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Ask Slashdot: How Many of You Actually Use Math?
An anonymous reader writes with a question that makes a good follow-on to the claim that mathematics requirements in U.S. schools unnecessarily limit students' educational choices: "I'm a high school student who is interested in a career in a computer science or game development related position. I've been told by teachers and parents that math classes are a must for any technology related career. I've been dabbling around Unity3D and OGRE for about two years now and have been programming for longer than that, but I've never had to use any math beyond trigonometry (which I took as a Freshman). This makes me wonder: will I actually use calculus and above, or is it just a popular idea that you need to be a mathematician in order to program? What are your experiences?"
The bulk of programming jobs have nothing at all to do with math beyond the high school level.
Its mostly counting beans and keeping records. Really, it is.
Gaming, (image rendering and manipulation), statistics, and rocket science are a few of the obvious areas that come to mind where more advanced maths may be necessary. Even these fields have packages available to do the heavy lifting once you figure out what it is that you want to do. Knowing what to do the key. This kind of programming constitutes about 1% of the available jobs and 98% of the chest thumping on slashdot.
Sig Battery depleted. Reverting to safe mode.
If you want to be an efficient programmer in some specific domains, an understanding of higher math allows you to optimize your code. In game development this becomes important when you are trying to have your cutting edge game run on older hardware.
How Many of You Actually Use Math?
Last I added it up, three of me.
The only math course in college that I felt applied directly to software engineering was discrete math. It's all about logic, graph theory, etc. and provides the basis for computer science.
That said, most software doesn't really require calculus, geometry, or even trig. But certain fields (AI comes immediately to mind) require a significant math background.
There's no -1 for "I don't get it."
Comment removed based on user account deletion
go google quaternions, or rotation matricies
properly understanding these sort of techniques that are used widely in 3D programming applications without having knowledge of linear algebra is damned near impossible
It doesn't matter if you use it in practice. You'll learn to think critically to solve abstract problems. Don't buy into the hype that you don't need math.
Calculus is virtually unused in computers. It was designed as a shorthand for a world that didn't have computers. What you need to be learning instead is Linear Algebra.
now we need to go OSS in diesel cars
Follow-up:
Math is nothing more than a language that allows the speaker to make very precise statements. If you can't see how this is useful in programming then no-one can help you.
Others do what they can, mathematicians do what they want.
You are probably not gonna use what you learned in Huckleberry Finn or History, either.
There's a reason these are taught, and it's not all about pure facts.
(-1: Post disagrees with my already-settled worldview) is not a valid mod option.
I don't use much math in my work on radio telescopes, which is mostly making gizmos to control physical stuff. Someone else worked out the algorithms long ago, and I do the hardware end of it.
But I work with coders who have to do some rather intense math to solve problems (mostly coordinate transformations or path generation) that had been solved poorly in the old software.
The determined Real Programmer can write Fortran programs in any language.
While programming is not necessarily math-heavy, mathematics gives you experience with problem solving, sometimes in unconventional ways. It's really the only technical problem-solving you do in school, and it's an important learning step, for what it teaches indirectly as well as what it teaches directly.
It's not necessarily the actual math skills that are important - it's the understanding of the concepts behind it that will increase your understanding of any kind of process, job, or task - programming being one of them. Knowing what the area under a curve means is probably more important than knowing how to calculate it.
I don't use calculus or any kind of advanced algebra in my day to day work (in communications, far from programming) but I'm sure glad that I understand the basic concepts, thanks to a first degree in engineering.
Although you might not use a lot of advanced math learning it changes how you solve problems. I found it abstract algebra and formal logic the most useful.
If you really want to get into game programming, the advanced math will be your friend. Supposedly even some ancient (and infurating) concepts like quaternions are coming back in computer graphics. For anything else, it still isn't going to be a waste of time. The analytical skills and "mathematical maturity" obtained by taking a good calculus course (and actually applying yourself rather than just trying to pass) will go way further than the actual calculus will for most people.
Checkout ai-class.com to see some of the ways in which Math gets used in computer science. That class touches on just a few topics and doesn't go very deep. When you work in the machine learning field, there is a lot more math that you'll find helpful.
