GAP use in teaching

[olexandr-konovalov]

We are collecting information about the use of GAP in teaching mathematics or computer science. If GAP is used in any way in teaching in your institution, we would be very grateful if you could briefly answer the following questions:

1) In which institution and where are you working?

2) For what courses or types of teaching is GAP used?

3) At what mathematical level are these courses?

4) How many students are taught in these courses?

5) For how long (approximately) has GAP been used in this way?

6) Is there any teaching material publicly available?

7) For publicly available material, which links may we add to https://www.gap-system.org/Doc/Teaching/teaching.html ?

A few brief statements are sufficient for our purposes.

The same question has been also asked in the GAP Forum, see https://mail.gap-system.org/pipermail/forum/2020/006029.html

[angeldelriomateos]

1) In which institution and where are you working? Universidad de Murcia

2) For what courses or types of teaching is GAP used? Grupos y Anillos (Groups and Rings), Códigos Correctores y Criptografía (Error Correcting Codes and Cryptography), Teoría de Números (Number Theory)

3) At what mathematical level are these courses? GyA Bachelor in Mathematics (2nd year, compulsary), CCyC Bachelor in Mathematics (4th year, optional), NT (Master in Mathematics, optional)

4) How many students are taught in these courses? GyA (about 60), CCyC (about 10), TN (less than 5 usually)

5) For how long (approximately) has GAP been used in this way? 10 years.

6) Is there any teaching material publicly available? No.

7) For publicly available material, which links we may add to https://www.gap-system.org/Doc/Teaching/teaching.html ?

[pedritomelenas]

1. In which institution and where are you working? Universidad de Granada

2. For what courses or types of teaching is GAP used? Álgebra I, Software en Matemáticas

3. At what mathematical level are these courses? Álgebra I, Bachelor in Mathematics (1st year, compulsary), Software en Matemáticas (Master in Mathematics, optional)

4. How many students are taught in these courses? Álgebra I, 50; Software en Matemáticas, 12

5. For how long (approximately) has GAP been used in this way? 4 years SM; more than 10 years the ones related to Álgebra I (though there they are simply used as a "calculator", and only for some lecturers).

6. Is there any teaching material publicly available? Yes. https://github.com/pedritomelenas/Software-Matematicas-GAP

7. For publicly available material, which links we may add to https://www.gap-system.org/Doc/Teaching/teaching.html ?

   • https://github.com/pedritomelenas/Software-Matematicas-GAP,
   • please remove those pointing to ocw.ugr.es (we are working to bring them back),
   • and keep https://www.ugr.es/~pedro/gap/.

[mohamed-barakat]

1) University of Siegen

2) Computeralgebra Praktikum I & II (Mathematical programming exercises) and exercises for the courses Algebra, Algorithmic Algebra, and Commutative Algebra.

3) First -- fifth semester

4) Until now around 15 students.

5) Since 2017.

6) https://www.algebra.mathematik.uni-siegen.de/barakat/teaching/W19/PraktikumCA/

7) I have to make a permanent link which always points to the current semester as I keep updating the content.

[olexandr-konovalov]

Many thanks @angeldelriomateos @pedritomelenas @mohamed-barakat !

[MWhybrow92]

1. University of Primorska
2. Theory of permutation groups
3. One masters course and one PhD course (both optional)
4. Masters: 4, PhD: 10
5. To my knowledge, one year. I think I am the only lecturer to use GAP in my course.
6. No

In answer to a separate question from @alex-konovalov :

I attended a software carpentry school for GAP as a PhD student and I now use the techniques that I saw there in my own teaching. I start off by making sure that everyone has GAP installed on their own machines. We then work through the lesson interactively making sure that everyone can follow and type out the commands in real time. I use a mixture of slides and live demonstrations.

[olexandr-konovalov]

@heikodietrich uses GAP in several courses at at Monash university (Australia):

• MTH4141 - Computational group theory http://www.monash.edu/pubs/2019handbooks/units/MTH4141.html
• MTH5141 - Computational group theory http://www.monash.edu/pubs/2019handbooks/units/MTH5141.html

[olexandr-konovalov]

GAP teaching materials and software packages written by Peter Webb (University of Minnesota): http://www-users.math.umn.edu/~webb/GAPfiles/

Several times I have taught the use of GAP as part of a graduate level group theory course in which I also explain some of the algorithms. I do this during 50 minute sessions held each week in a computer lab, over about 8 weeks. The format is that each member of the class sits at a computer and is presented with a list of GAP commands together with a small amount of commentary. At my direction they work through these commands and observe what happens. At key points we stop to discuss what has happened. I introduce the necessary background theory as it is needed.

[olexandr-konovalov]

https://mat.ug.edu.pl/~rlutowsk/pub/gap-short.pdf - "GAP – bardzo krótkie wprowadzenie" by Rafał Lutowski (Institute of Mathematics of the University of Gdańsk).

