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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."
we have to know math because the math majors cant program, usually. as a programmer, youll have to work with NUMEROUS different people from all sorts of other fields. you might be designing heat control systems, biochem simulation software, or electronic simulation software like me. the more you know the better in this field, i think.
use your turn signal! you people act like it's divulging information to the enemy
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.
Neural Nets store their information in matrices of varying dimensions. Without knowing how to manipulate them, you'll be in a world of pain.
..i never want to touch their code. usually it lacks basic logic. the programmer/designer usually does not have a good grasp on other mathematical concepts either. this is true for even simple business logic. the code is usually inefficient...in my experience anyway. the math really helps you to deal with thousands of processes working together, as well as potentially avoiding deadlock by looking at things on a grand logical scale. again, just my experience. take the math.
Perhaps the most related, useful, but most underappreciated related discipline is statistics. Of all the non-CS classes I took, stats is the most relevant to my day-to-day life. For example, doing analysis of performance and tuning software system, I often see people use bogus statistical analysis, and making mistakes based on those results. Even if your curriculum doesn't require it, I would highly recommend taking a stats class or two.
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.
Most people don't ever use mathematics much more complicated than basic arithmatic, so why do we have to take it in school? Math isn't about math; it's about thinking. Complicated problem teach impressionable young minds how to tackle problems logically, using what you know to be true to determine what you do not. I happened to love it (of course), but a lot of kids were always complaining about how they were never going use Modus Ponens in life. Turns out they were very wrong...
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.
The SCIENCE of programming requires math. The art of programming may not. There is a distinction. That is why the lawyer in the next office over from me was able to put together a fairly good system to manaage his office and case load in a 5GL but couldn't truley understand the difference between a quick sort and a bubble sort. Of course, almost no one writes sorting algorithms any more. If you are writing a program that utilizes mathmatics to accomplish a goal ( e.g. the matrix algebra used in 3D graphics development ) it is not the programming that requires the math it is the problem space. The thing to remember is that, in a way, when you are studying computer science you are not learning how to program you are learning how to learn to program. Now and Information Systems degree would be more about learning to program and leaving it at that.
The majority (I'd say 70%) of the skills I've obtained have been acquired by means of self-teaching and learning from friends.
This is pretty much the case no matter where you go to school. A good school will only give you the tools and understanding to be more efficient at acquiring and utilizing the skills. A good school will not be teaching you those skills.
The rest of the world is filled with mono-educated outsourcing fodder that have crammed a narrowly-targetted CS education into as short a time as possible, memorizing syntax and call center protocols. The best possible insurance of future employability for someone considering CS is to add something else to your curriculum to expand your horizons. Math is certainly one likely candidate, but some other excellent combinations are CS and Music, CS and the Humanitites, CS and Foreign Languages, or CS and English. The suggestion is somewhat counter-intuitive. Most CS majors will frown on your interest in the Humanities. Exactly. Set yourself apart. Study what you are interested in, distinguish yourself from the pack, and seek an advantage through challenging, broad study.
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
From the article:
If you have the chance to take calculus in high school, I may surprise you with my advice. I would not automatically jump at the opportunity for a couple reasons. Please forgive me as I climb onto my soapbox, but keep in mind that I am a math teacher and I know a lot of this from experience.
First, high school calculus teachers tend to be the teachers in the math department the longest. The problem with this is that while these teachers are more experienced, they have been away from calculus longer than the other math teachers in most cases. Besides that, these teachers are often near retirement and may not be as motivated as younger teachers.
Second, calculus is the upper-crust of high school math. In college, it's one of the lowest math classes offered. This results in a completely different teacher mentality. A college calculus teacher will be used to working with struggling students because for many of them, that is the toughest class they will ever have to take. But high school calculus teachers will be more used to working with the top students in the school. If you aren't especially gifted in math, you may find that you don't get what you need from these teachers.