Realistic physics requires it. On top of that, the more math you learn before entering the field, the more opportunities will be available to you as a programmer. Don't cripple yourself while you're still young.
Damn_registrars has no butt-hole. Damn_registrars has no use for a butt-hole.
How many of you use the problem solving skills that were developed in math class? I may not use math everyday, but I certainly solve complex problems that I'm sure others with less math education would struggle to solve.
Logic is math, and EVERYONE needs logic.
Even if you never write a proof or solve an integral in your working life, it's important to understand how math works. Life, all of it, is one big word problem. If you don't have a basic understanding for the mathematical nature of the universe, you're simply not going to be able to navigate it as well. If you don't understand how mathematical arguments work, you won't be able to offer useful opinions on the matters of the day.
I'm not sure that everyone needs to know calculus, but everyone needs to know what calculus is and what it's used for. Everyone needs to be numerate.
Give me Classic Slashdot or give me death!
...then you certainly won't use any. If you do know some and are comfortable with it you will find many uses. On the other hand if you struggle resentfully through the minimum required math certain that you will find no use for it, you will be right.
Warning: this article may contain humor, sarcasm, parody, and perhaps even irony. Read at your own risk.
Clearly I've been watching too much Breaking Bad.
The CB App. What's your 20?
Trig as you already know is great for 3d stuff.
Calc is great for decision logic and business intelligence
Stats are great for business intelligence type work
As someone who did horribly in high school and college math, I did the minimum for my degree. I've retaught myself much of stats and calc because I found them useful in my personal projects. I find them more rewarding now that I have applications to use them in. I was a bad student though early in life. YMMV
Most of the math in the corporate programming world is really elementary. Basic algebra or less.
My current job title is "Bioinformatics Analyst," and I need to at least understand a good bit of math that I didn't learn in highschool. While it's rare that I directly need to implement complicated mathematical programs, much of my job involves tuning parameters for specialized software.
I need to have a good understanding of the changes that are likely to result from adjusting parameters X, Y and Z before I submit a job that takes upwards of a day to complete. To do that, I need to read the papers and understand the algorithms.
Agreed. Any graphics engine uses a ton of linear algebra under the hood, so you'll need that if you ever want to modify one or write your own. Also, if you want to do any kind of physics simulation (which you probably will, if you're doing games), you may need calculus (but maybe not, since video games fake as much as they can get away with).
I explicitly release the above into the public domain.
You don't really need math. But the thought processes learned through math training are really useful.
I use linear algebra and calculus everyday.
As a geomatics engineer, my programming often involves using and understanding different levels of vector calculus as well as some basic linear algebra.
By the time I'm 30, I probably won't use it as much. In the meantime, I use it everyday to solve different problems.
Reading Slashdot headlines is not normal.
On Meth, it is.
Meth. Not even once.
APK quotes people (including myself) without context and should not be trusted. Just thought you should know.
The more you know the more opportunities you will have and the more earning potential you will have. I've used college level math in programming projects before. I have a friend who's a PhD making buckets of money doing very high level math. So if you want to make buckets of money doing high level math related programming, you will need to learn high level math. If you're comfortable making decent money limited to projects going no higher than high school math, then that's all you need.
So Trig is like 3 houses in Monopoly. You've made a huge leap in earning potential but you're not at the top yet.
Work Safe Porn
Purity
The CB App. What's your 20?
If you can't do the maths up through at least a year of linear algebra, and didn't make at least a B, I don't want to hire you for any of our technical jobs.
now we need to go OSS in diesel cars
The key areas for math in general computer science are algebra and statistics. Even if you are not actively using algebra, the thought processes in programming are very similar. Statistics are critical for analyses of system behavior. Linear algebra is useful occasionally, but mostly it's just something that is nice to have been exposed to.
I never use calculus, but it was in taking a calculus class that my algebra skills solidified, so the coursework was not wasted. In general, you should always progress one step further in coursework than you expect to actually need.
Also, there's a big difference between knowing enough to get an entry-level programming position, and knowing enough to have a career where you end up designing major projects.
Which is also why there is a lot of high school level code out there.
