31–40 of 165 posts
So far, my vote is for Calculus.
Disclosure: I am a mathematics teacher. (I teach prealgebra to elementary-age pupils.) I am NOT a programmer. But I think the correct answer to the question is "it depends." In other words, even though you have specified a level of programming, "bog standard, journeymen, CRUD programming in Objective-C," and even though you have laid out the usual progression through the usual school mathematics topics in the English…
Can you expand on that? What do students do in other mathematical areas if they don't do proofs? I did all of my studies in France and I don't how much of a difference there is (though all my friends who have studied both in the US and in France found the maths classes a lot easier in the US).
I voted for discrete mathematics for two reasons: (1) It has relatively few pre-requisites in comparison to advanced calculus (which I'm assuming means something like a first course in real analysis). (2) It isn't rote. There's more creative thought involved in solving problems. Even high school calculus is often extremely rote. I think programming is rarely rote, even if it's just a CRUD app. You have to strategize…
Similar to your son, I have been programming since an yearly age. We had Macromedia Flash back then, and over the course of my academic life, as i progressed in the Mathematics courses, my programming capabilities increased with leaps and bounds. For example, the movement in my games was usually similar to Pacman or bomberman. No arcs, or curved paths existed. As i learned about 2D motion, i started making Platformers. As i learned trigonometry, I started making games involving curved paths on a 2d plane. Even a realistic Car game. i remember coming home from high school the day they taught us about "Radians" and began usign the sin, cos, tan funtions of ActionScript (because the documentation said it used Radians and that never made sense to me before). It was that very year i programmed game AI that would chase the player in a realistic way.
So yeah, math helps
Given that, programming is everything and anything. Which is why a good programmer would always focus on the problem not the knowledge required to solve the problem. Because if you embark on tough project, find solutions is essentially like making a discovery.
In my opinion you shouldn't ever first learn books(apart from the very basic ones) and then go in search of problems. The right approach is to look for problems, and while solving them and you can learn the knowledge required to solve those problems as you go along.
Programming is analogous to nearly everything in math. Programming is only a tool, which you can use to solve various problems around yourself modeled in some mathematical form(In short everything).
Which is why programming is the most awesome profession ever. Because by nature it lets you probe and grok the nature, working and science behind everything. That is why programmers are so good at problem identification, solution design and problem solving in general.
I voted for discrete mathematics for two reasons: (1) It has relatively few pre-requisites in comparison to advanced calculus (which I'm assuming means something like a first course in real analysis). (2) It isn't rote. There's more creative thought involved in solving problems. Even high school calculus is often extremely rote. I think programming is rarely rote, even if it's just a CRUD app. You have to strategize…
My first course in real analysis didn't have much in the way of prerequisites at all. I loved it because everything was covered ground up (including concepts like "limit").
Programming is a progression from being able to give logical directions and knowing some simple arithmetic and commands all the way to knowing all kind of obscure things from discrete mathematics and linear algebra, perhaps with some application of things from calculus, statistics, and trigonometry occasionally thrown in.
However, what will separate proper journeyman code from mush is design and organization, something which is not entirely in the realm of math. There's a reason that programmers talk a about design patterns and waste a lot of time naming things.
So in a sense the cognitive root and differentiator of journeyman code is more analogous to the root of an understanding of architecture and planning than math.
Keep in mind that many professionals (occasionally myself included) do not even write journeyman level code.
I'm not sure I understand the question. Programming can be a mix of many things: reasoning about associations and state, designing processes or interfaces, or—most saliently—modeling a domain that may or may not mathematical in nature. To compare a programming language/runtime with a US math curriculum makes about as much sense to me as asking for the Richter magnitude of a sledgehammer.
Programming can require many things, but the OP specifically asks about this: > bog standard, journeymen, CRUD programming What do you think are the cognitive demands of that task, however defined?
Just like math, you can go as deep into a programming language or concept as your mind will carry you so there's no equivalence relation.
You will (probably) never pull out pencil and paper and do arithmetic (simple, with fractions, averaging, etc.), simplify an algebraic expression, convert to standard form, factor a quadratic, solve a system of linear equations, calculate the area of a polygon, prove something about triangles, solve an inequality, divide polynomials, take the slope of a line, etc. This is what "math" consists of in K12 and very littl…
No. This is wrong. The correct answer is abstract (modern) algebra.