Here's the problem with those ideas:
1) In Calc I in HS, you're looking at a class of 30 people. 50, max. In Calc I in college, you'll likely be in a class with something on the order of 100-200 people. See, *everybody* takes Calc I their first year, not just the comp. sci's. All engineering majors, all the math geeks.. Hell, even English majors probably have basic math as a requirement... So most of the time, it's a big class, usually a seminar type of deal. If you're having a hard time with it in there, then you'll also likely need to take another not-for-credit class where they can give individual instruction or take some extra tutoring on the side. Whereas in high school, you've not only got a smaller class, you've got an experienced math teacher, who likely knows his stuff, and you've got a year to learn it as opposed to 1 semester only. Okay, so the HS teacher may be less motivated, but you've got a longer time period, a smaller class, and you're in that class with the top students in the school (who can probably help you out somewhat) instead of in there with everybody in the whole school (who likely need just as much help as you do).
2) Yes, calculus is the upper crust of high school math. It's also a heck of a lot easier than a college level math class. But here's a thought: The high school class doesn't usually count towards your college GPA, while the college level one does. What's so bad about taking it twice? Take the high school calc if you can swing it, then take it again in college. You may still have a hard time in the college calculus, but it'll be somewhat easier because you've got at least some background to it already.
- Give a man a fire and he's warm for a day, but set him on fire and he's warm for the rest of his life.
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
Excellent article. I like the line, you need to come to grips with one important fact first: computer science has more to do with math than computers. I couldn't agree more, and this is something that many freshman CS majors need to realize quickly.
Heh, I just finished my CS Masters which included a class on Advanced Neural Networks (SVMs and classifiers).
You would not believe how much math is involved! There was one proof in a whitepaper I read that used calculus, algebra, trig, linear algebra, and geometry. In one proof!
My recommendation: take all the math you can. Make sure you take linear algebra (vectors/matrices), trigonometry, calculus, probability, statistics, and anything else that looks interesting.
Why does a CS major need math? Let's see:
Graphics engines - trig, geometry
Physics engines - Calculus, trig
AI - Statistics, probability, calculus, linear algebra
Basic GUIs - Geometry, algebra
Networking - Statistics, linear algebra
And of course, you can't do ANY of the above without algebra.
Another interesting quote: If you have the chance to take calculus in high school, I may surprise you with my advice. I would not automatically jump at the opportunity for a couple reasons. I think I agree on this one. You're going to start at ground zero when you take Calc I in college. So use high school to become badass proficient in algebra and trig.
"You cannot find out which view is the right one by science in the ordinary sense." - C.S. Lewis on Intelligent Design
Taking theoretical computer science classes may seem like a waste of time, but I highly recommend it if for no other reason than because you're not going to learn this stuff on the job or on your own. Taking an extra class on object oriented programming or databases instead may be tempting, but you can teach yourself most of what you need to know about these. Take advantage of the time you have in a university and learn about the logical foundations of your field. For those who love computing, it's an experience which you won't forget!
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 is all so true. I am a computer science major at the Tufts School of Engineering, and the math requirement is huge. I appreciate it though, and I am seeing all the time that the more comfortable I am with math, the more clever and efficient my solutions to large computing problems becomes. Math is the basis of computer science. It allows us to *compute*, which is the obvious origin of computer science. The function of these machines is to process computative operations, and Math is the tool by which we can understand these things, and engineer new more efficient ways to perform them. CS without math is nonsense, who proposed that anyway???
sigSEGV - doy!
Unfortunately, graphing calculators were invented. They're the bane/saviour for many an engineer, since they allow you to get away with an awful lot when you're pressed for time, but they allow many people to skip out on the fundamental lessons of geometry. Personally, I used them in school but not before I had a firm grasp of triginometric principles, ie, I memorized sin-cos-tan tables and could figure things out on paper sans calculator.
I'm amazed these days at what kids use calculators for. My buddies fiance is student teaching a class of 8th graders and says that for simple *addition*, kids are breaking out their TI's. Really, if you can't add 96 + 48 within a few seconds in your head, you've got issues. Graph paper is going the way of the dodo, unless you're an electrical/computer engineer, then you take stock in engineering pad companies.
--trb
Modded "flamebait" but it's a good point. DeVry, ITT Tech, Phoenix U and so on have questionable standards. Why? Because their main purpose is to separate students from money, not teaching. I think that even a more or less unknown state college is better, at least their mandate is to teach, not separate money from the marks. The parent also mentions that he thinks these schools primarily teach management, and that is certainly true of Phoenix, who's primary clientele is management looking for the coveted Masters so as to be able to move on to tenured PHB status.