If you never learn more than you need then you'll never know if you have learned as much as you need.
Learning more math won't always make you a better programmer. But it will show you whether you can do something better than someone who knows less math.
If you want to get into post-graduate studies, this means taking the GRE test. There's a lot of math on the GRE that you have to do quickly.
None of it is terribly difficult, but I found that I was very out of practice, which slows me down quite a bit.
If you can do high school math in your head quickly, it vastly improves your score.
I've been in the CS industry for nearly 12 years and offloaded nearly all my high school era math off to calculators and spreadsheets. Very rude awakening when I took my first practice GRE.
/sig
Also, you'll never be able to verify that your algorithm is working by manually processing sample inputs. That's a tremendously useful ability to have. See the following thought process:
>> "See if I give it A, it should give B, but instead it gives C"
>> "Let me try it by hand"
>> "My algorithm is wrong" or "My implementation of the algorithm is wrong" or "I'm using the wrong algorithm to solve this problem" (knowing the difference saves you notable amounts of time)
>> "I now have an understanding of the actual problem and can solve it"
Yeah, you'll notice that a lot of the richest and most successful people never completed college. And that's fine but in my humble opinion, that's a risky bet to take. I've done interviewing for developers for a fortune 500 company and seeing a college degree on the resume doesn't cause me to kick back and say "Oh thank god, they have taken Multivariate and Differential Equations calculus, now all my Spring applications are going to be able to compute the triple integral (by parts) of a toroid in three dimensional space as it passes through a fluctuating field exerting a force on it!" (Yes, I know that makes no sense at all) No, what that tells me is that we're going to be able to throw you in an environment where you have no clue what to do but resources to go out and find what to do. On top of that, you're going to be able to digest the driest and shittiest of documentation (like a calc book) and come back to me and have gleaned some working knowledge from it. Sure, you might have to go to the next cubicle and say "What is up with this stack dump?" And you may have to seek out an authority (like a professor) but you're going to come to some answer for our problems.
In short, it tells employers that you know how to play ball and high order concepts don't frighten you. I'm not going to throw integration by parts at you on the job but it is good to know that you stepped up to that challenge -- even if it was just to get to a final, pass it and move on. In short, I went to a liberal arts college, I took classes on music theory, calculus, physics, Native American studies, advanced literature, etc and in those classes I created four part inventions, mounds of calculations, papers, powerpoints, etc and I have used little if any of that in my day to day job post college. But in mastering those processes I learned how to play ball. Now, I'm not saying you need to go take music theory and Native American studies. But the thing with Calculus is that all software development is logic and math. So don't you think you'd want to get all your i's dotted and t's crossed so that any employer that looks at you knows you have studied beyond the requirements of math for writing software into a realm so lofty they won't even be able to use it? I'm sure glad I did.
My work here is dung.
I developed a game using Unity3D.
I make heavy use of trigonometry, and a very small part of calculus.
Your question really depends on what you want to do:
There are other fields that are not typically taught in math courses but in CS that are heavily math related. Like performance analysis. This I use a lot, but once again, it really depends on what you work on.
I do a lot of database work so it's set theory all day long. It's in a bit of disguise as it isn't what normally is though of as math but set theory is a math field.
You should not waste your time with it. Otherwise, you might end up competing with me for the interesting jobs. Neither of us wants that. ;)
Depends on the Maths, depends on the CS.
"Logic", if it can even be considered a branch of Mathematics, is always important. The various topics under "Discrete Maths" often overlap with CS. The habits of rigorous thinking, proofs, use of counter-examples, etc. are all indispensable to proper programming.
That being said, my personal experience in web and systems programming is that as long as you don't go into game and graphics programming, you don't really need to apply any "mathematics" beyond high school level, if even that. The curious thing is even though you may not really consciously use mathematics, better programmers generally do have a pretty good grasp of higher mathematics....
But then, I've really never done any damn calculus in my programming career (not that it's particularly long). In fact, unless you're doing something very domain specific which needs the actual maths, usually an approximate solution will be simpler, easier to maintain, and less error prone. (It's not always easy to resist the temptation to implement the fancy solution though)
(PS: And I speak from personal experience -- as a programmer it's often helpful to have friends that actually know their maths very well :-p)
Don't quote me on this.
