Anybody else dependent on a computer algebra system (CAS)?

[forkandwait]

HI all,

I am working my way slowly through some classical mechanics books, and I don't think I could function without my CAS (most often my trusty HP 50g, sometimes Giac/Xcas).

I have never been very good at pages of algebra, often dropping negatives or whatever, bad enough that working through Physics problems over and over again was just too painful. Now with a CAS I can double check my work, solve for t without dropping an exponent, etc etc. However, I feel guilty. Should I worry that I am missing out on something? If I sit for the FE test someday will I regret leaning on the CAS? Other thoughts?

It isn't that I don't know how to do algebra, I am just too inconsistent to keep it together without a type if there more than half a dozen lines.

Also -- I follow Morin's advice and don't look at the answer unless I have to and have taken 24 hour cooling off period; usually I am able to find my own mistakes by cross checking now that it doesn't take hours to rewrite pages of equations trying to find a dropped negative.

For context, I am an autodidact in my forties, with a B.A. in math (liked proofs but not lab or lots of applied algebra). I work as a data analyst / computer programmer. Right now I am working through Morin's Problems book, and hope to switch to the big red book once I get some basic AP Physics skills.

Thanks for reading, looking forward to hearing anyone's thoughts.

 

[Hercuflea]

I recommend using the mathematical typing software Scientific Notebook. It's much easier to keep up with minus signs, etc. when you can copy and paste. There are also lots of hotkeys you can use and program. I'm pretty much able to do math faster through typing at this point than I am through handwriting.

 

[cgk]

OP, there is no problem with depending on a CAS. This is not very different from depending on a calculator for performing non-trivial numeric calculations. It is important to have a basic understanding of what the CAS is doing, in order to understand its limits[1] and to find the occasional mistake it might make (e.g., applying simplifications which are invalid unless certain additional assumptions are made). But far beyond that? Nope. There is little reason to try to become good at something a computer is MUCH BETTER AT in any case. Doing algebra by hand is one such case, not the least because even in non-trivial applications (e.g., symbolic integration) a computer can apply many powerful algorithms a human cannot. Very are very few people in this world who can compete with Mathematica when it comes to computing symbolic integrals.

Just focus on the physics and the higher level problems---most of those cannot be done by computers. We have powerful tools nowadays. We should use them. Would you also feel guilty about washing clothes with a washing machine, instead of doing it by hand?

[1] e.g., to find clever substitutions or transformations (e.g., of coordinates) which make a problem much simpler... a CAS can normally not do that.

 

[nickbob00]

Since you won't have to take pen and paper exams, assuming you understand how you could solve the problem by hand, there is no reason to do by hand what computers can do better. Many working theoretical physicists do complicated calculations by computer.

 

[Matrix0]

I understand the importance of being able to solve problems without relying on a computer algebra system. However, I also understand the value and efficiency that CAS can bring to complex calculations and problem solving. It is a tool that can greatly aid in our understanding and analysis of scientific concepts.

There is no need to feel guilty about using a CAS. It is simply a tool that can help us in our work, just like any other technology. As long as you understand the principles and concepts behind the calculations, using a CAS should not be a concern.

In fact, many scientists and mathematicians use CAS in their work, and it is becoming an increasingly common tool in the field. It allows us to focus on the more important aspects of our work, rather than getting bogged down in tedious calculations.

However, it is always beneficial to have a strong foundation in algebra and problem solving techniques. So, I would suggest continuing to work on your algebra skills, even while using a CAS. This will not only help you in situations where a CAS is not available, but it will also deepen your understanding of the concepts.

Overall, I believe that using a CAS is a valuable tool for any scientist or mathematician. As long as you continue to strive for a strong understanding of the principles and concepts, there is no need to feel guilty about using it. Keep up the good work and continue to learn and grow in your field.