The Moxart “Perspectives in Mathematics” program was conceived to provide enrichment to exceptional high school and undergraduate students. High school students whose advanced placement mathematics courses are not providing enough challenge, and undergraduates who need a deeper and sturdier background can benefit from the program.
Thank you for not dividing by zero
Moxart is addressing a need that cannot be filled in ordinary mathematics courses. Most of these courses present a great deal of material, often so much that getting through the syllabus is a challenge. Teachers are also constrained by the need to serve all their students, which takes time. Thus there is little opportunity to discuss the deeper implications of the material.
The Moxart “Perspectives” lectures fill that gap. Developed over a period of many years, the purpose of the lectures is not necessarily to present new material — although there will certainly be some — but to pull together in a meaningful fashion material the student already knows.
Some of the Moxart lectures do this by starting with a concept and using it repeatedly to prove disparate theorems. The student learns the concept as a powerful technique for tackling various problems, and may also see that the theorems are less disparate than they seemed.
Other lectures present just one theorem but provide several distinctly different proofs, along with meaningful applications to other areas of mathematics. This gives the student an in depth grasp of the theorem, which is not possible with just one proof, let alone no proof. It also teaches that there are many ways to approach problems, and that some get results much more easily than others. Commentary on the proofs and comparisons of their strong and weak points are an intrinsic part of the lecture.
The “Perspectives” topics are offered either as single lectures or as a complete series at a very modest cost. A high school or college with even a few very talented mathematics students may want to arrange for these lectures.