"Who are in control, they are not in control of anything - they don't even control themselves!" - Glen Beck
A good school should be teaching you that your schooling never ends. As in, never stop learning or you will be left in the dust. Any school that doesn't enforce this opinion on their students in any subject matter are already putting their students at a disadvantage.
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.
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.
If you drop the coding part of CS and focus exclusively on the theory, then fill in the rest with math and physics, I daresay that the result will be far better coding skills than if you focus on coding and throw in math and physics and theory as an afterthought.
The reason is because math is a formal language, just like any programming language. Except math is far more expressive and complicated than any programming language. We handle the complexity by writing functions and abstractions to simplify it. However, in order to abstract, we have to dot all of our i's and cross all of our t's and lay out the law on when the abstraction will or will not work. Sounds familiar?
The beautiful part is that there is no compiler and no test suite you can run against your "programs". You have to do it all in your head. If programmers were able to better predict the behavior of their programs, or if they were to write their programs in such a way that it could be done, then we would have far fewer bugs, or at least debugging would be easier to do.
So, if you are a pro at math and physics, then programming languages is a toy to you.
Why physics, and not just math? Math is programming for programming's sake. Physics is programming tied to reality in some way. Or in other words, you are practically applying the discoveries mathematicians make, and fudging stuff they haven't discovered yet, all in the interest of getting an answer that agrees with the way stuff really is. Physics adds that dimension of "reality" that is inescapable, just like real programming has the shadow of the "user" or "API" or such that is inescapable and must match what people want to see.
There is one area that math and physics won't teach you, but it is easy enough to pick up as it is a rather simple system compared to, say, Thermodynamics or Quantum Mechanics. That is the way computers really work and the limitations thereof. This is the field of data modelling, data theory, B-Trees, and hashes and stuff, or the details about the various hacks people have come up with to stick mathematics into this system.
The radical sect of Islam would either see you dead or "reverted" to Islam.
What type of programming do you do, exactly, where the algorithm isn't the major focus of your work?
Not to defend the guy, but sometimes people use their knowledge unconsciously. For example, when I worked out a new collision detection algorithm for 2D games, I didn't need to write down the Big-O formula because it was straightforward enough for me to visualize the equation in my head. It took me a lot of time to realize that I did that,
One has to wonder how many CompSci majors have claimed that it was a waste of time, then went off to use their education in the back of their head.
Javascript + Nintendo DSi = DSiCade
That depends on the employer. If you're going to work for a clothing chain, they probably just want a basic code monkey who can hook-up the modules they already bought. If you work for a company that makes money selling your software, they definately do want you to know and use your science skills. It is the difference between being a resource and being an expense. You'll find the exact same issue with other careers where you can do it right or just get it done.
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
Bingo! Actually you see this a lot in first year trig or algebra classes being taught by grad students. They are up on the board solving some equation using standard trig or algebra when they see a nice shortcut via calculus, like the area between two curves. Solving the area between two curves is a real bitch using regular algebra or trig, and it is trivial when you use Calculus - like baby slobber trivial. So they do it, but none of the students have a clue what they are doing, because they don't even know that calculus even exists ...
Many of the things that programmers take for granted as 'baby slobber trivial' are actually applications of advanced math - stuff like boolean operations, one to many relationships, many to many relationships, arrays with more than 3 dimensions, shortest path, sorting routines, loops, recursion, different types of conditionals, etc. These are simply part of our thought processes, an extension of how we think - but we were not born with this knowledge. Anybody that has spent time reviewing code from a 'self taught coder' knows what I'm talking about (no offense to the self taught coders.)
Glonoinha the MebiByte Slayer
Does programming really have that much to do with math?
I see or hear this question all of the time in relationship to a degree in computer science. The short answer is:
You can make a living at programming without knowing much about math. Most programmers can get along with some basic algebra skills, and understanding boolean logic.