You won't command much credibility if you can't even spell "orthogonal" right.
I do most of the design and programming on A Tale in the Desert and Dragon's Tale and I've seldom/never needed to do an integral or solve a system of differential equations. Understanding those concepts does frequently influence game design, however, so having taken those courses was important, at least for the kind of games I do. (Giving specific examples would require that you are familiar with gameplay for each of those games, but feel free to contact me directly if examples would be helpful.)
:)
But on to specific branches of math: You'll certainly use linear algebra doing 3D programming, and IIRC that's considered "beyond" calculus. (If you're using OGRE or Unity 3D, at least at the API level then I'm surprised you haven't run into this.) Applied Math, which is often a college freshman course for a CS decree is crucial to all sorts of programming, especially games. Combinatorics is critical for game design, though if you're just planning to be a programmer, not so much. Numerical Methods will teach you exactly when and why rounding errors to happen, how they can compound each other, and in general help you write squeeky-clean math code. The game I'm working on now is a gambling MMORPG - I probably don't even have to say how important statistics is, if this sort of thing is in your future
Notice how different each of the math subjects above is? A lot of this comes down to learning how to learn, and that's the one thing that in my experience differentiated high school academics from college.
what about other NON college education.
http://articles.chicagotribune.com/2012-03-11/news/ct-oped-0311-page-20120311_1_college-costs-rise-kayla-heard-college-attendance
"Yet, give Santorum his due. He touched on a reality that deserves more public discussion: College isn't for everyone. Some very bright students thrive better while learning a hands-on trade, for example, than they do in a classroom. Others simply can't afford the time or tuition of college because of their personal circumstances."
College is not for all and there others ways to learn then going to a big 4 year plan. College needs to be cut down / cut up into small chunks that can better fit fasting moving tech and can work for people who are working and want to gain more skills but can't fit into the college time table.
http://articles.chicagotribune.com/2012-03-25/news/ct-oped-0325-page-20120325_1_collegiate-learning-assessment-college-students-richard-arum
"I recently wrote about the possibility of testing and certification for what I called a "college-level GED." Like the current GED test for high school equivalency, it would award certification to bright, hardworking job applicants who want to show potential employers how much they know, even though they never graduated from college/"
community colleges and trade schools are not the party schools that some colleges are.
"Ohio University's Richard Vedder, my former economics professor who gave me the collegiate GED test idea, is even more blunt in his assessment of today's academia: "Universities are becoming more like country clubs," he said, with climbing walls, indoor tracks and other luxuries that give students "something else to do with their free time besides drink and have sex."
I didn't use math much past counter++; until I learned some hard core math. Then I had a new hammer and the math in my code grew to the point where I now need GPUs to keep up. I love OpenCL.Discrete math rocks. I look back at my old pathetic basic algebra self and shudder.
Often it is useful for either figuring out what is going to happen when some set of algorithms get pounded (instead of just coding up a script to bash them) or in cool analysis of data that otherwise just sat silently in some log file.
If you just want to make a living, then you'll probably never need any higher math.
OTOH, if you are at all serious about programming as something you want to be really good at, then you need a _lot_ more.
I've worked with low-level game code (Quake asm), with video & audio codecs (MPEG2, h.264, ogg vorbis), with crypto (one of the AES candidates) and I wrote most of the code for the compiler sw workaround for the Pentium FDIV bug.
I doubled the speed of a Computational Fluid Chemistry code base, so that simulations ran in half a week instead of 7 days.
I've also won a couple of international code optimization contests.
The key here is that except for the h.264 optimization all of this has been pro bono, my daily job at a Norwegian IT company has almost never _required_ me to know a lot of math, but having math as a hobby means that I tend to spot all the bogus calculations in Powerpoint presentations. :-)
Terje
"almost all programming can be viewed as an exercise in caching"
Students who do well in the more advanced undergraduate math courses (real analysis, abstract algebra, etc.) may never specifically use those precise topics, but good performance in those courses serves as a strong testament about being able to deal with abstraction, work precisely, and construct correct arguments. Those skills will serve students well and may impress employers/managers that the student actually is pretty good at thinking and problem-solving.
