Slashdot Mirror
Math And The Computer Science Major
An anonymous reader writes "What sort of math are CS majors expected to take? Why are these classes useful? Does programming really have that much to do with math? Lineman.Net has published an article that answers these questions and more. If you are considering a CS degree, be sure to give it a look and make sure you are taking steps to prepare for your college career."
Coding is not as important a part of computer science as you may think it is. CS is full of theorems and proofs. Computer science is the science of making algorithms more efficient. Programming is about implementing algorithms.
Useful?! You can't do anything without it. You can't study graphics without maths. You can't study 3d graphics and simulation without quite advanced maths. You can't study audio without maths. You can't study just about anything in computer science without maths.
Only a Mickey Mouse comp sci course would not require maths to quite a high standard.
I usually thought of it as the difference between learning how to program vs memorizing a bunch of useful code snippets and how to translate them to different languages.
You are in a maze of twisted little posts, all alike.
However, writing a web front-end to a database (which is what a *LOT* of people end up doing for years and years) requires practically NO math 90% of the time. Of course, it't that 10% that will get you.
> we have to know math because the math majors cant program, usually
Conversely this is the very reason why physicists and mathematicians have good job opportunities in IT, consulting or banking. In many cases it's easier to teach a physicist programming (or economics) than to teach a programmer the relevant understanding of mathematics.
Of course it depends on what you're progrogramming and of course a programmer who is good at the kind of maths required for the job will have the edge anyway...
I find that the math courses I took in college had about as much relevance to the comp sci courses I was taking as the comp sci courses themselves had to the actual work I do as a computer programmer.
On the one end of the spectrum is pure theory, and proof, and on the other hand, we have complete practice, and "get it done now".
Math is a great theoretical background for computing, and made some of the algorithmic courses a breeze.
Ironically, I found the proofs in algorithms classes an attempt by computer scientists to say "see, we are a real discipline, we do proofs too", but I found that I wanted the CS courses to be a counter to all of the proofs and theory I got in my math courses. I wanted some "hands on" learning.
Once I got out in the real world, especially with languages like Java, even the CS theory/practice (this is a hash table, now write one), I found that most of the data structures/algorithmic stuff had been written and I just filled in pieces.
Where am I going with this? I guess basically that math is useful for comprehension in CS classes, but depending on the programming you do, you may not even use the CS you learn in the real world, let alone the math. But understanding is good.
Rhymes that keep their secrets will unfold behind the clouds.There upon the rainbow is the answer to a neverending story
If that's what you want to do, don't waste your time in college, because they won't teach you that. Connecting a webserver to a database isn't science, is it? But if you wonder how complex SQL queries can be simplified and executed with the least amount of resources, then CS is for you, and there will be math.
Amen. Don't think programming takes too much math? Try writing a game, any game. I was writing up a Rogue clone and got around to path finding. The number of algorithms to use are just sick, and they're all math intensive. Not so much algebra/trig stuff, but the spatial relations stuff is all math based.
Other programming...calculating and distributing load, memory management, all math based. If you ever write anything with sound or electricity (lots of embedded stuff), it's all math based.
Many CS majors will enter the work force only to do data moving programming (ie, take form input, store, retrieve, repeat). However, even those sytems have to have somebody load balancing them which gets into timing and...well, we all know how it goes. Math isn't just a filler class in a CS majors curriculum.
--trb
Ya know...maybe it's just my field (computational biology), or the fact that I've been in school for far too long, but the more I code, and the more math that I use, the more I see the two as different faces of the same beast.
You don't have look at much interesting software before you realize that the difficult problems -- the ones that are fun to solve -- are inherently mathematical. And conversely, once you start seeing programming languages as expressions of underlying mathematical forms, they start to become very similar to one another. And I'm not even referring to bleeding-edge research code, either -- look at P2P networking, and you're staring into the eyes of a massive, graph theory problem.
Anyone can write a shell script. Very few people can express mathematical concepts in code.
Let's try not to let fact interfere with our speculation here, OK?
This isn't about ego. There's simply no point in choosing CS if you shy away from math and won't be working in a field where CS skills are required. You wouldn't enjoy it and consequently wouldn't allow yourself to apply CS methods. There's nothing wrong with connecting databases to webservers. People want that done. It's just not computer science.
-Because that person might be writing your SQL queries too.
-Because elegant and reusable code usually comes from the minds of people interested in solving problems.
-Because that person might be able to understand the problem domain better than some I-don't-give-a-shit-about-anything-other-than-code programmer.
-Because that person might work in other areas of development eventually. Did you hire the person for ONLY their database-to-webserver knowledge? Was that shortsighted? Maybe you'd rather have a well-rounded and generally smart person to solve those new problems.
We have a very rigorous hiring program at the firm I work for. We look for intelligent people with a wide base of skills who we think can easily adapt to new problems and environments. We DON'T look for specific knowledge in anything but our most senior positions. We have had wild success in finding very talented people because we are not looking for a person with skill A. How long will skill A be relevant for anyway? Will the person with skill A be able to do good work if we try to teach him skill B later? That seems pretty important to me.
