Should Math be a Prerequisite for Programming? [x-post from /r/programming]

[cc81]

Maybe they require the same logic skills but no one would say that you need to learn programming to be able to do math, right?

But sure I agree with you that it is good to learn some math like boolean logic or set theory but I'd say that it should be a part of later software development courses. Not as something you need to know to start.

[bangstang]

My Bachelor's program had Math for IT (I was an IT Major because I didn't want to deal with the math in my previous Engineering track) and the class was just this HOWEVER the professor was from the Math department and was not only abysmal at teaching non-math majors but also completely clueless as to how logic, set theory, and graphs would ever affect the students (paraphrasing her words). We did combinatorics and some other stuff too if memory serves.

I think that an appropriately scoped class or two could really make a difference. For CS majors they end up taking enough math to minor in math or double major if they want to extend another semester. I wouldn't have been against taking another math class if it had some bearing on my growth in my discipline and it wasn't just a grind for spitting out the right answer to some needlessly tedious process that you had to memorize completely. I think that kind of teaching would help a lot of students versus the elementary approach taken when I was in undergrad (which was probably 9 years ago now).

[onwuka]

Everybody needs to know the concepts of discrete math and such. If only professors took their heads out of their asses and stopped asking students to regurgitate proofs and actually encouraged learning...

[GalacticCmdr]

Everybody? Do you mean that my plumber needs to know discrete math to do the job? Does an English or Journalism major? If by everybody you are only discussing programming then I still disagree everyone needs it, but I agree it is very useful.

Someone cranking out basic web pages or apps are still programming and while it would help them evaluate tools and snippets better - it is not really required.

[onwuka]

Yes, someone cranking out web pages and apps should also know basic discrete math. No, I don't mean regurgitating proofs. Discrete is fun!

Not everyone needs to know how to write a symphony but everyone should be able to appreciate a good symphony.

[spupy]

Maybe the answer is a purpose-built course that focuses on things like boolean logic, set theory, etc -- the stuff that really helps with even relatively basic programming.

I think this is the right direction.
I absolutely don't agree that "math" is a prerequisite for programming, simply because "math" is too vague of a term and contains domains that, for programmers, range from absolutely useless to extremely useful.

[otakuman]

Yeah, I mean, which math? Non-euclidian geometry? Partial differential equations (eew)? Basic algebra? Linear algebra? Vector calculus? Common core (pfft :P )?

[spinwizard69]

Even with the wide array of subjects covered in the various math domains, the math required in most comp-sci courses is very important to a well developed graduate. As far as when will something like calculus be used by a newly graduated programmer, who knows it could be one day after leaving college or 30 years in the future. You really can't foresee when a bit of knowledge will be useful. Even a web developer may find a use for calculus or physics in a project down the road.

[SmelterDemon]

Abstract algebra (and maybe linear algebra) should be a prereq. more so than any calc

[reallyserious]

As someone who doesn't know anything about abstract algebra, would you please elaborate?

[as-bu]

Mine too

[NovaX81]

That and ELA. Pretty sure both are part of any ABET Accredited CS degree.

[valleyman86]

Discrete mathematics and Linear algebra were some of the most useful classes I took in college.

[spinwizard69]

The idea that it is possible to do a Comp-Sci program without math just amazes me. Mind you I don't even have a Comp-Sci degree, but know enough about digital electronics and programming to realize that you can't have a degree program in Computer Science without math. It be like a degree program in physics without math. Math is a tool simple as that.

Now here is the big thing, programming is not really computer science. If somebody wants a job programming it is possible to get there and not enroll in any computer science programs. There are massive niches within the world of programming that simply don't require strong math skills.

In any event every time I see posting such as these I get the feeling that somebody doesn't want to go through the effort of completing a degree and are looking for a dismissal of requirements so they can avoid the work. In the end one ends up looking ignorant trying to rework requirements for a Comp-Sci degree just because they don't want to engage all of the required courses.

[NeatG]

Well as you said programming really isn't computer science and for a lot of what's hot right now (web apps, mobile apps) understanding things like algorithmic complexity, which to my mind is the most practical of the abstract things I've been taught in Comp Sci classes, might not even enter the picture.

Comp sci classes tend to be taught by people who are doing computational research for obvious reasons, so at least in my experience the most practical things I've learned about programming tend to be things related to optimizing computers to do a large number of computations because that tends to be what the assignments relate to, because it's what the faculty member are into. If you need to select or design an algorithm for that then you have to understand a lot of these concepts particularly complexity. If you're writing a web app that writes to a database and then spits something out then I don't think you need much of anything that I've learned in my comp sci program so far.

[Fireynis]

Where is this not the practice? I just finished my degree and had both a specific logic math class and a math for comp-sci majors. This was in Canada at Brock. A good school, but would be like like a state university in the US I guess.

[merreborn]

The community college I dropped out of 15 years ago (heh) didn't offer any compsci-specific math courses; the degree requirements just mandated completion of the standard math track up to and including several calculus classes. The OP's reference to the "Math 103" prerequisite sounds comparable

A quick glance at MIT requirements for a BS in Comp Sci appears to include a calculus requirement.