Linear algebra as mentioned above is probably more likely to be specifically useful in applications: modeling, graphics, science and engineering settings, as typically relationships are too complicated to be understood effectively by anything besides a linear approximation. But many linear algebra courses are technique-based and rather cookbook, missing an opportunity to take advantage of good more abstract approaches.
It's psychosomatic. You need a lobotomy. I'll get a saw.
I have an MSCS from Stanford, but it's from 1985, when the logicians and expert systems guys were running things. So I have lots of number theory, combinatorics, automata theory, and mathematical logic. I even took "Epistemological Problems in Artificial Intelligence" from John McCarthy.
So what did I end up needing? Tensor calculus. I realized that expert systems AI was stuck. The future of AI capable of dealing with the real world seemed to be in nonlinear control theory. Which is all calculus and statistics. I struggled with that, and got legged running over rough terrain figured out and patented. But this was 1994, and the simulators sucked, and I couldn't get any further without better simulators. So I spent a few years beating on that problem, and produced the first simulator that could do a ragdoll falling downstairs.
By 1997, I had that solved, but it was kind of slow. A 200MHz Pentium Pro just wasn't enough engine to get it up to real time, and that was the top of the line in CPUs back then. By then I was burnt out on the problem, and it wasn't making much money, so I sold the technology off to Havok and went on to other things.
I didn't see that what was needed was to couple nonlinear control theory to Bayesian statistics. That's what makes all those quadrotors zip around so precisely. Modern statistics barely existed when I was in school. Now it drives everything from finance to speech recognition to advertising, so it gets worked on and people study it. Nonlinear control alone never had that big a market, so the field didn't get enough attention to move it forward.
So I needed more math, and different math, than I got in school.
But a huge amount of computer science is not about modeling the physical world. It is about organizing data or doing accounting or serving up web pages. Advanced calculus does not help at all with that.
If you do not have a decent grounding in set theory, please do NOT attempt to do any significant database work.
Basic select, insert, update and delete can be dealt with via modern ORMs. Anything beyond that, such as joins, intersections, unions etc. are almost entirely set theory. Where is that covered in the traditional mathematics curriculum?
Yes, some ORMs purport to do that stuff, too, but they rarely do it well.
True story: I was taking a database course as part of my college education. The professor introduced us to relational theory, including an algebraic notation which described subsets of fields in a record and subsets of records in a table. Then, over the course of three class periods later in the semester, he taught us SQL. It boiled down to "this is how you do xxx in SQL." From that, we got table creation/destruction, selects, views, subqueries, aliased fields and tables, inner and outer joins, the whole enchilada. I've been able to build on that and do some pretty heavy-duty SQL work but I had to know the underlying theory. Being subsequently trained in RPG, where much of the legacy code does NOT use SQL (and you invariably don't have time to replace it with code which does), that theory comes in very handy.
We understood the underlying theory, all expressed via math. Learning SQL was a simple matter of learning how to express our desires in a language the computer could understand.
You need at least algebra to understand O(n) notation. Without that, you're usually stuck either cluelessly gluing together someone else's libraries (a LOT of that in modern SoftwareDev) or continually recreating O(n^3) (or worse) algorithms.
If you aren't going to learn calculus, one can only hope you never need to do any kind of Numerical Analysis. Any course where you're allowed to use Mathematica, because the calculus (such as taking the third or fourth derivative of a function) is "overhead" relative to the material being covered, is the very definition of "heavy duty." And, since physics is largely the application of calculus, avoiding calculus means you also need to avoid anything which involves physics. Stuff like game design (Angry Birds uses plenty, Angry Birds In Space uses more), putting rovers on Mars, wireless network design (wave propagation between obstacles and through different media is very calculus intensive); you know, the COOL stuff.
For the typical web developer, creating shiny web pages which do extremely simplistic database work, you probably won't need calculus. Ever. Is that all you ever aspire to be? And how long can you continue to do that without being crowded out by graphics design wizards with increasingly intelligent design tools?
