Poll: What level of math is programming roughly analogous to?

What type of programming, what paradigm, at what scale, and dozens of other questions... I can think of numerous areas where each of these is not only "analogous", but directly used.

  - Want to even think of committing to scalaz/haskell? Category theory
  and lambda calculus.

  - Want to develop a physics engine for a modern 3d shooter?
  Geometry, trig, single/mutli-variable calc, algebra, and differential equations.

  - Want to do some NLP? Discrete math, automata theory,
  not to mention a strong background in linguistics.

  - Want to do some ML? Bayes statistics.

  - And so on..

I've always been amazed by how little is needed to squeak by in some scenarios and also how much is needed to do truly amazing things. The more you learn and push, the more you realize you don't know.

Edit: This was prior to OP clarification. :)

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.

I have always found geometry to be the most similar in terms of content. Geometry is where most people are introduced to proofs, which are similar in a lot of ways to programming. Also, you often need to know some amount of geometry in even CRUD apps to properly deal with interfaces, charts, etc.

That said, I spend 90% of my time writing geometric analysis libraries, so I am biased.

For Objective-C (or any objective language): geometry. Qualities of objects, and their role in relation to other objects are really all there is.

Also, memory, which is all we are manipulating at the end of the day, is linear; points on a line.

You can get by with an "algebra" level understanding of programming.

However, concepts such as recursion, and other metaprogramming don't really make sense at that level.

You can make rote crud apps with an algebra level understanding of programming.

Geometry proofs

Mathematical Logic

[x] Discrete Mathematics

No. This is wrong.

The correct answer is abstract (modern) algebra.

I have a slight problem with the question. Math is used when programming or creating models, but both are tools. I find it hard to compare the two in the way you're asking, so I think this poll is bogus. Programming requires abstract thinking as does math at the algebra level and beyond (more so at the calculus level and beyond). Other than asking what level of math is required to program X, it's hard to ask what cognitive level quantified by mathematical ability is required because cognitive levels both aren't easily quantifiable and also don't directly correlate with mathematical ability. There are lots of ways to do the same thing.

As for me, I have taken math to the level of Differential Equations and Linear Algebra.

Despite what others are saying. This is a very good question. And extremely relevant.

The answer depends on how great you want to become. Take as much math as possible to find the best solutions. I come from a background of the hard sciences, I never took programming in college and I was able to pick it up quite easily because of my strong foundation in mathematics, analytics and logic.

I have seen it said that mathematicians break down into analyst types (calculus) and algebraist types (algebra). The difference in approach is usually described along the lines of "in analysis, you have an object under study and you want to describe how it behaves in some sort of limit condition. You have a mental model of the problem and you work to formalize what your intuition tells you" vs "in algebra, you have an object under study and a set of rules. You apply the rules in a mechanical manner until you produce an interesting-looking (or desired beforehand) result".

Under such a worldview, my personal view of the mental requirements of a simple CRUD type of task is that the ability to apply definite rules called for in the "algebraist" approach is closest (and extremely necessary). I've read many comments that beginning programmers can have a hard time understanding that the computer will do exactly what you tell it to do, and nothing else; applying algebraic rules is a very similar concept.

Geometry is an unpopular choice in your poll, but I think it has some of the same flavor of recognizing that "by labeling this complicated term 'x' and this other complicated term 'y', we can transform the current state of the problem into exactly the preconditions for theorem T" that I'm thinking of.

Anyway, overall I vote for algebra 1.

roughly around algebra.

programming has an "advantage" over math in that you can just program something and see what happens and therefore gain an intuition and craft your way around things. mathematics is much more deprived in this respect, for a variety of reasons.

overall i would describe programming as a precise form of writing, whereas math is a very pure science

The description is clear, but the title of the poll wasn't.

Note that if you're doing game development, a higher level of math will be required, than if you're writing a crud application that talks to an api; in the latter, understanding linguistics and a good common sense are more important.

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 little of it is obviously linked to programming itself.

You don't need any of high school math unless your specific application requires it (i.e. graphics involves polygons, anything quantitative involves arithmetic and unit conversion, you may want to report percentages and averages at some point.)

Things I remember from K12 math classes that were useful for programming in general:

- What variables are

- What functions are

- You can compose functions (this was obvious because I had been programming for 5+ years before function composition was introduced)

- Very basic set theory (Python list comprehensions resemble set-builder notation)

- Introductory propositional logic (though I learned this in the context of programming 7 years before I was "ready" for it in math class)

Learning to prove things about triangles (geometry) exercises some of the same skills as programming, but I wouldn't say it teaches them. Certainly none of the theorems or facts have ever been useful, just the process of reasoning.

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-speaking world, you haven't given enough information to match the levels.

Some people program insightfully, or so I am told by people who program, and other people program nothing but kludges. Among mathematics learners, there are great variations in the levels of "profound understanding of fundamental mathematics" (PUFM) among people who are studying the "same" level of mathematics. It interested me that you mentioned neither number theory nor combinatorics among your list of secondary mathematics courses, because in some other countries, those courses would come well before calculus. In general, any reader of Hacker News could learn a lot about what is missing in the United States (or, more generally, in the English-speaking world) in elementary mathematics instruction by reading Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States by Liping Ma.[1] There is a lot to basic mathematics that is far from easy, if deep understanding is what you are looking for. In the countries that excel over the United States in mathematics instruction, proof is part of every mathematics course, not just part of geometry, for example.

[1] http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...

I wrote a driving game in C about that age and the hardest thing to figure out was vectors and sin/cos-stuff (you have to separate speed and direction even in a simple driving game) so I guess the programming part is easier than that. Although it's just hard because I didn't know about those concepts at that time. And of course, the code was very simple.

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 about how to approach the overall architecture of the program and make predictions about how early design decisions will affect future extensibility and more.

I think programming actually requires linguistic skills. When you program you are actually writing in a language, and you have to respect it's syntax and structure.

Therefore I don't think it should be compared with math. Unless you are writing a program for a very specific scientific problem that requires the elaboration of a mathematical model.

Usually the computer does all the math, all you need to do is type the operations you need it to calculate.

I'm not saying they're completely unrelated, I just think linguistic skills are more relevant in most cases

It's not.

There are certain levels of math or logic needed for various programming tasks, but it is not 'analogous' to any level.

For example, function composition is very useful in programming and thus Algebra (or was it Algebra 2???) comes in handy for understanding that at a basic level.

However, if you're doing graphics programming, then you often need experience with geometry (composition of basic shapes to form more complicated shapes, linear algebra (matrix operations), and modern algebra (quaternions).

I use a bit of trig to do graphics programming but that's about as much Math as I've used when programming.

Algebra: Functions, variables, and manipulation of basic data structures.

I learned programming before I learned how to manipulate variables in math, and my prior knowledge helped me figure out how to deal with most of algebra.

Just yesterday I decided to begin reading a Calculus book (I never went to college). The very first thing covered was ƒ(x) which describes input being passed into a function. Needless to say, as a programmer I am very familiar with this concept.

So far, my vote is for Calculus.

As a game designer, i'd say Physics, algebra, geometry come in VERY handy. Now, i am not familiar with how these topics are taught in the US system, but assuming your options are a progression, i'd say pre-calculus should do it.

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

I wouldn't look it that way. Programming is an art which aims to solve any problem in any domain using logical reasoning and systematic application of solutions that requires to solve the problem. Or even build a whole new thing.

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.