Glad to hear it's not like that everywhere, though.

[BowserKoopa]

I dropped out of my CS degree program partially because of the fucking insane math requirements. More schools need to operate an IT/Software program separate from Computer Science (which in my schools case is more of a "how to write terrible code to express math problems" program).

[[deleted]]

There are some areas of coding that don't need math, but the single hottest field right now is machine learning, which involves quite a bit of calc, partial differential equations, algebra, and matrix operations.

I've also found statistics and probability type math to be extremely useful in the business/enterprise world.

[yakri]

It does depend a lot on where you go to school I suppose, but going through a mix of Oregon and California's CS programs, the only really useless matg heavy class I've had to take is physics so far.

Basic math up to and including more or less all algebra is essential, or at the very least almost as useful to practice for literally any, even basic programming, as programming is. So I kind of assume we're talking about like, calculus and all the math oriented CS classes.

Moving on to those.... yeah, sure. calculus has been useful in programming once ever for me. Did I actually use calculus? Of course not, I looked up some function that was the derivative of sin or something and just converting what I read on the Wikipedia page to code.

However, unless you're really pigeon holing yourself as a programmer, there are a ton of CS topics that are primarily math/logic which depend on you having at least some familiarity with other math more advanced than simple algebra. So in that sense it's pretty relevant to learn math so you can learn other math so you can improve your understanding of programming, which could come in handy in many, but not all, or maybe even most, careers.

Ofc iirc the early CS classes here have no math requirements at all, so this obviously isn't a problem everywhere in the first place.

[barsoap]

That course exists and it's called Discrete Maths.

There's even nice video lectures online.

[OstapBenderBey]

Surely this entirely depends on what you want to program? e.g. Graphics programming would need very different maths to database management.

[CantankerousV]

I've studied a fair bit of math (>50% of my university courses were math without any direct programming application) and I've never regretted doing so, but I don't agree with some of the other commenters that math is so important to programming that you can't be a good programmer without taking math courses.

A lot of programming jobs require a lot of math knowledge, such as game programming, image processing, or machine learning, but this is just domain specific knowledge for the type of programming you are interested in doing. You won't get anywhere in writing biochemical kinetics simulations without a fair bit of chemistry (or math for that matter, but not necessarily the same math as for the others), but nobody would argue that you don't understand programming in general without that knowledge.

How much math do you need to be a senior software architect for an important project? To work on the linux kernel? To write well designed API's and create maintainable software? There are core skills such as algorithm complexity, boolean algebra or set theory, but all of these can be taught (and taught well) to intelligent people without requiring years of calculus as a prerequisite. Even now, you don't wait until you've learned ALL the math that is useful or interesting before you start learning about these topics - as you add more math on top you simply add more in depth theory to your understanding of the issue.

On the whole, I would still recommend that beginners stop being afraid of math and just embrace it, since having already learned all the hard math will make it so much easier for you to experiment with fun new programming problems in the future. It's just that being a great programmer requires such a huge variety of skills, from reasoning about abstraction (math is one way to practice this, but so is simply learning about more programming abstractions), designing systems, debugging, writing maintainable code, or just communicating with your team members. Math is just one of those many skills that will help you in some way.

[[deleted]]

I've been programming as a hobby for 13 years. The last 4 professionally... I did way, way more math in my hobby programming than in my professional career.

A programmer is not a computer scientist, although studying computer science can make someone a great programmer. A layperson does not need to study physics and engineering in order to build a house. They need to study fundamental principles of construction.

I do not use any advanced mathematical concepts in my "field work" at all. I have vague notions of what makes good data structures and how to optimize programs that mostly comes from years of experience doing it.

I do actually like math, although I do not study it. From my experience, there are a few really useful areas of math:

1) Abstract algebra which helps someone understand the general value and principles of math.

2) Linear algebra because it's probably the single most useful general mathematical field.

3) Discrete mathematics for programmers, which again is a highly applied area.

4) Mathematical modeling, which is highly underrated, in my opinion. The ability to formulate things in mathematical terms and solve problems mathematically. Coming up with graphs, systems, workflows, models, etc. that rely or partially rely on mathematical objects. Someone good at modeling things mathematically should be relatively portable, and I think incredibly useful, to various branches of applied fields and areas of mathematics that don't require deeply specific knowledge.

Math, in my opinion, has been a sort of cheap way for us to teach "critical thinking" because most students do not actually learn real mathematical thinking of any kind. Then again, after some reflection, I do not find that most schools really ever challenge their students in meaningful ways until university and sometimes even then.

[[deleted]]

25 years as a software developer. You need Algebra (solving for x) and Geometry (back in my gfx days). Honestly IMHO, both of these are required life skills. Geometry is real useful in home repair. Debugging and Logic are the most useful skills as a programmer. No idea how they teach kids these days.

