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An Independent Study Explores Abstract Algebra
Junior Chase Wayland spent this semester immersed in a self-designed study to explore concepts beyond elementary algebra.
Wayland wanted to learn more about abstract algebraic structures like Groups, Rings and Fields and the mathematical relationships between, within and across them. So he asked Math teacher Sven Carlsson to be his advisor for an Independent Study that would help him develop:
- An understanding of Abstract Algebra
- Proof skills and creative thinking
- Math communication and teaching skills
Wayland proposed a curriculum that incorporated more than 30 topics using online resources from Harvard and MIT, in addition to websites like MathOverflow and YouTube, during 10 class sessions. Carlsson worked with Wayland each week to digest new concepts and curricula, filling in the blanks and serving as a sounding board to help explain complex ideas in an understandable manner.
As a final project, Wayland papered the hallway with flyers to attract students, and Carlsson invited all employees, to a presentation on the Insolvability of the Quintic—or, stated differently: There is no general formula to solve a polynomial of degree 5 or higher.
In his presentation, Wayland took his audience on a mathematical journey through the foundations of modern math and algebra, beginning with an introduction to group theory, describing rings and fields and sharing Galois theory—a connection between field theory and group theory.
Parker commends Wayland on pursuing this Independent Study and sharing his learning with the school community.
Photos from the presentation are available here.
Francis W. Parker School educates students to think and act with empathy, courage and clarity as responsible citizens and leaders in a diverse democratic society and global community.