Do you use Mathematica/Maple to help you with problems?

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  • #1
dRic2
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Hi, I was wondering if you suggest to use such softwares to handle complicated calculations during your studying. Generally the exercise given by my professors can be handled with pen and paper, but I often run into "complicated" problems in textbooks that require some heavy calculations. For example, when you solve a differential equation or an integral you may have to spend a great amount of time to make the solution "nice and beautiful" so that you can deduce physical insights on the problem more easily. It is not that I'm lazy (because up until now I did everything I can on paper), but, sometimes, a little help with the math could save me a lot of time (and stress! :biggrin:). Again, I like math, it is just to speed things up a little.

thanks
Ric
 

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  • #2
phyzguy
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I use Mathematica all the time. I assume you have no issue with using a calculator to calculate square roots, trig functions, or logarithms. You don't do these by hand, do you? How is using a more capable tool like Mathematica to help with heavy algebra or calculus any different?
 
  • #3
dRic2
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I don't know. I just grew up this mentality. To be honest, I have to say that if I do the "dirty work" I feel like it will be easier to remember (you know, after all that suffering to go through the math...). During my BS degree it wasn't really necessary, but now I feel it could be very useful, so I think I'll give it a try :wink:
 
  • #4
Wrichik Basu
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I believe it is not wrong to depend on technology for learning purposes. Let's take an example. Will you find out ##\sqrt{29}## on pen and paper every time you need it, or will you use the calculator? I think in majority of the cases, the answer would be the second option.

I have been using Matlab (similar to Mathematica, but the Android app is free) since a long time while doing my studies. Though it's not permitted in my institution, I feel it is very necessary for learning purposes. I have used it mostly for graphing. Equation solving is another great utility that I have been using.

Now, why and where should you use Matlab/Mathematica?
  1. While solving a problem, if you find that you have encountered some calculations that are lengthy, but you know how to solve them, then go for such software, as it saves time. But sometimes do the calculations on pen and paper as well so as to keep practice.
  2. If you encounter something that you do not know how to solve on pen and paper, but you know how to do it in software, go ahead and use the software for the time being, but make sure to learn the process later.
Many people say that this will result in "technology-dependence", a condition where you will not be able to move a bit in life without technology. But I think in today's world, this is somewhat needed to save time. For example, when you are recording an NMR spectrum, in 100% cases, the graphs will be given to you by the computer itself, and perhaps you will not want to do the messy calculations, like Fourier Transforms, on pen and paper. Similarly, for generating higher order Legendre or Hermite polynomials, it is best to use software rather than solve the equations yourself. For solving Schrödinger equation for complex quantum systems, you will almost always need some software that can work with symbolic expression.

Graphing is of vital importance as it helps you to visualise what you are doing. In most institutions, during practical classes, you have to plot the data points on graph paper by hand, then draw the best fit line, and do further calculations. But things become simpler and more accurate when you perform a linear regression on the data points using software.

What I wanted to say is, in short, it is not wrong to use Mathematica for problem-solving. However, for examinations, you need to prepare yourself such that when you will not be allowed to use the software, you can still do your work. If you get into research fields, however, no such limitations will exist.
 
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  • #5
gleem
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How is using Mathematica or whatever different than copying the solution from a friend or paying someone else to do it.
 
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  • #6
Wrichik Basu
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How is using Mathematica or whatever different than copying the solution from a friend or paying someone else to do it.
Here one can learn something even when he/she is making his/her work easy. For example, while searching for functions that do some specific job in matlab, I have learnt quite an amount of maths.

The reason is similar to why one would use a high level language like java instead of assembly language or machine language.
 
  • #7
dRic2
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How is using Mathematica or whatever different than copying the solution from a friend or paying someone else to do it.

Two days ago I calculated a Fourier Transform but I spent 1 hour trying to simplify the result according to the book. Yesterday I was doing a recap exercise on electric dipoles and, at I certain point, I just had to brutally integrate a function over and over... It took me 4 min with Mathematica and 30 min with pen and paper an a huge amount of mistakes due to distraction while integrating.

I'll be using mathematica mostly in similar occasions. I think this can be very helpful, but I'm asking to hear different opinions. The problem, to me, arise when you're facing something that you can do with pen and paper in a few minutes and decide to go for Mathematica because you are lazy: that's risky, but I hope I can manage it.
 
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  • #8
Dr Transport
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Technology is fine, but how are you going to do the work in an exam if you can't do it by hand beforehand. I have no issues with using Matlab or Mathematica but you'll be in a situation where you won't have access to it and be screwed.
 
  • #9
dRic2
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Technology is fine, but how are you going to do the work in an exam if you can't do it by hand beforehand. I have no issues with using Matlab or Mathematica but you'll be in a situation where you won't have access to it and be screwed.

I know. That is why I use it only for exercises that I find on my own in textbooks, not for the ones assigned by professors
 
  • #10
phyzguy
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How is using Mathematica or whatever different than copying the solution from a friend or paying someone else to do it.

So do I understand from your comment that when doing problems, you re-derive every result from first principles, and calculate all needed functions (logs, sines, cosines, etc.) with pencil and paper? It obviously wouldn't be fair to use a calculator, because that would be the equivalent of copying from the people that wrote the software for the calculator, right?
 
  • #11
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In graduate school, I knew some foreign students who were spectacular at doing trig identities. I didn't see the point then and I still don't. If one understands the principles behind the calculation, I don't think there is anything wrong with using modern technology to do the "grunt-work". Becoming technology dependent would be an issue if there is a fear that the technology will not be available in the future, but the opposite is true. Future technology will put the current technology to shame.
 