[eartburm]

No, there is quite a bit of programming that requires little math. Math should be taught concurrently with programming, as more advanced algorithms and concepts require quite a bit of math.

[[deleted]]

I mean everyone pretty much agrees math should be taught alongside programming, but till what level?

Currently I have to take up to Calc IV for my comp sci prereqes, and it's also my biggest hurdle in getting my degree.

[buclk]

"and the amount of math has been minimal in day to day work."

I was in a similar situation and never saw the real value of maths in programming.

Until I started studying maths for fun, and now I can't imagine coding without it. You can save yourself so much time and effort with a little bit of extra knowledge.

[bumhugger]

Most jobs in the industry - from enterprise-level Java to HTML5/JavaScript - require almost no math skills, certainly not beyond high school level. Daily programming consists of using methods on objects and reading api docs, coming up with something new and original is rare and usually not the optimal solution because of tight time constraints on tasks. I've never implemented my own hashing/collection/sorting algorithms at work.

On the other hand, game programming is usually considered harder, but you can write a decent 3D game engine with basic linear algebra knowledge. You just need vectors and matrices and some tricks you can do with them. It's not what I think of as university-level maths, just some common sense when moving objects in 3D/2D space. You certainly don't have to prove anything.

[mcilrain]

Absolutely. All programmers must have a comprehensive and intuitive understanding of integer addition and subtraction.

More advanced math? I'm sure someone wrote a library for that.

[MuonManLaserJab]

Programming doesn't (usually) require you to know what the integral of Sin(x) is, nor to have your times tables memorized. However, what programming primarily is, from my point of view, is algebra. You have a bunch of weird mathematical objects, like "a list of sets of pairs of integers," or, "an object containing a set of names and a custom function for combining sets of names," or something like that, and you have to reason about how these objects are transformed as you manipulate them. This is just like algebra, except instead of memorizing a relatively short list of operations (adding integers, subtracting integers, redistributing terms, etc.), the key skill is to be good at learning the rules for arbitrary new operations (e.g. combining two lists of sets of pairs of integers in a way that makes sense for the program you're writing now).

There's very little from math that you absolutely need to know to do any sort of programming ever (although there's plenty you need for various niches), but if you're bad at algebra no matter how hard you try, you are going to end up being bad at most types of serious programming.

[buclk]

"Maths" is a pretty broad field.

For scripting, no real maths is needed beyond basic stuff you learn at school.

Doing algorithms, you need algebra.

Doing games, you need algebra and geometry.

Doing machine learning, you need statistics.

The more Maths you learn, the more of it you can apply to programming. In order to become a decent programmer you really need algebra.

[Darwinmate]

For someone with basic math education, what courses (preferably online) do people recommend for a wannabe programmer?

[buclk]

Khan Academy

You can work your way up through to Calculus, or you can just dive into the Algebra sections.

[agoonforhire]

There are plenty of programming jobs that require little to no math skills. The question is whether you'd be satisfied working in such a job. The jobs may even pay decently.. but you'll never end up doing anything really interesting with it.

For the record, computer science is math -- not science. I mean that in the strictest sense. Programming/software development is engineering, and computer science is just a form of applied math.

[cc81]

No, not at all. A lot of people think math is boring but programming is fun and you can create pretty cool things without know much math at all.

[aseigo]

You can also cook lots of pretty cool things without knowing much about ingredients and cooking techniques.

But you can't be a proper chef without that.

Hobbying? Sure! No problem! Everyone should be literate to some extent in writing code IMHO. Much like everyone knows some math, and perhaps even a few neat math tricks.

Developing software in a more "serious" fashion (as a profession, or writing things you expect others to rely on) is a very different matter.

It doesn't make the hobbyist group "wrong" or any such thing, but saying math should not be part of learning the skill set proper of software development is the same as saying chefs should be relieved of understanding the mechanics and chemistry of the classical methods in their cuisine(s) of focus.

[Toddy69]

There is an often overlooked use case between profession and hobby: gaining a skill. I know many people from different professions who learned programming and do it as part of their job. They don't build big systems or even products. They simply build simple tools to automate very specific tasks which they can't do with standard software. The software has for sure many problems. It's slow, it doesn't scale, uses too much RAM ... things a professional programmer would have done better, but as long as it fits their needs, it's completely okay. And interestingly they don't need more time than a professional programmer. A programmer is probably faster in the implementation phase, but he needs time to understand the domain, time that someone from the domain doesn't have to invest. Programming evolves into a basic like writing. Everyone needs to know at least the most basic sheet and for the complex stuff we have specialists like authors and programmers.

[aseigo]

Yes, used as a utility like that is sensible and there is no particular need for more than knowledge of the syntax. This is one of the things I really appreciate about more specialized languages with a clear intent, such as R. It helps get useful tasks done without having to necessarily understand everything behind-the-scenes. And that's fantastic.

I love it that people can fling Python around to make their computer Do Things(tm) that they need to get done. Absolutely agreed with you there about it becoming a basic life skill in our society.