The long answer is that the question asked in the context of a discussion of computer science shows a lack of understanding of what the field of computer science is. Computer science is not about java or c# or sql. Computer science is about understanding and analyzing why a computer acts a certain way given a certain set of conditions. It is about understanding the best way of instructing a computer to perform tasks. Its about knowing that a computer cannot perform certain tasks no matter how well it is programmed. What does this have to do with math. All of the tasks I mentioned are addressable with some mathematical analysis. A computer scientist will write a program to demonstrate a concept or test a theory. A computer scientist will not write a program to do inventory controll for walmart, unless there is some novel or interesting problems in that task that no one has tackled before. In general someone graduating with a cs degree is well versed in theory, and will have to catch up on the practical aspect of the field. For example, I graduated with a CS degree having only seen one Design Specification Document. I now deal with them every day.
There are many trade schools out there that will give you training in a group of technologies (c#, sql, java, html) and call it a computer science degree. The best of these schools turn out software engineers (a very good skillset to have) the worst of these schools turn out people who are capable of passing a cetrification exam and that is it. In general these guys (the software engineers)can jump right into the business of writing software much more easily than someone with a straight cs degree. However the devry graduates tend to have trouble designing and understanding larger systems, and the ramifications of their decisions within those systems. I find this due to the lack of theoretical underpinnings to their education.
Don't get me wrong. I'm not saying every trade school graduate is not capable of dealing with and analyzing large system analysis. I'm just sayind that in my experience that these graduates come out a little less well equiped for the task. And yes I know several CS graduates who are dundering idiots, so you don't have to tell me about your experience with one.
When I want your opinion I will beat it out of you.
Being a mathematician won't make the switch go off that allows you to expertly use object oriented programming. Nor will it help you create a good GUI. Nor will it help you validate date formats. You need a firm grasp on the math you learned in middle school, but the need to be a mathematician has diminished in many computer science workplaces to the point that the "need" is now a simple "added bonus".
When coding was entirely procedural and focused almost entirely on crunching numbers, well, yes, math was a big deal, but the paradigm's changed greatly now. Now aptitude in pure logic [rather than a broad math bkgd, much less pure calc] is much more important in my experience. Relational database design and object oriented programming require great understanding of set theory, not calculus. I AP'ed into sophomore calculus and had two semesters (plus an audit of DiffEQ) in college, and haven't used that stuff once since entering the workplace (on my sixth year).
When I look to interview and hire new programmers to my team, for pure intellectual skills I'm looking at good coding style, properly factored (as in refactoring) coding examples, and the ability to explain, say, why an example database schema is or isn't in good third normal form. The math I've seen in my tasks is very basic, whether the product I've helped develop was a simple web-based MIS, county-wide tax system, or financial tracker for the largest non-profits.
In fact the only time it's been useful for me to understand mathematical concepts [beyond set theory] was when I thought our resident Geographic Information Systems (GIS) experts weren't considering all the ends and outs of different map projections. Even then, what I was commenting on was well outside of my job description of a database admin.
It's good to know math, all other things equal, but in today's programming workplace, the emphasis on math in CS programs is unfounded. I'll even daresay that's why so mnay people who weren't schooled as programmers do so well -- I know about as many programmers that have impressed me with their proverbial skillz that had a degree in the humanities or no degree at all as I do those with a CS background.
Wake up & catch up, CS programs, and teach what's useful in "the real world"!
It's all 0s and 1s. Or it's not.
This is a problem that is found in many math classes at large state universities. The classes are taught by professors that are at the school to do research, and have no desire to teach first year calculus to undergrads. Its just something they have to do while they're trying to work their way up to full professor. So they do a terrible job and don't really take the class seriously, knowing that it won't matter in the grand scheme of things. Worse, some of these professors feel their job is to weed out as many first year students as they can, so there is no real instruction going on in the class. The only students that really succeed at math in U.S. schools are the ones that have the desire and ability to teach themselves.
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
Writing a web front end to a database certainly is computer science. Especially when you enter the realm of web-based enterprise software or use technologies like .NET.
* Object oriented design
* Reusable components
* Disconnect clients
* Distributed services
* Application integration
* Replication
* Remote objects
Web applications raise the bar when you start talking about issues such as:
* Transactions
* Concurrency control
* Unpredictable user interactions
* Browser incompatibilities
* Security
Even if you don't use the computational aspects of math it doesn't mean you aren't using math or that math isn't necessary for certain CS fields. Math is the basis of all CS. Without a good understanding of math and the critical thinking skills that go along with it a person in CS becomes the type that just gets the job done. A person with strong math skills is much more valuable.
http://www.askthevoid.com
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.
