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Here’s a sample problem from discrete math when I took it in university: For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd num
by chongli 1y ago
Here’s a sample problem from discrete math when I took it in university:
For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd
number of parts, and each part is congruent to 1 modulo 3. Prove that:
|Cn| = [x^n] (x - x^4)/(1 - x^2 - 2x^3 + x^6)
Where [x^n] indicates the coefficient of the x^n term in the formal power series generated by the rational function (rational representation of the ordinary generating function).
I doubt many elementary school students would be able to solve problems like this.
- rak1507 1y agoWhy not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.
- chongli 1y agoAnd the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets). There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.
- rak1507 1y agoYou definitely don't need to know any of that background to be able to arrive at the answer. To fully understand everything maybe, but all it takes is: a = x^1 + x^4 + x^7 + ... = x(1 + x^3 + x^6 + ...) = x/(1-x^3) a + a^3 + a^5 + ... = a(1 + a^2 + a^4 + ...) = a/(1-a^2) Substitute + simplify. I don't think this is beyond a (fairly smart) elementary school student.
- redczar 1y agoYou obviously have not taught mathematics to high school students.