Algebra

[barry glisson]

Being new to computing I don't understand all of the emphasis on algebra. Is programing an algebraic aquation? Is networking involved in a mass of calculations that you spend all of your time entering into some file on a server? I've read a few books but haven't seen one that wanted me to do an equation yet. When do I get to that part? barry

[krusty the klown]

It's probably because computer programming and algebra require a similar mindset. I do some FORTRAN programming to solve a series of differentlal equations - the only equations in my program are the ones I want to solve, rather than the actual FORTRAN code required to solve them.

By definition, mathematical equations should make sense (whether they do to you is a different matter). Mathematics is logical, it follows rules and can bend them but not break them, rather like a game of chess. Very often people who are good at algebra are good at chess also - I reckon they require a similar mindset! If you think about algebra, it is effectively a way of interpreting a problem and placing it in terms of a form of code - like writing down an equation that tells you the trajectory of a bullet, given certain inputs. A computer program is similar in terms of taking a real-life problem and interpreting it into a form such that we can use a tool (the computer) to solve it.

("OK, so why do I need to learn algebra, why can't they just spend more time teaching me to program?") - Dunno!

[Ptrper]

Hey Barry,

Currently, I'm enrolled at Devry trying to get a B.S. in telecommunications management. Wanna know the funny thing? My general education classes seem more complex than my core classes do at the moment. I have just finished one trimester, and college algebra was one subject that I aced (not trying to brag...) Anyway, I've got Quantatative Methods next. Why we need this for Telco is beyond me, and I know that the school is trying to make money also. Oh well, everything is a step in a staircase. Just don't get stuck trying to stay within the parameters.

[gyoung]

Barry,

Its about training the mind. It's all about logic and logical thinking. That's what algebra is designed to teach you.

All programming is is logic. Computers depend upon it.

[qball]

aptly stated, krusty (HEY!,HEY!HEY), undertow.

The fundamental core to any PC CPU is binary math. Everything is represented by 1s and 0s. From this simple representation comes every abstraction you make about computers.

A file is merely a collection of 1s and 0s, though we call it a 'file'. In the gui world, most think of it as an 'icon' or some other object. Regardless, they all resolve back to 1s and 0s.

Regardless, programming is instructions that are done in a specific sequence under certain conditions. Logic, or more appropriately mathmematical logic, governs or rules the manner one uses to accomplish this (an algorythm).

[barry glisson]

Thanks for the response I see where this makes sense but an understanding of physics seems more apropriate to me. I mean if you can understand the hole flow theory in transistor functionality I think you should understand computers. barry

[Bazango]

Boolean Algebra provides the formal basis for digital computers. Programming languages also have a formal basis in a broad class of mathematical structures that fit loosely into the field of algebra. To have a look at what a vast mathematical field algebra is and how computers fit in see this britannica.com site,

http://www.britannica.com/bcom/eb/article/3/0,5716,120643,00.html#Article ,

and especially,

http://www.britannica.com/bcom/eb/article/6/0,5716,120646+14+111000,00.html

and,

http://www.britannica.com/bcom/eb/article/6/0,5716,120646+16+111000,00.html .

See this for formal languages, although linguistics is also a mathematical concern that is related as well,

http://www.britannica.com/bcom/eb/article/8/0,5716,119908,00.html#Article .

[Undertow]

All computers do is divide, multiply, add, and subtract. The only thing a computer knows is numbers. Therefore, if you want to know computers, you must first know what computers know.

[[hd580]]

barry,

Algebra and some of the higher level math (Combinatorics, discrete, a little calculus) are critical for upper level computer science. Most of the intro classes involve teaching you some language, but past that and into the graduate level computer science is nothing but mathematics theory.

It doesn't simply just put you in the same mindset, but you actually use math to solve computer problems from things as simple Big(O) computations to Artificial Intelligence or something.. (i dunno, I'm not a CS major). If you open up a journal of ACM (Association of Computing Machinery) proceedings, all of the papers written have, like, these huge equations that demonstrate the Professor or grad student's research in computer science. I've never seen code.

As far as thinking like computers, 1 & 0's, boolean algebra: that's more of an engineering/physics approach. Algebra is not needed at that level since that's mostly digital logic and computer architecture and I'd wager most CS curriculums just brush that surface.

Krusty,
OK, so why do I need to learn algebra, why can't they just spend more time teaching me to programBecause after the intro classes, they stop teaching you to program and say "We want you to do this assignment. Oh by the way, since we're going to spend so much time on the math concepts involved, we don't have time to teach you Lisp, which you'll need, so go learn it on your own."


[This message has been edited by [hd580] (edited 11-01-2000).]

[Ted61]

When you do networks everyone wants real time. If you are familiar with packet transfers, you know how much data is transfered in a 10mbps system.

Here is a simple math problem for you. If people arrive at an email machine at an average inter-arrival time of three minutes. The average transaction is 2 minutes. What is the probability that you will have to wait in line?

Just think, you are only one packet.

Algebra is the foundation.

Ted

[jeana]

Right, sometimes before writing a program you need to figure out the fastest or best route to your desired result. Lots of math is used in proving that one particular way is the best way to do things (supposedly saving other people from wasting their time writing a slow program.)