Logic
Poll: What level of math is programming roughly analogous to?
101–110 of 165 posts
Re: Poll: What level of math is programming roughly analogous to?
#102Disclosure: 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…
> 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. 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…
When I took a maths GCSE, (UK qual,) most of the work was memorising equations and using them. You didn't prove them or understand how they worked or anything. Like teaching someone to program by memorising the functions in the standard library.
Re: Poll: What level of math is programming roughly analogous to?
#103Earlier quoted context omitted.
This is philosophical mumbo-jumbo. When people program, they (usually) don't do math. And that's it. The fact that you can view a programming language as a formal system, and the fact that computer programs can be viewed as mathematical proofs of mostly totally uninteresting propositions, doesn't magically turn programmers into mathematicians, just as the fact that the brain can be viewed as a chemical and physical s…
It depends on what you mean by "do math". Both a proof and a program are just syntactic manipulations following a particular set of rules. The exact rules differ, but the underlying system doesn't. Proving something in a low-level way--just following inference rules--and executing a program are basically the same things. This is abundantly clear if you formally study operational semantics, but even people who haven't…
Quick comment: I think people are emphasizing too much the 'logic' of mathematics, over its content. Mathematics is NOT about rigorous thinking and logical patterns (unless of course you study logic). It is much freer, pattern-based, and intuitionistic than that. It just so happens that rigorous/logical argumentation is the best way to communicate mathematics.
In this sense, programming is much more algorithmic, and hence I would argue, not particularly like math (the content) at all.
Re: Poll: What level of math is programming roughly analogous to?
#104Earlier quoted context omitted.
US math courses for high schoolers often goes along the following path: Algebra, Geometry, Algebra II (basic linear algebra, but often not discussed as such, and other concepts), Trigonometry, Precalculus (1/2 semester each of the last two) and then Calculus. Of course, that adds up to 5 years so unless a student took Algebra I in middle school (year 8) they won't complete the full sequence, leaving calculus for coll…
> The structure of formal proofs is taught in geometry. That's pretty much the only course where students are expected to prove theorems about the subject via proofs. In most of the other courses students are taught the formulas and techniques, axioms and theorems, but then apply them, rather than attempt to develop or prove them themselves. They're also, typically, not shown a proof of the theorems they learn, they'…
> being able to reason rigorously and correctly
At whatever level of Math (or any subject) you develop this skill, you are ready to be a programmer.
Re: Poll: What level of math is programming roughly analogous to?
#105Programming 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…
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Re: Poll: What level of math is programming roughly analogous to?
#106Programming 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…
>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.
What kind of specialiazed math formulas you might need for some specific parts of a program is another thing altogether to whether programming in the large itself is analogous to math.
Of course if you need to do FFT you will need a specific set of math. But programming the main logic of any program is quite similar at their level of analogue-ness to math.
Re: Poll: What level of math is programming roughly analogous to?
#107Earlier quoted context omitted.
This is philosophical mumbo-jumbo. When people program, they (usually) don't do math. And that's it. The fact that you can view a programming language as a formal system, and the fact that computer programs can be viewed as mathematical proofs of mostly totally uninteresting propositions, doesn't magically turn programmers into mathematicians, just as the fact that the brain can be viewed as a chemical and physical s…
It depends on what you mean by "do math". Both a proof and a program are just syntactic manipulations following a particular set of rules. The exact rules differ, but the underlying system doesn't. Proving something in a low-level way--just following inference rules--and executing a program are basically the same things. This is abundantly clear if you formally study operational semantics, but even people who haven't…
If the question of the poll was "My son eats carrots, what level of piano-playing does it equal to?", would you then say that eating carrots and playing the piano are fundamentally the same, because they are both reducible to physical laws and are just manifestation of different kinds of brain activity?
We all get it, and we all agree - programs can be viewed as a subset of mathematics. Every CS undergrad knows this. It is conceptually misguided to view this piece of information as revealing anything deep about what programmers do, just as it is conceptually misguided to view our ability to reduce both fishing and singing to brain activity (or to reduce everything to the laws of physics) as saying anything deep about what fishermen do. It doesn't became any less misguided simply because examples exist where math can be directly applied to programming, and vice versa.
It is philosophical mumbo-jumbo because you are taking two activities with clearly distinct meaning in everyday language, and instead of simply acknowledging that we can invent a new meaning for them under which they are the same, you instead convince yourself that this new invented meaning is the only fundamentally correct one (or somehow "deeper"), and that it also has the power to show that the 'everyday' meaning is wrong. But you are not showing anything about things we already know - you are simply presenting new, different ways of looking at them, that bear little relevance to the question at hand (A circle is topologically equivalent to a square. Does it mean that our 'old' preconceptions of difference between circles and squares are now wrong?).
The activity of doing mathematics, as those words are used in everyday language, is different from the activity of programming, even if in some senses (perhaps in more than one) they can be viewed as the same. The activity of running is different from the activity of fishing, even though they can be reduced to similar building blocks.
I do not object to the mathematical connections you present, I object to the philosophical interpretation you give to them.
Re: Poll: What level of math is programming roughly analogous to?
#108If you voted you don't understand math or programming. Programming is recipes for a computer to follow. In many cases there is Zero math involved. You can write plenty of Data Entry code and never use a single numeric function. Conversely you could write a single line of code that required all the math skills of a Quantum Physics Doctorate. Programming is not "math" it is recipe authoring. It is more analogous to hom…
> You can write plenty of Data Entry code and never use a single numeric function. Numbers are not math. (Anyway, I agree that the poll is strange.)
"God made the whole numbers; all else is the work of man." -- Leopold Kronecker
Re: Poll: What level of math is programming roughly analogous to?
#109Having gone through Mechanical Engineering school and also developing software (coding C++ and others) for the past 12 years...I see programming as more assembling physical systems and getting them to interact much more than how well programming can be related to any particular mathematics.
Re: Poll: What level of math is programming roughly analogous to?
#110This question should establish a separation between the content that mathematics teaches, and the cognitive abilities that develop as a result of learning mathematics.
Could an 11 year old dive into the CRUD with an 11 year old's mathematical knowledge? Absolutely. Will he/she have the ability to rough it through debugging challenging problems that may emerge without the years grit developed as a result of solving difficult calculus and linear algebra problems? Possibly. Perhaps not.
Either way, you sound like an awesome dad :) I say let him have at it!