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

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

#51

Post by zachrose »

rickhanlonii wrote: post #38
thaumasiotes wrote: post #18

Earlier quoted context omitted.

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?

Then the answer is "it depends". You can program at a level with a cognitive demand on par with Algebra (however defined), and you can program at the level of Complex Analysis. There's no one-to-one map between the two. 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.

Yes, but I'm also skeptical of the idea that some math subjects are cognitively more intense than others.

The "cognitive load" or whatever is really just a function of how much you've practiced and internalized that area of math. Calculus builds on algebra, sure, but once you've internalized algebra you don't have to "think real hard about algebra" _while_ you "think real hard about calculus."

Running a 10k for the first time is not the same as running your first 5k twice.

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

#52

Post by derleth »

simonsarris wrote: post #46

Programming isn't analogous to math, programming is a communication language with really strict rules that uses math of all stages. Different tasks involve different math. I'll give some common examples for laymen, but they may seem obvious in hindsight: Programming a very rudimentary "snake" computer game is [using] using Algebra. If your son (or anyone) understands variables, assignment and adding them together, th…

> If your son (or anyone) understands variables, assignment and adding them together, they fundamentally understand Algebra.

A more important part of algebra is symbol manipulation, and understanding why some manipulations are valid and others are invalid. That symbol manipulation is the core of grade-school (or trivial) algebra. Being able to 'see' how to solve a problem, and being able to abstract general rules to solve whole classes of problems, all flow from that.

Of course, there's a disconnect between using '=' to denote a state of being (the state of equality) and using '=' to denote an action (the action of assignment). As an example, 'x = x + 1' is either trivially nonsense or trivially valid. Haskell actually uses '=' in the mathematical sense, to denote a state of being, and SSA languages such as Erlang come pretty close to it, I think.

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

#53

Post by nilkn »

thaumasiotes wrote: post #36
nilkn wrote: post #24

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…

> It [discrete math] has relatively few pre-requisites in comparison to advanced calculus (which I'm assuming means something like a first course in real analysis). 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").

While that might technically be true on some level, ask yourself if the average student would do well if they started with Rudin's Principles of Mathematical Analysis in 11th or 12th grade having taken absolutely no calculus prior to it.

There's a reason most universities require students to have completed the entire calculus sequence and often even a special "introduction to proofs" class before exposing them to a book like Rudin's.

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

#56

Post by jborden13 »

At that level, I'd say literature is more important and more of an analogue than mathematics. If your programming can tell a good story and the user can interact to move the story line along - you're golden. But math can be very important/helpful and if he can comprehend Algebra, then he's got it 98% covered - at that level. End of the day, the more he knows the better off he'll be...

Just an opinion.

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

#58

Post by nostrademons »

tedsanders wrote: post #54

Math doesn't come in levels. It only seems linear because it's taught that way. You can teach kids group theory before calculus without a hitch.

Yeah, I was surprised by the framing of the question. Math is not a set of levels, it's a set of tools that are each useful in certain situations, many of which build upon each other. The branches of math that are most useful in programming are set theory, logic, linear algebra, and statistics, and most of them don't even appear in the U.S. high school math curriculum.

I still remember getting to college thinking I was hot shit because I learned calculus as a freshman in high school, and then realizing I had no clue how to construct a proof. Calculus is taught in schools because it's how you send rockets into space, and in many STEM professions it's a dead-end that isn't all that useful for the job.

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

#60

Post by ramgp »

Obviously it depends.

Creating a software solution (program or app, whichever is it called these days) goes beyond programming/coding it, and it often depends on the problem you're trying to solve aka the problem domain or simply domain. That's why creating an mobile app to track a list of things to do on a person's day requires a different process for creating it than creating a solution for an self flying aircraft, weapon, banking, or medical system.

So, I don't think programming in general is bound to any math level. Some systems may require some specific math in order to create an adequate solution for them.

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