[olexandr-konovalov]

Report: Student Seminar in Combinatorics:Mathematical Software (Group Theory andSymmetries) by Loreno Heer https://inf.ethz.ch/personal/fukudak/lect/mssemi/reports/08_rep_LorenoHeer.pdf

[pedritomelenas]

M. D'Anna, V. Micale and I gave the course "Semigruppi numerici e applicazioni" at the Scuola Superiore di Catania, during the academic year 2016-17, where gap was used: https://github.com/pedritomelenas/SSC-Semigroups

We gave an introduction to numericalsgps and guava.

[pedritomelenas]

C. Alonso González, R. Guerrero Francés, M. A. Navarro Pérez, V. Ortiz Sotomayor and X. Soler Escrivà, from the Universitat d’Alacant and Universitat Politècnica de València made an innovative teaching experience of the use of GAP in some algebra courses at the Universitat d’Alacant. GAP was used in the courses Group Theory and Coding Theory. The results of the study where published in https://rua.ua.es/dspace/bitstream/10045/101711/1/Memories-Xarxes-I3CE-2018-19-141.pdf (see the whole volume in : http://hdl.handle.net/10045/98732). In their conclusions, the authors mention that the experience was positive and that they are considering the possibility of extending it to the rest of math courses with algebraic content.

[olexandr-konovalov]

H/T @pedritomelenas: Semigruppi numerici e applicazioni (March 2017): http://www.scuolasuperiorecatania.it/it/semigruppi-numerici-e-applicazioni-0

[ManuelAFDelgado]

1) In which institution and where are you working? University of Porto, Portugal

2) For what courses or types of teaching is GAP used? Number Theory and Applications; Semigroups, Automata and Languages (the package Automata); Algebraic Coding Theory (the package GUAVA); other courses in algebra (GAP is mainly used to show examples; students are encouraged to produce their ones to help them in the learning process)

3) At what mathematical level are these courses? Bachelor in Mathematics and Master Mathematics (optional in all the cases)

4) How many students are taught in these courses? A few hundreds over the years.

5) For how long (approximately) has GAP been used in this way? Over one decade.

6) Is there any teaching material publicly available? An introductory book on number theory and applications (to cryptography), in Portuguese, is to be published by the University of Porto (U.Porto edições). The examples in the book, so as the solutions to some computational exercises, are in GAP. It is a joint work with António Machiavelo.

7) For publicly available material, which links we may add to https://www.gap-system.org/Doc/Teaching/teaching.html ? For the moment none.

[olexandr-konovalov]

Many thanks for further answers @MWhybrow92 @pedritomelenas @ManuelAFDelgado !

[olexandr-konovalov]

@ManuelAFDelgado you wrote

How many students are taught in these courses? A few hundreds over the years.

Thank you, this is useful - would it be possible to get an actual estimate for 2013-2020, please?

[olexandr-konovalov]

@pedritomelenas wrote:

The results of the study where published in https://rua.ua.es/dspace/bitstream/10045/101711/1/Memories-Xarxes-I3CE-2018-19-141.pdf (see the whole volume in : http://hdl.handle.net/10045/98732).

Indeed, the full volume has a longer report, with more graphs and testimonies, so you should look at http://hdl.handle.net/10045/98732 -> http://rua.ua.es/dspace/handle/10045/98732 and download a PDF from there.

[ManuelAFDelgado]

@ManuelAFDelgado you wrote

How many students are taught in these courses? A few hundreds over the years.

Thank you, this is useful - would it be possible to get an actual estimate for 2013-2020, please?

About two hundred of my students had some contact with GAP during this period.

[pedritomelenas]

I asked my colleagues at the Universidad de Almería (Granada shares master in mathematics with Almería, Cádiz, Málaga and Jaén). They were also using GAP in the course Software en Matemáticas in the last two years. They have three or four students per year.

They have been also using GUAVA for Coding Theory in the course Criptografía y Teoría de Códigos in the degree of Computer Science, since at least 2012. The number of students in this course is between 25 and 30.

http://cms.ual.es/UAL/ht/estudios/titulaciones/titulacion/asignaturas/asignatura/TITULACION4100?id=&idTit=4100&idAss=40007321&idCaracter=O

GAP was also used in the courses Ampliación de Matemática Discreta/Matemática Discreta II during several years, mainly for polynomials over finite extensions of finite fields. Between 2004 and 2011 the number of students were around 100.

http://cms.ual.es/UAL/universidad/departamentos/matematicas/docencia/asignaturas/asignatura/index.htm?id=6250&idTit=4000&idAss=40002202&idCaracter=B

[olexandr-konovalov]

Many thanks for help, @ManuelAFDelgado and @pedritomelenas, that's very useful!