The discussion revolves around potential project ideas in group theory for high school students, particularly focusing on the suitability and complexity of various topics. Participants explore various applications and concepts within group theory, considering the educational level and background of the student involved.
Participants express a range of opinions on the suitability of various topics, indicating that there is no clear consensus on the best project idea. Concerns about the complexity of certain topics and the student's preparedness are common themes, but multiple competing views on potential projects remain.
There are limitations regarding the student's background knowledge, particularly in linear algebra and modular arithmetic, which may affect the choice of project. Additionally, the requirement for a "scientific" project without illustrations or visualizations poses challenges for certain topics.
The very bare understanding I have of abstract algebra is solely from having deep knowledge of linear algebra. Unless this high school is a super-duper magnet school, I just don't see how anyone will have type of mathematical sophistication to do anything in this.malawi_glenn said:Problem is, this student has not taken my "linear algebra for high school students" (yet)
No idea what a magnet school is.swampwiz said:The very bare understanding I have of abstract algebra is solely from having deep knowledge of linear algebra. Unless this high school is a super-duper magnet school, I just don't see how anyone will have type of mathematical sophistication to do anything in this.
I like this point of view. There is no such thing as being too young to understand. It is only a matter of language, maybe of time, but not a matter of content. I will never forget, and I am absolutely sure she has forgotten, how my then-daughter of six years of age could handle negative numbers, including some basic arithmetic in ##\mathbb{Z}[ i ].## Of course, it was more about playing games against boring car rides. However, it shows what humans are capable of without the pressure of grades or the narrow - and in my mind silly - corset of a curriculum.malawi_glenn said:You'd be suprised what some of my students can ro at the age of 17-18. Some of their project work is more sophisticated than most bachelor theses...
I have seen a few kids over the years that are extremely brilliant, and new able to handle pure mathematics. the school I got my bs from has an early entrance exam. Where the majority of students are between 16-17 (close to 18). Currently, there is a 14 year old student taking ring theory, and should graduate next year. But yes, it is not the common experience of most high school students.swampwiz said:The very bare understanding I have of abstract algebra is solely from having deep knowledge of linear algebra. Unless this high school is a super-duper magnet school, I just don't see how anyone will have type of mathematical sophistication to do anything in this.
Analysing some subset of moves in chess using group theory.Office_Shredder said:OK, but the important question here is, how did the project go? What did they end up doing?