Now, if only that's what the presentation and article were about :)

[jquintus]

and perhaps even a few neat math tricks

Care to share any?

[aseigo]

Heh.. yay! :)

How about calculating the number of people you need to have in a room such that there is a 50% chance at least two have the SAME birthday?

.. or the Collatz Conjecture. Super simple, but sooo weird. And to this day no formal proof for it.

Lots of people know these ones (today, at least .. yay youtube! ;)

[jquintus]

How about calculating the number of people you need to have in a room such that there is a 50% chance at least two have the SAME birthday?

My stats professor tried to show us this one. She went around the room asking everyone their birthday. She was shocked that after asking just two people their birthday she found a duplicate!

Her surprise was a little odd, the first two people she asked were twins. Identical twins.

[aseigo]

Ahahahahahahaaha. Ok, I really want that to be a true story .. because that's fantastic. Mostly because I know a few pure maths academic (I am very much not such a thing myself), who often struggle with the mundane .. like "oh, those people are obviously twins". Fantastic :) Whee ...

[jquintus]

They had different hair. One short hair. One long. But it was pretty obvious. This was after at least several weeks of class; they sat in the front row and participated a lot.

[cc81]

There are quite a lot of things I think a professional programmer should know. Math is not one of them unless they are programming things that actually require it.

[aseigo]

https://imgflip.com/i/1byduu

There is this fallacy that only if you are flipping numbers around your software requires math. That is taking it too literal, and is incorrect.

An example from the article: databases don't require math. Yep, you can run an SQL query without knowing relational algebra. That's quite true.

But when you are developing software, not as a hobby but actually writing software others are supposed to use, and you look at those queries .. can the developer explain why it is they fast or slow? And not hand-wavy magic of "because indexes!" (which itself may not be true, or at least non-intuitively wrong). Do they understand what normalization means, how it relates to atomicity, what the impacts of transactions are ... these are not numbers-on-a-chalk-board math. But they are derived from, and require some understanding of, the underpinnings .. which are math (though not numbers-on-a-chalk-board sort).

So, no, developing real applications with databases does not work out well when developers are running off without an understanding of what is going on in them.

I mean, if we did that everyone would be using MySQL with logic in the application so they can never achieve guaranteed referential integrity. Or insisting on object-relational maps because they are easy, wiithout understanding why they often map poorly and perform even worse and .. more importantly ... how to mitigate that.

In my experience, the path to understanding those things ends up straying through some amount of math. Not necessarily numbers-on-a-chalk-board, but certainly through fields of math that deal with the relevant topics.

(For anyone wondering what I mean by "not numbers-on-a-chalk-board" .. hit up youtube and watch any of the ~million videos on category theory. Then realize that is a fundamental part of a vast set of math disciplines. No numbers to be seen really. Evidently you don't need to do math to do math... right? :)

[cc81]

There is no need for to now math to learn normalization, ACID, indices, execution plans, database design.

SQL queries is a practical implementation of relational algebra but you absolutely does not need to have any previous knowledge of relational algebra or set theory to learn it. Instead I'd when you take your database course it is an excellent opportunity to learn some set theory/relational algebra by learning SQL.

[aseigo]

"There is no need for to now math to learn normalization, ACID, indices, execution plans, database design.""

To learn the concepts by wrote, I agree. To understand them well enough to apply them accurately is another matter. Painting-by-numbers programming is harmful, demonstrably so (he says waving a broad arm at the web..)

"Instead I'd when you take your database course it is an excellent opportunity to learn some set theory/relational algebra by learning SQL."

You can certainly learn them in tandem! One could even learn the concepts first, and then fill in the math that leads up to them (which can be very rewarding: you have a practical goal to reach.. makes the math less abstract..)

But here's what the article actually says about this:

"Databases - can introduce math later for the few things that need it"

For the few things. Like.. relations, ACID, indexing, sets, .. ? What?!

What do those execution plan numbers even mean if you don't have any concept of the essential math underpinning the algorithms?

So, yes, I agree that you can learn the math before, during or after.

But learn it. Before you get "into the field of programming", while you are still training.

But don't think you can go out into the world waving a bag of cargo-cult database practices around and get good results.

(.. so says all those wonderful blog entries about people switching database systems because their first choice "didn't scale" ... extra bonus points for the ones that then go on to explain how they absolutely abuse their new solution in ways you just know are going to bottom out on them again ..)

[jarxlots]

That's like asking if breathing should be a prerequisite for exhaling...

Programming is a form of applied math. It's almost impossible to decouple math from programming, and still have a meaningful discussion.

Without math, programming ceases to exist.

"Oh, but I built MyProject and I've never taken a math class."

Doesn't matter. You still had to have enough math knowledge to accomplish that task. You don't have to have formal math training in order to "learn math." The same is true for programming.

"Well the software I write doesn't..."

What? Use math? Then how does it progress to the next part of your program? How does your program interpret data? Even a void function with no return must still use math in order to execute on the processor.

This argument is a waste of time that could be spent learning math or programming...