... by the Dew of Mountains the thoughts acquire speed, the hands acquire shakes, the shakes become a warning
The only time it's really appropriate to stop learning is when you're dead. (Though I suppose if you think learning can only happen in a school you may as well be...)
The point is whether or not the math they teach in high school is useful for anything and should be taught. The problem with this thinking is the high school years are rather formative for many people - the subjects they are exposed to and their experience with them can have profound impact on the decisions they make that will form their lives and professional careers.
So take math. It may not be "useful" but it will influence you and your worldview, and that's important.
BUT! If I were to change anything, I'd shift Calculus later and put more focus on Prob & Stat - A better understanding of prob & stat will make your life better and really help keep your bullshit detector well tuned.
Also, this comes to mind and is worth watching, tangentially related.
=Smidge=
Understanding why the math works makes the programs work. Understanding probability and statistics make my inline sampling calculations correct. Understaning how spline calculations work make my curve approximation code (or even the use of curve approximation libraries) correct.
Yes, there are a lot of good libraries out there. They are optimized. They are error-correcting. They are correct. And knowing what they do and how they work enables you to use them effectively.
When you talk to your clients (or your bosses) and they ask you about how you did something, the ability to pull the core math and explain it will go very far.
It is kind of like lifting weights. The lifting isn't its own end. It makes the daily (carrying 40 pound boxes of cat litter into the house) mundane. So it is with math. Understanding simple things as polynomial interpolations for higher-order polynomials can make or break your ability to project storage estimates. Understanding O() notation will help you program well.
Don't scrimp on the math. There are enough bad systems out there for other reasons already.
Not everybody needs to use a nondeterministic finite state machine every day, and not everybody needs to calculate the transitive closure of a sparse connectivity matrix every day, but these are (simple) examples of reasonably commonplace algorithms that you can't really understand without being able to do the maths.
As an even simpler example, you can't really use SQL effectively without understanding the maths behind a relational database. I know this for sure, because I keep coming across SQL applications that were clearly written by people with no understanding of the maths, and I get paid lots of money to fix them up properly.
Nobody divides by 1024!
I use a lot of math in my work. From ballparking load estimates using basic math to behavioral analysis using linear algebra to data analysis using calculus, I use it all the time. Set theory, logic, graph theory, statistics, on and on -- it all contributes significantly to getting the job done right the first time. Having a background in a variety of maths also helps to visualize problems and shape solutions. I've added as much to my math skills since becoming a professional programmer as I did in school.
There are fields in software, like interaction design, that don't require a strong higher math education, but if you have a good math background it will give you the freedom to explore more opportunities.
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US: Math
UK: Mauthe
In undergrad (CS) I did more math than was required, and honours math at that. When I started grad school I was introduced to a transform we were using to analyze medical images. There's an article somewhere where I'm quoted as saying that some smart grad student is going to come along some day and improve the algorithm for calculating that transform so that it's actually practical. It turns out the smart grad student didn't come along, so I had to do it. That involved a lot of calculus, both continuous and discrete. Now I mostly develop new medical image processing techniques and analyze data, which involves fairly high level statistics. Statistics is all calculus and, when you get further on, calculus and linear algebra.
You say you want to be a game programmer? Here are some of the papers from SIGGRAPH this year. Take a read through some of them. This one might be a good place to start... most of the authors are from Pixar. How much math do you see? How much math do you understand? These are the algorithms you'll be working with by the time you graduate. Note that there isn't a lot of continuous calculus in these (but a lot of discrete!). Somebody has already done much of the hard work of discretizing it for you. That's not always the case.
You can probably get away with not learning any math and being a run of the mill code monkey. If you want to be good at what you do though, learn the math.
No, the point of a challenging degree program is to maintain academic standards. To be awarded a degree you need to have achieved a certain standard. If the sole aim was to limit the number of graduates in a program you would simply limit the enrolment. When we have been hiring IT staff one of the things we have looked for is a degree because this shows that they have some depth of knowledge beyond the basics. Sometimes the confidence that this brings can be very important for adapting to new situations.
The point of high-level math and physics classes is not because you "need" them in your job as a programmer. It's a way to limit how many CSE degrees are granted. I was told this straight-up by my college advisor ...