As an individual with a B.S. in Computer Science I find all this negativity towards CS Majors absurd. If you are considering a B.S. in Computer Science you have to decide what you enjoy doing. Do you enjoy programming, solving problems, implementing solutions that require in depth technical knowledge of how both hardware and software function, etc? Or are you more of a customer service related, implement technology solutions with knowledge of how hardware and software interact, and want to concentrate on using pre-existing software apps to provdide solutions? Obviously, this is just the tip of the iceberg in deciding MIS and C.S. A lot of my friends from school loved doing web programming (HTML, XML, some applets, and web design), but hated the whole theoretical aspect of computer science. If you can't take the theory and its inter-relation with math then you should go MIS.
Computer Science is itself inherent to math. You can't really separate the two. Sure you can implement all these solutions with A+, Network+, CCNA, MSCE, but how much do you really understand about truly optimizing performance. What about tailoring apps to employers requirements? Cost/benefit analysis of code? Sure, all that helps, but your not really implementing a complete solution just by setting up a network and providing support. There's so much more to it and that's where the theory, programming, and math come in.
Sure you can get by without the math and theory, but how are you going to implement better solutions and design without them? Even with a loose understanding, CS majors have a skillset and problem solving ability that IT majors just don't have. A good question for potential CS majors would be can you make a contribution to the linux development community? If not, maybe you should concentrate on getting an MIS or minoring in IS with a major in business or another field of interest to improve your marketability.
In the end I guess it comes down to each person's ability and interests. Math is inherent to computer science, but focuses on better development and better development techniques while understanding the underlying structure of systems. If you don't want to understand this underlying strucutre and don't care about innovation and theory then stick with IT. IT is innovative, but is more system functionality and maintenance rather than optimization, efficiency, development, and extensibility.
Studying maths trains the mind in a different way of thinking that doesn't come naturally to most people. That training translates very well to computer jobs, even if the particular exercises are never repeated again. I personally think competence in music is also very important to computer people as that teaches other forms mental discipline and patience, especially to those who find music hard.
I do enterprise Capacity Planning and Performance Tuning for big databases. (Anywhere from 100 to 1000 Gb) I cannot tell you how often poorly designed application architecture causes nasty performance problems, precisely because management thinks that anyone can connect a web front end to a database. Our typical developer has no idea how to optimize for db performance. The application owners don't like hearing you need to re-design your application, because we can't tune it any further. I am tired of telling them that throwing faster hardware at the problem will not help, as a faster machine will only choke the database harder. It is obvious to me that these "developers" do not have adequate problem solving skills to effectively do their jobs. Their code may be clean, but the application design is so poor that its performance will always suck.
Math (and all problem solving skills)are very important for a developer, otherwise one is just a code monkey.
I will not be pushed, filed, stamped, indexed, briefed, debriefed, or numbered. My life is my own.
I don't completely disagree but there are a lot of issues; it's not just that there are professors who aren't interested in teaching. I'm an assistant professor in a math department. I teach numerical analysis to classes comprised of about 75% computer science majors and the rest math majors. There are several things beyond the control of a professor that can impact the quality of instruction. One of the biggest is that many of the students are not interested in the topic; they just want to pass to meet their departmental requirement for a numerical analysis course. Hence I get students trying to copy homework or codes. Just last week I had two students turn in spline code that was a bad C translation of Fortran code. I haven't hunted down the source but their codes were identical and neither student knew Fortran. Having to check for this sort of thing takes time and does not make it easy to teach.
To make matters even worse, the students put off taking numerical analysis until they are about ready to graduate by which time they have forgotten much of the calculus they learned in their first two years. In less mathematical disciplines, many students put off taking calculus and end up forgetting their high school math. And that's assuming the high schools did an adequate job preparing them for calculus in the first place.
And then there are teaching load issues. Math departments generally teach more courses than any other department with the exception of English. Everyone has to take some math. Proportionally we are overloaded with classes to teach. Further university guidelines on tenure are often not written to take this into account. Mathematicians at many universities are expected to write as many papers, get as many grants and supervise as many graduate students as computer science professors while teaching more courses. For some reason this doesn't always work even when the professor has the best of intentions.