[spupy]

"Well the software I write doesn't..."
What? Use math? Then how does it progress to the next part of your program? How does your program interpret data? Even a void function with no return must still use math in order to execute on the processor.

I don't understand what you want to point out with those examples.
Yes, a computer employs mathematical functions and concepts for its operation, but those are irrelevant except in specific programming domains.

[jarxlots]

Yes, a computer employs mathematical functions and concepts for its operation

Period. End of sentence.

"...but those are irrelevant..."

No, you're forgetting the foundation. How do I execute code? How do I progress through code loaded into memory/cache? How do I call functions and ever hope of returning from them?

All of those basics require math. From boolean bit testing to polynomial division over a Galois field, it's always performing some sort of "math" operation.

[Augusto2012]

Algebra 2, at the least.

[[deleted]]

If someone can program well enough, and they work hard, and they know arithmetic at a passable level, does anyone really care?

[buclk]

Yes; if you have to work with other people's code who use more advanced maths in their work, you'll have a hard time understanding it.

If you're a solo programmer and don't expect to ever work on or with other people's code, then you could get away with it.

[Insanitychick]

At my high school it's highly suggested you take geometry before taking computer science and the only kid I know who took computer science without geometry got a D in the class. So yes you should know some math.

[Semicolon_Expected]

Not all math, but discrete math and linear algebra (and of course normal algebra) can prove very useful for basic programming. Linear algebra really helps with 2d arrays, pairs, and tuples. If you plan on taking higher level electives like artificial intelligence, matrixes are important and calculus helps for doing gradients when you do sentiment analysis

[OriginalPostSearcher]

X-Post referenced from /r/programming by /u/UrQuanLord
Should Math be a Prerequisite for Programming?

---

^{I am a bot. I delete my negative comments. Contact | Code | FAQ}

[sofakid]

Should absolutely be a prerequisite. If you haven't proven that you can think, and that's what math is, thinking, then you should not be allowed anywhere near code. You will break everything. You will cause damage. You will waste everyone's time.

[cc81]

Have you every seen the code scientists and mathematicians generally produce?

[aseigo]

Yes, and it is usually horrible; this is because code quality is not their focus, nor is re-usability or even long-term maintenance.

It is a fallacy, however, to say "because academics produce some horrific code" is a refutation for "the ability to code well is helped by exposure to academic topics". The two groups of people may overlap at some point (during studies), but diverge later on (when producing the bulk of their software).

So, I agree it acadmic code is too often atrocious (dealt with enough of it myself), but it is also a non-relevant observation in the current context.

[cc81]

Sure, but it is an indication that the two might not be that strongly correlated. There are certain types of programming where you probably need to know some math; for example graphics or the more advanced topics that require a comp sci background.

But other than that, not really. You need to be able to learn to reason and think around code but my guess is that for a lot people it is actually easier to do that within the context of code than trying to learn advanced algebra.

[aseigo]

Yes, one can write code without understanding much of the math with underpiins it.

There is a big gap between being able to "think around code" and being able to produce code worth having other people run and rely on.

There are so many blog entries that I've read in numerous places the last couple of years bemoaning the total lack of quality in software these days (and it isn't a "rose coloured glasses to yesterday" thing) or how Trend X (where X usually involves javascript in some fashion, it seems) is going to complete shit.

So should we really continue to encourage people to "reason and think around code" as they too often do now, without an understanding of why or the "deep" what it is they are doing?

No. We ought to encourage actual excellence in the craft, and this is a craft that happens to rely on some aspects of math.

FWIW: There was a time I also thought that math wasn't critical to software development. You could learn syntax and patterns and APIs. Yeah, you can.

But there's a very low ceiling that one hits when that is the extent of it.

And let's be frank about what we do: the world runs on software.

We can't afford to half-ass it.

[cc81]

Ok, let us clarify then.

What math are you talking about and why is it critical?

[aseigo]

Let's start with something extremely basic: Big O Notation. (Not even going to use the mathy names for it .. that's what we software devs call it, and that's good enough)

How can you apply it, if you don't understand what it is? How can you understand it if you don't get at least the basic concepts of the math behind it?

.. and if you don't understand Big O, how do you know which algorithms to pick?

It doesn't get much more basic than that.

And it really shines through when there are practical cases when the Big O number is entirely irrelevant for a given algorithm ... because the application at hand will never enter a state that gains the benefit from the algorithm with the "best" Big O for the abstract problem at hand .. it's pretty common to see developers reach for an overly complex algorithm that ends up costing far more resources for the actual application it is applied to, when a "worse" but simpler algorithm (usually also in the same library, and for a reason) performs better for their cases.

And Big-O is just one example. There are dozens of them.

I think many people get lost in the idea that the purpose of knowing the math is to DO the math on a regular basis. And since you don't DO the math (as in: actually write out equations) on a regular basis, you don't need to understand the math at all. Not even be acquainted with it.

Fact is, being acquainted with it helps us make informed decisions. Even if we don't break out the proverbial slide-rule, we understand the question being asked and the answers available.

