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>This dynamic isn't unique to ECE 352, or even Wisconsin – I saw the same thing when TA'ed EE 202, a second year class on signals and systems at Purdue. The pro
by h_spacer 6y ago
>This dynamic isn't unique to ECE 352, or even Wisconsin – I saw the same thing when TA'ed EE 202, a second year class on signals and systems at Purdue. The problems were FFTs and Laplace transforms instead of dividers and Boolean2, but the avoidance of teaching fundamental skills was the same. It was clear, from the questions students asked me in office hours, that those who were underperforming weren't struggling with the fundamental concepts in the class, but with algebra: the problems were caused by not having an intuitive understanding of, for example, the difference between f(x+a) and f(x)+a.
>When I suggested to the professor that he spend half an hour reviewing algebra for those students who never had the material covered cogently in high school, I was told in no uncertain terms that it would be a waste of time because some people just can't hack it in engineering. I was told that I wouldn't be so naive once the semester was done, because some people just can't hack it in engineering. I was told that helping students with remedial material was doing them no favors; they wouldn't be able to handle advanced courses anyway because some students just can't hack it in engineering. I was told that Purdue has a loose admissions policy and that I should expect a high failure rate, because some students just can't hack it in engineering.
I think that fundamentally the problem is in mathematics.
Our notation is from the 18th century at best, yet because it is hard people think it's meaningful.
Standard maths notation makes sense for polynomials: a_0 x^n+a_1 x^(n-1)+ ... + a_n = k is the only type of general expression one can write without the need to use parens. Everything else is a kludge added on top of that notation to fix one problem with it, but only in one specific field. Which leaves you with dozens of dsls to specific types of areas of maths/engineering/physics/etc
I'm a big fan of lispified typed lambda calculus. There are no exceptions, and any specific notation is defined in terms of rewrite rules. The fact that types are required also makes it clear what you're talking about.
Unfortunately I'm in a minority of one whenever I've talked to working mathematicians, even though I can tear through papers and proofs an order of magnitude faster than when I try and use standard notation.
- BoiledCabbage 6y agoIt's absolutely a huge part of the problem. Mathematical notation is horrible, it's imprecise, it's inconsistent - it's a hold over from a legacy time. But anytime it's brought up, mathematicians get upset. The issue will never be addressed, but it's a disaster.
- h_spacer 6y agoI think it will when we finally have a language that is useful for all of: jotting down expressions, manipulating them by hand, and being consistent enough that automated theorem provers/proof helpers can use as their internal representation. The issue right now is that the impressionistic maths notation works well for humans and there is no computer language that: 1). has good notation 2). is useful to mathematicians out of the box Mathematica, sage, axiom, etc all have internal representations that are essentially the system I'm talking about but the user facing language is a mess in all cases. It's not a simple problem and I don't even know what the solution looks like. It will have a lispy notation (tree serialization), and use rewrite rules (generalized macros) and types (some type of type inference with explicit typing annotations), but other than that I feel like someone trying to invent Algol in 1947.