A Mathematical Trivium
This is a set of basic mathematics problems that Arnold devised for physics students. The original text is an article Arnold published in 1991, in Russian Math Surveys 46:1 (1991), 271-278, titled A Mathematical Trivium. The article opens with a two-page preface complaining about how poorly students in 1991 knew mathematics, especially physics students. Following that preface come 100 math problems, billed as the mathematical bottom line for physics students.
Since these problems were written for physics students, they differ from typical math competition problems: there aren't many proof-based questions, mostly computations and model-solving, and quite a few involve rough approximation and estimation, with a distinctly physical flavor. Although the author calls this "the bottom line" of mathematics for physics students, plenty of these problems are still challenging even for math majors. There are some scattered answers to be found online, but they're rather fragmented. Here I'd like to share the problems with everyone. Whenever I find the time, or happen to run into related research, I'll work through some of them and share my solutions with you all. I hope anyone interested will try their hand at these and share their answers with everyone too.
1more
2
3
4
5
6
7
Downloads:
Arnold's original published article (English version): Arnold发表的原文.pdf
English questions (clear scan): Undergraduate_Competitions-Arnold\'s_Trivium-1991-177.pdf
Chinese translation packaged as images: Arnold\'s_Trivium.zip
Online version at Art of Problem Solving: http://www.artofproblemsolving.com
Translated automatically with claude-sonnet-5; all equations are reproduced verbatim from the source. Copyright remains with the original author.