Ideas for group theory for high school math project

[swampwiz]

Problem is, this student has not taken my "linear algebra for high school students" (yet)

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]

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.

No idea what a magnet school is.
But yes linear algebra is very good to know. But you can do the entire discrete mathematics by Biggs without knowing any linear algebra.

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...

 

[fresh_42]

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 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.

 

[MidgetDwarf]

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 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.

When I taught calculus to high schoolers, I actually introduced a bit of analysis, and they were fine with it. Like others mentioned, language, presentation, and teacher support or what is needed, and not caring what administration says.

 

[Office_Shredder]

OK, but the important question here is, how did the project go? What did they end up doing?

 

[malawi_glenn]

OK, but the important question here is, how did the project go? What did they end up doing?

Analysing some subset of moves in chess using group theory.