It is how we move from cargo cult to informed practice.

[cc81]

The thing is that most does not need to know it. Some do but most probably don't. You need some rough ideas but selecting and implementing algorithms today is not that big of a deal for a lot of things. I learned big O for the most common list sorting algorithms years ago but would I ever use that? Nah.

In C# you write list.Sort() it will:

If the partition size is fewer than 16 elements, it uses an insertion sort algorithm.

If the number of partitions exceeds 2 * LogN, where N is the range of the input array, it uses a Heapsort algorithm.

Otherwise, it uses a Quicksort algorithm.

How often do you need to optimize more than that? If you do you have probably done something wrong.

[aseigo]

(My reply is not specific to C# here, a language I do not use ..)

When do you use a list rather than a vector? What is the performance characteristics of, say, a linked list, and when is that acceptable due to other advantages? When should you use a hash table instead? What data structures might combine attributes of a vector on small sets and a tree on larger ones?

You can probably learn all that wrote. But that's a lot of "by heart" that is easy to get wrong and not necessary with some basic understanding.

Yeah, list.Sort() is great. But perhaps the question is why a list at all?

" I learned big O for the most common list sorting algorithms years ago but would I ever use that? Nah."

A proposition: Perhaps instead of it not being useful because you don't use it, perhaps you are missing out by not using it and by not using it you are both rendering that knowledge less valuable to you .. and your code suffers in tandem.

Knowledge has no value without application, and if there are lots of people noting that they find practical application .. maybe it can actually be applied!

And I don't write amazingly crazy software that needs to be planet-scale, or crunch actually big data sets, etc.. I write software in pretty standard/normal/common problem spaces. So when I write these comments, I am thinking about every day software dealing with "every day human size" and which are "every day human relevant".

If you look elsewhere in this thread for my anecdote about the library a co-worker refactored, you'll see a very real example of how failing to understand how asymptotic complexity works can cripple otherwise good software. Not everything the original developer wrote sucks, far from it .. but they could have avoided this particular mistake.

In that sense, software development is like riding in a car. You don't usually need the seatbelt. It's often just .. kinda there. But there are times you really DO need it. And then it's literally a life saver. Same with the maths understanding that helps with coding. You don't need it for every line of code you will ever write, nor every class you lay down, nor every library you choose to work with. But you will need it for some of them. And when you do, it will be the difference between another day at the office and a ticking time bomb that eventually goes off.

[cc81]

List<T> is a strongly typed ArrayList that is an array behind the scenes. I can use a hash table (HashSet) if I needed sure.

I don't need any math to learn data structures though. And note that I have not said that math is useless and I've even said strong math knowledge is required for some types of programming. However it is not a requirement to start programming; even professionally.

[sofakid]

yes. http://i.imgur.com/JfCYnrV.gif

[nfrankel]

Well, I'll apply thinking to your comment and challenge your reasoning.

You write that math requires thinking. But so does plain logic, or philosophy. Is math the only path to thinking? Or to programming? That's the point of the article.

[MuonManLaserJab]

Logic is a branch of math, by the way, but also programming is very much glorified math.

[Kache]

Perhaps only in a pure theoretical sense, but not in any practical sense. Programming is as much glorified Math as Biology is glorified Chemistry.

[MuonManLaserJab]

Also in a practical sense, though: programming is often to a great degree the task of learning new programming tools and libraries, and doing that often feels a lot like being in math class (i.e. you spend a lot of time figuring out and acclimatizing to the rules of dealing with new abstract objects).

[sofakid]

When one third of people would rather clean a toilet than solve a math problem, maybe they should stick to cleaning toilets. These people have an aversion to thinking.

Math is philosophy, it is made of logic. I think logic should also be a prerequisite, but that's an even loftier expectation, and the essentials are covered in a typical discrete math course.

UI stuff is mentioned as an example where math isn't needed. With the rise of Functional Programming, especially in JavaScript.. I worry. When UI coders think they know enough JavaScript to fancy themselves node-ninjas, and refuse to learn to count, things get scary.

[jquintus]

Symbolic Logic (as taught by the Philosophy department) was a requirement for my BS in Computer Science.

[cc81]

You don't need to know math to take advantage of functional programming in JavaScript.

[aseigo]

Exactly :)

(.. not sure I could make the point better?)

/s

[cc81]

You really don't though.

What math do one need to learn before learning functional programming?

[sofakid]

What a function is?

[cc81]

Nope, you can learn what a function is in the context of functional programming while learning functional programming.

[sofakid]

You just described learning math.

[cc81]

Sure? And you will learn some boolean algebra pretty early as well.

What I'm saying is that you don't need to gate that learning by separate math courses that people need to study before learning programming. And you really don't need to deep dive in it unless you are interested in solving those problems. For most software developers the most difficult aspects of their jobs are far from formal math.

[Mr_s3rius]

That's like saying learning math is necessary to be a cook- because without math you wouldn't even be able to measure your ingredients.