The closest thing to a solution that I know of is to hire non-tenure-track lecturers to specialize in teaching calculus, college algebra, etc. That is already done at most schools but often there are rules about retaining such faculty. Even when they are doing a great job (and many do---teaching is what they do and they take it seriously) university policy can prohibit renewing their contracts past an arbitrary time (e.g. 3 years). This makes it difficult to maintain a staff of good teachers.
There may be professors slacking off but in my (possibly biased) opinion the institutional problems are more common. Students shouldn't be able to put off taking math. The universities should hire some portion of permanent faculty that is dedicated to teaching. And promotion guidelines should be written to reflect what the university realistically expects from both tenure-track and non-tenure track faculty in each department.
Possibly that's more griping than you wanted to hear about university politics...
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.
I graduated with a double major in Computer Science and Math. I now work as a software engineer in a large defense company. Many people interchange the terms Computer Science and programming. These terms are not interchangeable. Computer Science is the theory which provides the building blocks that programmers use (often with no underlying knowledge of what is going on). The act of programming really falls more into the term Software Engineering.
Computer Science is theory. In most fields, the theoretical people make heavy use of math. The same is true in Computer Science. Algorithm and development is inextricably linked dependant on math. So if the question is "Does CS have that much to do with math?", the answer is a resounding yes.
Programming or Software Engineering arguably doesn't have as much to do with math. As other posts mention, there are programming/software engineering jobs that use little to no math. However, there are a very large number of jobs that need math. Whether you have one of these jobs or not, you can still benefit from having taken more math.
The issue is not that you took a class that taught you how to do the math that you need to accomplish the job. The issue is the critical thinking skills that math develops. When I started my software engineering job after graduating, the first project that I was assigned to required lots of math that I had never seen in school even though I was a math major. I was able to do the work not because of something I learned, but because of the critical thinking and logical reasoning skills that my math classes had helped develop. My math background also gave me a familiarity with the basic mathematical tools that I needed.
There will always be new problems that school has not prepared you for. If you go to school to learn how to solve the problems you will encounter in the workplace, then you are in for a big surprise. The important thing to get out of school is the ability to think critically and learn new concepts.
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!
And that's all bullshit. Believe me. I'm a computer science major, and I connect web sites to databases. Everything that you do in the business world (business apps, yada) has very little to do with pure computer science.
The closest thing to it is probably doing the DB work itself, and making sure that your tables are normalized, and that you have the keys / indices done correctly. Sorry, but everything in your list is basically just a concept in programming, which you can learn outside of the realm of computer science.
You need to restart your computer. Hold down the Power button for several seconds or press the Restart button.
That is NOT computer science, simply because writing a frontend to a database requires minimal applications of that stuff. A nice litmus test for codemonkey versus computer scientist is whether you will have to create or use a single algorithm that is not in the standard library. Web applications do not require that 99% of the time, so they can be developed almost completely by codemonkeys.
If you can publish something you developed in a scientific peer-reviewed journal, it's computer science. If you simply put together something from prefab pieces, it is NOT computer science.
Anyway, saying that you need to know computer science to program a frontend to a database is like saying you need a degree in electrical engineering to wire up a house. The truth is, there are way too many people with CS degrees and not enough CS positions. But don't mix CS with coding. They are very far apart.
Here here and amen! When looking for programmers [...]
Ok. Let's nitpick: It's not "Here here". It's "Hear, hear". Why do I bring this up? Because so many people here are saying that yes, you need math and problem solving skills. No one mentions that being able to communicate effectively (and correctly) is also very important.
I think the new tendency in the IT industry is to have well-rounded people who can do a good technical job, but still perform passably at the graphic design and copy writing stages. I'm not just talking about Web Development here. Every area of IT is approaching this point.
As deadlines and Time-to-shipment get smaller, programmers are getting thrown more to the forefront of the development cycle. This means dealing with humans, whether it be through well structured language, fanciful graphic design or good interface design. A lot of people are still stuck in the "I'm a rilly good coder, I don need that language stuff aniways" attitude, and I believe that is detrimental to the industry as a whole.
Overcaffeinated. Angry geeks.
I totally agree with your coder vs programmer insight, but took objection to this:
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.
