i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?historical past/issues:My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)

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i&#039;m seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?historical past/issues:My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.i have taught this magnificence three times earlier than. (a part of the purpose that i&#039;m posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik&#039;s dice.the students&#039; math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren&#039;t. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed &quot;pre-calculus&quot;: trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.So, any ideas? preferably, i&#039;d like to find some thing a bit &quot;sexy&quot; (like the Rubik&#039;s cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of &quot;see&quot; institution idea on the cube became pretty popular.(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)

Cooper Church · Accepted Answer

I grew up in PR.China, and changed into pretty disappointing with the pre-university training in mathematics. i am very glad to look one educator such as you posting such a query here.Combinatorics, graph concept and wide variety principle, for my part, are right fields you could pick out substances from. with the aid of selecting some subjects referring to &quot;massive theorems&quot; together with Fermat&#039;s closing theorem (of course in noticeably naive approaches) can surly appeal to younger college students.I think this can be executed subject matter by using subject matter, as opposed to stucking in simplest one small discipline. I believe one most important problem in mathematical schooling in China is that there are too many restrictions on exceptional branches. There are too many questions including &quot;what area does this problem belongs to?&quot;A e-book to advocate is &quot;proofs from the e-book&quot; written by means of Martin Aigner and Günter M. Ziegler (with illustrations by Karl H. Hofmann). although that is wriiten as a graduate stage e-book. you can actually locate materials suiatble for excessive college college students. more importanly, it can greatly enhance the scholars&#039; taste in cutting-edge arithmetic.

Mark Mcbride · Accepted Answer

i&#039;m no longer certain how properly this will work in practice, however i&#039;ve always been interested in introducing mathematical rigor through an summary algebra direction, instead of through analysis. As a motivating query, you could have the problem of squaring the circle (as an instance), even though this would contain going into a lot of principle pretty fast. (it&#039;d additionally be extra appropriate inside the west, in which squaring the circle and trisecting the perspective have been problems of hobby seeing that antiquity.)

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