# Student seminar on automatic proofs of binomial identities (Spring Semester 20)

The seminar is now over. Thanks to all participants. For archiving purposes, you can find below the planning, the written reports and presentation slides from the students (the seminar was conducted online because of CoViD-19), and the general instructions.

Planning (Thursday 3-5pm, room Y27H12):

• April 23rd: Sister Celine's method (Maximilian Janisch; see the report and the slides), and Gosper's algorithm (Vanessa Hauri; see the report and the slides),
• April 30th: Zeilberger's algorithm, by Noam Szyger (see the report and the slides) and ; Bettina Wohlfender (see the report and the slides)
• May 7th: Zeilberger's algorithm, by Alain Schmid (see the report and the slides).
• May 14th: Wilf-Zeilberger phenomenon, by Elena Silingardi and Annina Cincera see their joint report, Elena's slides and Annina's slides),
• May 28th: Algorithm Hyper, by Stefan Herytash (see the report and the slides) and Zouhair Ouaggag (see the report and the slides).

Source: A=B. M. Petkovsek, H. Wilf, D. Zeilberger, CRC Press. Available here. We'll focus on Chapters 4 to 8. I recommend to the students to read Chapter 1-2 by themselves before the class to get a general picture (they are introductory and non technical).

Instructions: Most chapters introduce the method on some illustratory examples. You are required to use another example during your presentation in class. The exercises at the end of each chapter can be a good source of other examples; giving full justification of some claims of the book is also a good idea. Your presentation should also include some computer-assisted example(s), showing computations in maple or mathematica using a beamer.

Written report: you are required to send us a written report with the content of your presentation. The report should contain the detailed statement, proof, computation that you want to present (not just references to the book). You can type it in lateX; very clean handwritten documents are also accepted. Please attach a maple or mathematica worksheet with your computer assisted example(s).
The report needs to be sent at the latest on Thursday one week before the presentation. We will then give you feedback, generally Friday before your presentation.

Validation: To validate the lecture, you need to do a written report, a presentation and attend other sessions of the seminar (I will circulate a presence list).

The TA for the lecture is Raul Penaguiao. You can contact him with precise questions (not just "can you help us preparing our presentation?", but rather "We do not understand this specific step of that proof") during the preparation of your presentation.

For the presentation, you are free to distribute the content of the chapter as you want (general presentation of the algorithm, proof of some theorem, computer-assisted example). The presentation of each student should be between 30 and 45 minutes.