That's nothing to do with the point you were making.. he was just a vendor/method snob. Most Linux/BSD/*NIX people would similarly mock a company who used 100% Microsoft solutions. Most C++ programmers mock Visual Basic programmers. Most Oracle geeks would mock a company who relied on mySQL, and so on.
Come on, if you're suggesting SQL Server 2000 is in the same league as Oracle, that's just plain wrong. He shouldn't have been bagging on your company, that's unprofessional, but the fact he thought SQL Server 2000 was stupid was hardly an indication he was a moron.
Don't worry about the math. It's usually the easiest course in your university schedule - and I tell you that as someone who failed high school math classes constantly and who dropped out of high school because of math (that's a long story, though). Math *is* your friend. How's that? You can be guaranteed that if you do all your homework, you will get an A+ in the course. That's it. No reading, no stupid assignments which get marked by TAs who know less than you, nothing. It doesn't even matter how good or bad your teacher is. Just do all your homework and you'll get an A+. It's a non-linear relationship, do 50% of your homework (every second assigned problem) and you'll get a B+. Do 25% of your homework and you'll get a C+.
I wish that were true. I did all my homework for my math classes and really studied my ass off, and the best I could do in some of them was a C. I'm no math expert, but I guess it depends on where you went to school at and who your professors are/were.
Statisitics: Ugh. Mostly just plug numbers into equations and know what they mean. Not difficult, just boring.
Again, it depends on what you took. I had to take two high level statistics classes for my Systems Analysis degree, and I must say those were my favorite math classes by far. I called it "Applied Calculus". The first class covered probability, and the second class actually covered statistics. What I had thought about statistics before I took the class was more along the line of means and averages. Those topics were covered on the first page of the first chapter, then it took off. Really, I learned more about calc in that class than in my calc classes because suddenly calc became useful.
If I were to ever go back to school and get a different degree, I would major in Statistics.
Just my 2 cents worth.
I worked freelance for hotels.com and some other big name firms. I am a highschool dropout. The CS grads I worked with were good, but not great. Other than one ex army CS grad I found the inability in my peers to aproach a problem from a new angle to be across the board. Something this new generation seems to be forgetting is that once upoun a time someone that knew ass from a $ prompt and didn't go to school got more credit than ninnies who excel at theory but cant code to save there own life. If you learn deep magic on your own without having it spoon fed to you then in my experience you are someone who really knows what they are doing. Often excelling at real world problem solving above and beyond hothouse flower programmers. Thats the difference between a person that can write a few cotton candy language database connections and someone that writes drivers on the bare metal. You either LUST after computers they consume your life. If you dont live sleep and breathe them for a few years then you can't achieve truly wizardlly status. You cant impart love with a university course. As to math being important to programming, if you cant see that a universe based purely on numbers requires you to be able to manipulate them in order to be really good at what you do, then you have no business in a cs course at all. I went from programming for a living to building harleys and hotrods / programming for fun but I spend just as much time in front of the keyboard now as I did then. A real geek just cant give it up. Sorry for any spelling errors etc. for some reason this thread irritated me and I just had to spout off.
Panel F, Relay #70
In 1974, Ted Nelson had some thoughts to share on this very topic in his revolutionary book Computer Lib. As the "crackpot, visionary, gadfly" he calls himself he stated that "Universities require higher math (usually calculus and at minimum linear algebra) before allowing students to program a computer. This is preposterous! This is akin to requiring a PHD in mechanics in order to drive a car down the road! Grade school kids can - and do - learn how to program computers with no math background at all!"
This is a paraphrase, because unfortunately I don't have my copy in front of me at the moment. But I believe I got it pretty close. While I agree with Ted on the whole, I also concede that it entirely depends on what you want to do with your programming projects.
If it's got anything at all to do with breaking apart, twiddling or mangling things like sound and video and many applications of graphics then yes higher math will be a requirement. It will also be useful in helping one think logically enough to handle programmatic tasks more easily.
That being said, there are still many many programmatic tasks you can accomplish...to make your life easier because someone else hasn't in the area you're programming in, or just to learn the internals - the process! - of programming: Ted was dead on (as he was about a lot of things!). No math will be required for a great many tasks!
Quod scripsi, scripsi.