- Topology; possibly a smaller field such as algebraic topology, differential topology, etc would be a better choice
- Dynamical systems;
- Analysis; possibly a smaller subfield such as functional analysis, numerical analysis would be a better choice
- Statistics;
- Number theory;
- Any other field/subfield of mathematics on students' choice

The goal of this presentation is to create an overall impression about the chosen field. One may speak about the history, relations to other field of math, important problems, solved and unsolved, etc. One does not need to go deep, and just Wikipedia may be a sufficient source of info. Ideally, the listeners get an idea on what motivates people to enthusiastically work in this field, and what they are doing there.

For this presentation, a student may already need some "slides", but not too much. This will allow the students to warm up for a more mathematically involved presentation. - Meanwhile, math presentations topics will be assigned to the students. Each student chooses a miniature for presentation from the textbook. (Alternatively, a student may select a topic which is not from the textbook for the presentation.) In any event, the presentation topic must be agreed upon with the instructor.

For the miniatures from the textbook, I endorse the topic automatically unless that same miniature has already been chosen by another student. For an alternative topic, a student may need to justify the choice.

The student prepares and delivers a presentation (approximately 30 minutes) on the chosen topic.

- Besides the above, youtube videos with mathematical presentations will be assigned to view. The students are required to watch these videos and to be able to discuss these videos in class, both from the math and purely presentational points of view.
- Assessment exam will be given towards the end of the semester as a part of the classwork. The exam consists of three parts; all three parts are take home assignments.

A typical class consists of a presentation (given either by a student or by the instructor) and a discussion. Each student is required to participate in the discussion. As the students may be not comfortable to discuss their peers presentations and performance, we will primarily discuss math presentations from the youtube videos.

The discussions are concentrated around the idea:

The questions to address during a discussion:

- What math have I learnt from this presentation? Why that math is important and/or interesting for me?
- Which relevant math I was not able to learn from this presentation? How the presentation could be altered in a way such that I could get this math?
- What are, in my opinion, advantages and shortcomings of the way the material is presented?
- What would be an alternative way to present the same material? What may be acquired/lost on this way?

Date | Presentation | Link to a video to watch / other discussion | Remarks/Comments | |

Jan 14 | generalities & intro | |||

Jan 21 | on math major | example of a presentation | ||

Jan 28 | on math major | example of a presentation | ||

Feb 4 | on math major | example of a presentation | ||

Feb 11 | subfield of math | example of a presentation | ||

Feb 18 | subfield of math | |||

Feb 25 | subfield of math | |||

Mar 4 | student's presentation | a mathematical fable | ||

Mar 11 | student's presentation | ellipces and Dandelin spheres | ||

Mar 25 | student's presentation | two squares theorem | ||

Apr 1 | student's presentation | the useless number | ||

Apr 8 | student's presentation | fundamental theorem of algebra | odd polynomials you may benefit by eatching that before: it exploits the same idea in a simpler setting | |

Apr 15 | student's presentation | euler's formula | ||

Apr 22 | student's presentation | visualizing quaternions | ||

Apr 29 | student's presentation | Riemann hypothesis |