So the question is really: what are the most valuable qualities that a new hire can have? If your firm thinks that 3+ years of java experience is the most important quality a new hire can have, then I really don't want to work for them. I have over 3 years of java experience, but I in no way consider that my most valuable quality as an employee.
Taft
I agree with you, but only to a point. In most cases, your employers will just care that it's done on time and under budget. But what happens when system performance is not acceptable? That's when you've got to figure some things out. Look for performance bottlenecks, etc. Times like this are when a math background (and I consider algorithms to be math) will be a life-saver.
Just looking at my co-workers, there are some who have strong math backgrounds. There are others with pretty minimal backgrounds, and it really shows in their code and problem-solving abilities. And guess who my boss has more faith in?
As a side note, I'm not saying that any of this requires formal education. You can learn a lot of this stuff on your own, if need be. It's just that if you've been to school, there's a hope you had to get through these classes and at least some of it stuck.
If all you have are silver bullets, everything looks like a werewolf.
And you will learn it, and employers will not give a shit, because they just want to connect a webserver to a database, which is not science, and when you realize that your ego about your science knowledge has prevented you from finding a job anywhere but McDonald's, you will realize the error of your ways, and you will want to connect a webserver to a database.
On the other hand, when your job of just connecting a server to a database gets outsourced to monkeys in the congo, the person who learned the math and the science will be getting a serious software engineering and design job.
Jedidiah.
Craft Beer Programming T-shirts
Here here and amen! When looking for programmers, I don't care as much about your specific experience as your ability to think. Early on in hiring, I thought experience in a space was the critical element (after all, it was an *easy* assement to make). After several programmers who had to be given specs more detailed than the code, I realized I was wasting a lot of energy because I was trying to work with coders, not programmers. I now make a clear distinction between those who can follow a crystal clear spec, but can't think independently (coders) vs those who can follow a typical rapidly changing spec (programmers) and those who can create a spec to solve a problem (analyst). I have nearly zero use for coders - they cost more to feed specs then the output is worth.
Anyone who thinks programming is "wiring front ends to databases" is probably a coder. Yes, there is quite a bit of that kind of work in the business space, but a programmer will not wire your database to a GUI: they will come up with tools to do so more effectively. Similarly, anyone who thinks "skill X" is the be all and end all of programming is probably a coder. (I once interviewed a guy who was pretty good with Oracle. Commanded a six figure income. When he found out that the offered project used SQL server 2000, he mocked our company, to our face and to the niche community we work for. In a bit of "the best revenge is success", he solicited *us* for work after the dot com crash. Seems he was out of work for over a year due to his disdain for anything but his tiny niche skill, and our project was looking pretty good.
Sig under construction since 1998.
You don't even have to do 3D graphics to get into this stuff. I wrote a space simulation engine for PennMUSH and stopped at no lengths on some things...it only updates once per second, but I want to detect collisions accurately. Calculus saved the day. I wanted to turn in a spherical configuration space (where most people doing this use a cylindrical one) - take the cross product of where you are and where you want to be, and rotate yourself the amount you want to turn around said cross product. This is probably close to 100 lines of code, just to turn a ship.
;-D
Any programming at all involves math. The better you are at math, the better a programmer you will be. If you are not good with math, you will not be a good programmer. HTML and what most people do with PHP et al. is not programming - it is markup.
My CS degree required that I take Calculus I & II, discrete math, a statistics course (I took the harder of the two accepted for this, a 400-level math), and a math elective or two. I took a graduate-level cryptology special topics class for one of the electives - it was three CS students and about 6 math graduate students. At the end of the semester, the professor wrote a list of 3-digit numbers, most of them on the range [400,599], and said "This is a list of math courses we've covered at least half of in this class. Take them if you want to know more." There were about a dozen numbers on the list. My other elective was Calculus III, which I took concurrently with Crypto, across the hall, from the same professor. That was a challenge, as he made it extra hard on me in both classes (both because I'm good but also because I'm a smartass). He threatened to encrypt my Calc final.
At the very least, a programmer should have discrete math, multi-dimensional Calculus including working with series and sequences, number theory, linear algebra, and diff-eq (I regret not finding time for the last two).
Like I said - your abilities as a programmer are directly proportional to your abilities as a mathemetician. There's not a science you can study properly without using math.
As a minimum, I would suggest:
- Algebra, Analytic Geometry, & Trigonometry. Know this stuff cold. After 30 years in computing, I still use it every day.
- Logic. Ditto.
- Calculus up to, but not necessarily including Differential Equations.
Very helpful at times:- Linear Algebra
- Probability & Statistics
- Numerical Analysis
- Automata Theory (offered in CS departments)
And if you're really into it:- Number Theory
- Topology & Graph Theory
A good grounding in one of the "hard" sciences like Physics can also be useful. And if you've got an aptitude for music, indulge yourself! Remember, it's not just the content of these discplines that makes them valuable. Each one teaches you to think in different ways. And an agile, flexible mind will make you more valuable to your future employers.Go for an education, not just training!