How Does Understanding Algebra Enhance Problem Solving in Computer Engineering?

[Jakov]

Hi everyone, I figured I need to "initialize" myself so I'm in first year of college, Computer Engineering specifically and the reason I signed up is, well I heard that this site is very effective at helping "newbies" delve deeper in any science related topic/issue. I also found couple of anwers myself to the questions on this forum that were bugging me a lot previously.
Recently I decided to grab on math and start studying it as thoroughly as I can, so I picked up some calculus books that I found of interest and recommended to me. I do a lot of research on almost every topic - I can't tolerate many high-level/abstratct ideas such as "let's let limit of a function be this" and not worry about it - but the thing is, I want to know how it works, how it (it being any idea) connects to everything else in a reasonable manner, so that I can use it to it's full potential and know what it can do.
For me this becomes very problematic with algebra, well when I see a particular algebraic relation, be it equation or inequality, for example y = m*x + b, when it changes to for example y/x = m, well this example is trivial, but for larger equations which have multiple variables, relations and functions - i can see the algerbraic manipulation occurring but with every different setup I feel like I don't understand how it relates with previous setup on a deeper level, anway, I'm getting a bit worked up over this.
I also tend to well not tend to but I get a lot of syncronicity with math when I take a piece of paper, pen, calculator and Geogebra ploter :) and start improvising and understanding how things actually work.

My golden rule for everything is that the amount that you put in is the equivalent of what you get back, so that's actually what I believe is the rule for any sort of optimization process, I mean you can't have an excess of information and not use it, you can't have wasted cycles and not use them, they are there and they can be and should be used...

Anyways, Thanks!

 

[Greg Bernhardt]

Welcome to PF!

 

[Windadct]

Hello Jakov and Welcome...

I know you did not directly ask for feedback - but that is what college is about... and as for math I personally see it as an analog for language... First you learn the words ( basic algebra) - then you make meaningful phrases ( think like in physics and mathematically describing projectile motion) - we then move to more and more complex sentences and then stories, where each element brings it's own mathematical description... Planets in a solar system ... Personally I spent years trying to look at a system and understand it all - until you "give up" and learn the elements well you can not really understand the whole system - and this takes time and patience and preactice.
A good house is built on a good foundation, a good foundation is built with good bricks, good bricks are made with good materials - etc... you can not take one class, or ask one question and get all of the answers...we learn the elements, and if we are lucky we eventually see the bigger picture, and the truly brilliant see beyond the picture and use mathematics to teach it back to us.

 

[Jakov]

Hello Jakov and Welcome...

I know you did not directly ask for feedback - but that is what college is about... and as for math I personally see it as an analog for language... First you learn the words ( basic algebra) - then you make meaningful phrases ( think like in physics and mathematically describing projectile motion) - we then move to more and more complex sentences and then stories, where each element brings it's own mathematical description... Planets in a solar system ... Personally I spent years trying to look at a system and understand it all - until you "give up" and learn the elements well you can not really understand the whole system - and this takes time and patience and preactice.
A good house is built on a good foundation, a good foundation is built with good bricks, good bricks are made with good materials - etc... you can not take one class, or ask one question and get all of the answers...we learn the elements, and if we are lucky we eventually see the bigger picture, and the truly brilliant see beyond the picture and use mathematics to teach it back to us.

Yeah, thanks for the feedback, but it has to be fun, I mean I am really patient and I like to study a lot because it's really fun - yes everytime you learn something you found out another area that you haven't explored yet that is even bigger, but the idea with that situation is, is that you can see it as something challenging not something that "you have to do". Yeah I would agree learning foundations is really important because math is language made for everyone and it is important so that we can communicate between each other, because everyone has their own language - imagination. And by me math is all about learning how to corelate your imagination with math, that's all, that's why nobody is "better" than anybody else and never will be, there are differences from person to person and everybody needs a set of different explanations for a given idea that's all that there is to it, but they just haven't figured out how to precisely express it. That's why everytime you "learn" some new concept it feels great because you can pinpoint it precisely and see what it is all about. And now the question is are "you" [i'm talking in general :)]ready to be patient and get throught it just like you said yourself. Anyway i get cought up oftenly just writting about stuff like this I feel like I can't really express what I want to say here so don't be intimidated if it's a long read but blame it on me. <- see this is what I'm talking about