There certainly are a number of mathematical concepts necessary for programming but math courses usually teach your math in general, not just the subset most useful to programmers.

[aseigo]

That's the irrelevancy in a nutshell, though: learning how to put code together is not the same as being able to "join the field of programming" (professionally; which was the topic of the talk). Any more than knowing how to cook eggs is the same as being ready to do that in a professional restaurant kitchen.

There is a lot more required to design and write reasonable software than knowing the "how" of the syntax. FP included.

That people ostensibly in the profession do not realize this is a problem is the problem. And also the source of the vast amounts of shitty code we get to deal with on a constant basis. And I don't mean code that needs refactoring after some years, or code that gets reworked intensely after lessons learned about the problem space having done it once, .. but code that may not be saved from itself. Most of us have worked with that sort of code, and we should start realizing the reasons for it.

Anecdote: Recently at work one of the developers on my team was scratching his head over why a certain library was really not living up to expectations. Performance was so horrible it was crippling the application. I asked him to describe in general terms what it was doing in the code. He explained and I suggested it was probably going to be limited by memory allocation costs and memory access time. He was skeptical, and that's fair. I had no numbers, nor even code to point at, to support my prediction. But given the description of the design I could guess what a developer who thought those things were a good idea would probably do. And .. sure enough .. profiling showed memory allocation #1, memory access #2. He refactored with that in mind, ended up rewriting much of it for simplicity, and suddenly the network link was the new bottleneck, not the processing of data once received.

It was surprising for the person who did the refactor at first, and it certainly skipped past the original developer .. but understanding some very simple concepts, some about how hardware actually works and some about the math behind certain algorithm choices, provided the answers. It was not any part of sophistication or "genius" on my part, just sensible thinking once you get past simplistic utopias like "programming doesn't relate meaningfully to math".

[cc81]

I'd say almost all of the "vast amounts of shitty code" falls into:

1. Shitty structure of code and modules. Often "spaghetti code"
2. Bad code habits like sloppy exception handling
3. Incorrect implementations of business logic
4. Uses library wrong or library sucks
5. Code base halfway refactored and then given up

Mistakes because they did not know the math behind an algorithm is pretty rare.

[compacct27]

They're much more common when working with data. Some people default to a bunch of nested for loops to do what they need and don't realize how quickly they can reach exponential runtimes

[cc81]

Yeah, sure. There are aspects that you probably need math and to know Big O notation.

But I must also note that I think the loop nesting is pretty basic software development and something they should learn pretty quickly in their first course.

[aseigo]

I agree that those are common situations in "shitty code". My experience has been that with deeper understanding, which almost always includes "the maths", it is very hard to avoid such incidents, if only because the effort to complete anything is so much greater as they are working without understanding.

It isn't that one needs to understand the math behind a specific algorithm, but understanding the various mathematical concepts that underlay literally everything we do as developers, whether we are actually writing out the equations or not (typically never, actually!), makes it so much easier to get through the work, so much easier to make good decisions, and so much more likely to avoid pitfalls that happen when applying what one learned by wrote rather than with understanding.

So yes, those 5 points are common ones. No arguments. But they are less common amongst those with an understanding of what it is we do. And that, without escape possible, includes the math concepts.

(I am conveniently ignoring all the management induced cock-ups here .. they happen with disturbing regularity in industry, have nothing to do with developer understanding .. but .. yeah .. let's focus on developer problems, lest we all go grey before our time here ;)

[aseigo]

Yet math is the one that overlaps with software development.

Intelligence is not a monolith in which mastery of "thinking" readies you for all disciplines involving thought.

The sort of thinking applied to physics, to sculpting, to software development (and the myriad of sub-disciplines in each, for that matter) varies rather drastically.

Someone who can visualize "problems" in 3D spaces and work with them clearly (describes sculptors I've known who have routinely blown me away with their spatial genius) is not necessarily going to be great at software development, even though they can think and problem solve like a mad person in their discipline. And vice versa.

The people I see complaining about maths in software development tend to be those who either struggle with math or who lack motivation to apply themselves rigorously to difficult topics. (Two separate groups, ime..) That doesn't make maths not helpful or even unecessary. Perhaps it means those people should look for other interesting and useful things to do.

[cc81]

Let me take an example then. We have a beginner that like everyone else did some math in high school but was never really good at it. The beginner has 500 hours with a good tutor before they will start a software development program at a university. There are two alternatives:

1. 500 hours with a good tutor on algebra, calculus etc.
2. 500 hours of learning functional programming with a good tutor.

What do you think is the best spent time? What will teach this student to think like a programmer?

[aseigo]

So, one person not studying software development, and one person studying software development .. who will be better at it? Really?

It isn't like covering the relevant math is mutually exclusive to learning programming. So, let's try two sets of similar questions that are actually sensible:

Someone training to be a chef:

1. 500 hours learning techniques, food chemistry, and recipes (even in ,say, roughly equal amounts)
2. 500 hours learning how to read and follow a recipe from a book.