Then like some advisors he is a dumb-a**. I've been offered some pretty crappy advice and insight from advisors, don't take what they say too seriously.
You are basically getting into the trade school vs university argument. A trade school can produce as good a programmer as a university. The point of the university is to provide a more well rounded education so that a person has more options.
I too had some chemistry, physics and years of math that appeared to serve no purpose other than to "weed out" people from the program. However to my surprise I once had the opportunity to participate in a project that would port some chemistry software from mainframes to PCs. I would be interacting with world class polymer chemists. They did not expect me to be a chemist but they did expect me to be scientifically and mathematically literate. The general ed chemistry and physics and the years of math for computer science actually turned out to be useful.
I tend to use math most days. Estimation, ballpark figures, cost per ounce etc and I no longer work in the computer industry. Now that being said, is there justification for higher level mathematics in computer programming.
Well, yes and no. The typical programmer isn't working on anything complex, just providing a bunch of criteria for a switch statement or copying information from one location to another, not a big deal, but when you start working with algorithms, not to be confused with (Al Gore)ithms an understanding of upper level mathematics can certainly help. Discrete mathematics is a no brainer since it focuses on logic and proofs which can help a programmer find edge cases and cut down on errors via the processes you learn in discrete mathematics.
Calculus and other higher math is generally useful in making algorithms run more efficiently. Brute force searching algorithms take a lot of time, binary is significantly faster, but using calculus can even improve on the binary search methods in the right circumstances. The thing is, if you don't have the knowledge about high level techniques you cannot use them. For instance, if you don't know sorting routines a bubble sort seems incredibly fast in comparison to sequel sorting however without the knowledge of sorting algorithms you wouldn't realize how ineffective bubble sort is in comparison to say merge sort.
Most programming isn't focused on efficiency and most things can be brute forced within a reasonable timeframe with modern computer systems, however, knowledge of calculus and other higher level mathematics can help quite a bit as techniques can be transferred into computer programs that need them.
I guess you could make the same comparison to electronics, does a programmer really need to know electronics, diodes, resistors, refresh rates and protocols to make a computer do something useful? Probably not, but if you do know those things it can make you far more efficient and effective than the person who does not know them depending on what type of programming you are doing. Whereas most systems are built requiring basic skills or specific study of one area, higher level mathematics provide tools that can be used in a wide range of applications and tend not to be limited to specific cases. With the knowledge of upper level mathematics, when you do run into situations where it can be used, you can pull out a book or do a search to find an efficient algorithm whereas when you don't have the knowledge you'll end up spending a lot of time re-inventing the wheel.
/* TODO: Spawn child process, interest child in technology, have child write a new sig */
Learning math teaches you to think. It is very worthwhile.
Facts take all of the premium out of arm waving - T. Reynolds
The bulk of programming jobs have nothing at all to do with math beyond the high school level. Its mostly counting beans and keeping records.
There is the activity of programming or coding, and the activity of software design. Coding by itself requires little behind HS math. Development/engineering, on the other hand, requires the person to have good analytic skills. From choosing the right algorithm or data structure to composing good architectures, they all boil down to understanding convergent and divergent series, discrete mathematics and combinatorics. To get to those fields one needs to have a good grasps of limits (ergo, Calc I). Similarly, every once in a while one has to make some form of probabilistic analysis at some point or another (ergo stats and Calc II).
Knowing mathematics at the calculus level or above does not guarantee a person to be a good software developer. But not having good analytical skills almost guarantee the person will end up writing flat class hierarchies, architectures without layering, writing n-cartesian SQL queries, and loops that execute very expensive invariants.
The error I've seen the most with developers with poor analytic skills is an inability to infer behavior from looking at code. That is, they are completely incapable of doing P->Q inferences. Worse still, they seem to have problems doing divide-and-conquer approaches. They cannot look at one piece of code, they have to look at the whole thing. When testing, they test the whole system in one single shot as opposed to testing and observing behavior of smaller pieces. In other words, they cannot handle complexity. They simply bang it - code it, compile it, run it, don't like the output, change it again, on and on until it prints the "right" thing (or things get hidden under the carpet.)
YMMV, but that has been what I've seen since I started my career in software.
