This discussion centers on suitable high school math projects focused on group theory for talented students. Participants suggest various project ideas, including the study of Lie algebras, coding theory, and the application of group theory to solve problems like the Rubik's Cube. The conversation highlights the challenge of finding original topics that avoid common online resources while adhering to project guidelines that prohibit visual aids. Suggestions also include exploring the history of group theory and its applications in modern mathematics.
PREREQUISITESHigh school math teachers, students interested in advanced mathematics, and educators seeking project ideas that challenge talented pupils while adhering to academic guidelines.
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?