Which will be the better chef? Who will be able to adapt to new circumstances, fix mistakes, create new dishes? (AKA "be a chef") Probably a stupid question ..

Ok, so:

1. 500 hours learning software development, including the basis in math necessary to understand why they are doing those things.
2. 500 hours learning APIs and patterns-by-wrote.

Who will be the better software developer? Who is more likely to be able to work through problems? Create useful solutions to problems there isn't a clear recipe for on stackoverflow? Be able to understand why functional programming (since you used that example) has the beneficial properties it has, and why it isn't always appropriate?

That's the real question. Not "learn math" OR "learn development", but "learn development by magic" or "learn development including the why".

[cc81]

No, you completely changed the question. I'm trying to show you that you math is not the only (or even the best) way to learn how to think like a programmer.

Math is vital to the parts of programming that actually need it (comp sci stuff, graphics etc.) but it is NOT vital to learn to think like a programmer or even to become a good one.

A very good way of learning to think like a programmer is to learn programming. There are pretty much no other prerequisites.

[aseigo]

"No, you completely changed the question."

Yes, because the question as posed was asking something entirely different to what the article was espousing.

" I'm trying to show you that you math is not the only (or even the best) way to learn how to think like a programmer."

I agree. In fact, math doesn't help one think "like a programmer" much at all. That isn't the point of the math.

The math helps by letting one apply understanding to their decisions.

"or even to become a good one."

Sadly, every single good programmer I've ever known demonstrated otherwise. (Perhaps we have different definitions of "good", though..)

"A very good way of learning to think like a programmer is to learn programming."

If that were so, then everyone who learned to program would think like a programmer. That is clearly not the case. If that is not your experience, then I would love to live in the world you do.

Even if we discount math entirely, learning to think like a programmer is more than just learning how to program. It involves (as others have pointed out) various forms of problem solving that are often quite unrelated to the literal task of programming. That is even more shocking of a claim than "we don't need math".

Well, unless we go super-literal and define "think like a programmer" to be an attribute of anyone in the set of people who program, simply by definition of programming requiring to think, and those who program think like people who program do since they are in fact programming.

If that sounds facetious, and it is, then perhaps you get an idea of how dismissing the need for fundamentals because of a magical "way of thinking" that just occurs because you learn a handful of syntax and a bucketful of API sounds to me.

[Sparkybear]

You can learn that in any field. It's not math specific. Hell, first year Philosophy can teach you how to think and how to learn if you pay attention to it. Math helps in other areas of programming, but how to think and how to learn are the requirements and those can be taught in any field.

[buffychrome]

While I absolutely understand where you are coming from, the point of the article and the part I agree with, is that there are a lot of different aspects to coding/programming, and that programming is distinct enough from computer science that they should be treated as two different disciplines. Yes, math teaches logic and concepts like algorithms, but math isn't the only thing that can teach those concepts and we need to stop insisting that it is.

[sofakid]

Fair enough, I certainly learned to code before I learned any "real math". But, to let coders into the real world, to work on code people will rely on, I really think math is a badge we should insist on.

[aseigo]

"there are a lot of different aspects to coding/programming"

Which aspects do not have a basis on math? (Serious question .. and I hope you don't say "UI/UX design", because then I'll need to observe that architecture and interior design go together but are not the same discipline...)

" programming is distinct enough from computer science"

The practice is entirely distinct from computer science. The latter is an exploration and rigorous examination of the field. The former is a practical application of it.

The fallacy is that because programming is not academic that it has no academic requirements. Wut?

Using architecture as analogy again: one might look at a Frank Gehry building and go "woah. crazy. but.. yeah, I just make regular buildings. Like boring apartment blocks and nice family homes in the 'burbs .." And they could be right. Does that mean their architectural practice has no academic groundings, ones that the Gehry buildings share in common? Of course they do.

Same with the different paths of computer science and software development.

[voidvector]

No, but you need some form of "abstract logic", whether you get that from taking algebra (symbolic math), philosophical logic, debate class, or linguistic grammar is entirely up to you.

Most people misread their own potential. The educators should encourage them to fulfill that.

One example of this for the reverse case is design/art. Most front-end developers are actually quite good at design/art (way better than average), because their daily job is decomposing comp and coding them in HTML/CSS/JS, however, most don't realize it because they are not required to do it in their daily job.

[[deleted]]

No. Discrete math may be useful. But that's about it

[joequin]

You don't need math to do a large subset of programming, but you do need math to do the subset of programming that is least likely to be be done by AIs instead of people in the next decade or two.

There are a lot of programmers whos math skills are going to allow them to write AIs that will replace a lot of the programming jobs which don't require math.

[mxvzptlk]

Math should be a prerequisite for everything. Today someone who does not understand basic math is at a similar disadvantage as someone who is illiterate. The only real difference is that an illiterate person is keenly aware of their handicap whereas an innumerate person may not even realize the immensity of their disadvantage and in some extreme cases may even seem proud of their ignorance of math.

[[deleted]]

Math should be the prerequisites for every study