If you are talking college, don't think of a 4 year Computer Science (CS) degree as anything to do with computers. Instead, think of it as a specialty field of mathematics that should have been called Computational Theory. True, you can learn about how to program your own compiler, make your own database engine, program your own operating system kernel, and other things related to computers - but there is going to be a lot of discrete math that requires calculus, and a lot of complexity theory and proofs to do also. So, yes, if you want a leg up get as much calculus out of the way and make sure you are taking a math course every semester to keep your skills sharp. (Trust me, I waited over 10 years before going back to college and even with "cramming" all the math in my brain before enrolling, I am far behind in my math skills.)
Along with CS is Computer Engineering (CE), which is more of building hardware. Circuit design, pathways, and all that stuff one intro course made me not care to do - and a lot of optimization is done in that field. Of course, any engineering field is going to be math heavy, so no real change there either (and also master your calculus based physics).
What you are probably looking for is a Software Engineering degree - which, as an engineering degree, will require mathematics also but focus more more on programming and software design.
Note the trend? 4 year college means lots of mathematics no matter what - and if you aren't in an engineering school but in a college of letters and sciences, then be prepared to have a liberal arts education (read: basic biological studies, basic natural science studies, an ethnic study, literature courses, humanities courses, and social science courses that will be at least 1/6 of your total credit load... as a coworker of mine said "a lot of BS work that I will never use". I disagree with him, my most useful courses have been english composition, contemporary art courses (which gave me a new frame of reference to draw on), and my environmental studies courses. They introduce new ways of thinking... and CS is all about thinking of new and efficient ways to solve complex problems.
The only way to avoid heavy mathematics (namely, at the calculus level and above) is to opt for a vocational/technical college. You know, 2 year degrees with titles like "Web Programmer" or "Database Administrator". Also, there are multiple fields to choose within the computer industry.
Of course, I don't want to discourage the 4 year route. It is hard, but worth it... and if you find you like academia, there are graduate programs that will open up a whole new way of learning. Heck, UW-Madison has imitated Cornell and implemented a Games, Society, and Learning program... its serious business, but their lab consists of a PS3, X-box, 5 networked computers, a library of video games, and tons of obscure board games - and something like that is most likely where I will be once I complete my undergrad (if tuition doesn't skyrocket... so if you are going 4 years, my advice is do 2 year transfer at a 2 year college that is less expensive and has significantly smaller class sized... Chem I and II or Intro Calc Physics I and II is much better in a class of 40 than 300.)
I went to college (for the 3rd time) at the age of 30. I had a hard time with Calc etc. and hated the first two semesters of Comp Sci, but got over that. I literally had to ask the Prof in 101 where the switch was on the machine.
My first job was with a government tax department. One of their biggest problems was that small businesses kept changing their names trying to escape from last quarters' tax bill. I got assigned to write a routine to track business names - really to invent a way to track businesses changing their names. This led to designing an artificial key for a business, and assembling a list of all their names and date the changes.
Then after some work I found that some of the businesses randomly changing their names would reuse a name eventually. Not smart if you're fleeing debt associated with that name, but what can I say? That created a closed loop that would circulate endlessly, or until a main frame operator got suspicious and stopped the job; or until I wrote code to escape a closed data loop.
Making a really long story a little shorter, you will need math, and the skills learned working on math, no matter what kind of work you do, unless you are just a code monkey coding things with all the complexity designed by a systems analyst with 2 degrees in math.
If that's all you want, to be a code monkey on a system you don't understand large parts of, then you don't need a degree in Computer Science. If you want to be any kind of scientist, or systems designer, like those who build gaming engines or rastor graphics programs, or tracking genetic variability in organisms being studied in labs in Research Triangle Park, NC; or at C-M University, in Pittsburgh; or Cal Tech where they just landed a curious robot on F'Ing MARS, then don't get a degree, don't study math, stay ignorant.
That kind of work is actually going on everywhere now, not just these examples I pulled from my a**, I never left my home state to have a good career doing important work. I didn't use Calc every day, but I knew that I could if I needed to.
"You can cure ignorance, but there is no cure for stupid."
Think of the Irony!