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  • #12
gleem
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So do I understand from your comment that when doing problems, you re-derive every result from first principles, and calculate all needed functions (logs, sines, cosines, etc.) with pencil and paper? It obviously wouldn't be fair to use a calculator, because that would be the equivalent of copying from the people that wrote the software for the calculator, right?

I figured someone would jump on my post. I'm disappointing that you had to go to manual calculations to make your point. I figured that the use of a book of integrals would have been brought up as an example not a calculator. But anyway do we not still teach children to calculate with pencil and paper before letting them use a calculator?

It is not reasonable to compare arithmetic to symbolic manipulation. When you have performed one addition you know (theoretically at least ) how to perform any addition it is just a matter of inculcating the process, So when can/should you move on to "better" methods? That is an interesting question especially for activities that have benefits. There is more to "learn" when working through problems in their entirety than just getting the answer. I believe that whole process contribute to the building of a sound mental infrastructure resulting in the promotion of creativity , expanding a repertoire of processes and developing an insight that would be of value in the solution of other problems. @dRic2 you say you use Mathematica primarily for working on your own problems which obviously is very useful and expedient how else could you even consider working extra problems considering the time involved.

I am not against computer algebra systems or whatever technology that can facilitate our efforts per se but their use and when is the question which we as individuals must answer.

My post is an opinion based on my experience and observations and offered for thoughtful consideration.

In the future as technology progresses will it be reasonable to eventually introduce such a convenience into elementary schools? Will we need to teach math as it is currently taught if at all?

Anecdote: As an undergraduate (pre-calculator era) we where encouraged to perform integrations unassisted. One never knew when she needed to integrate without a table of integrals.

"Accept the challenges so that you can feel the exhilaration of victory", George S. Patton
 
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  • #13
symbolipoint
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I have not seen all the current changes yet. I only remember the changes taking place from Yesterday. We still needed to show our problem analyses and setups, but later we were allowed to use our hand-held calculators to get our work done. Log tables became fashionable or at that time, practical until hand-held calculators were just too great as tools for getting our work done. Still, we needed to show our analyses and basic equational setups. That was in the instruction and learning processes. Even back then, if we knew we had several lengthy computations to do, like for lab work or research activity, or maybe for work in a job, we could (if available) create computer programs (technology) to help us get all our work done. Most of our fundamental learning was already taken care of and we wanted tools to do the long redundant computations. The reason for showing our diagrams, analysis and basic setup and steps was to show our learning, so that partial credit could be issued for assessment. Such showing of work was ALSO necessary for computer programming courses, again, to show our learning --- assigning our variables, flow charts, and printed results of our exercise programs.
 
  • #14
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There is a trade-off that we make every time we do some mathematics. At one extreme is taking the derivative of ##x^n##. At the other extreme is consolidating the terms of a 2-page summation of several polynomials. A person who needs a computer for the first is at a great disadvantage. A person who tries to do the second will spend many hours doing it and checking the results. One should be able to do the method that is most appropriate.
 
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symbolipoint
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There is a trade-off that we make every time we do some mathematics. At one extreme is taking the derivative of ##x^n##. At the other extreme is consolidating the terms of a 2-page summation of several polynomials. A person who needs a computer for the first is at a great disadvantage. A person who tries to do the second will spend many hours doing it and checking the results. One should be able to do the method that is most appropriate.
Yes, and by the time this person has reached the need to handle that "consolidating the summation of several polynomials", he has achieved a large amount of learning, and is now in need to do some work.
 
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  • #16
vela
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How is using Mathematica or whatever different than copying the solution from a friend or paying someone else to do it.
It really depends on the point of the exercise you're working on and how you use it. For example, if you're a student taking basic algebra and learning to find roots of quadratics, then using Mathematica to "do" homework problems misses the whole point of the homework. On the other hand, if you're a physics undergrad who needs to solve the same quadratic equation to diagonalize a matrix, Mathematica can be a time-saving tool.
 
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  • #17
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If you are turning in the work for credit it’s plagiarism and I will give you an F for the course. It’s the same as looking up a solution on a website, copying someone else’s solution, and turning it in as your own.
 
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“Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun!” -John A Wheeler

A lot of physics is intuition on when to do something. Algebraic systems can take that away if you depend on them too much.

What I do is: Derive the general equation by hand. Do problems by hand, and then check with an algebraic system. This allows me to get the best of both worlds: I learn how to do it by hand, but also learn how to build it up in mathematica/matlab/python. To be a well rounded scientist in this day and age, you need to know computational methods, simple as that. If you don't practice them at every chance, you will miss out on crucial skills.
 
  • #19
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1. At the General Physics level, most courses in college that I'm aware of do not let students use computers to solve problems during an exam. How does using computers to solve HW problems help you in such a situation?

2. At the advanced undergraduate level, say an undergraduate course in E&M, finding solutions to differential equations, etc. is actually part of the learning process. You may have studied those things in math, but you haven't seen it applied and solved in physics. You have to actually grind through it to find the intricate detail of the problem and to get a feel for how something like that is solved. So working through it is part of the learning process. And again, I do not know of schools that allow students to use such devices in exams.

3. I've used MathCad, Mathematica, etc. to do class projects, especially at the graduate level. Here, students are already expected to have grind their way already and have an intimate knowledge of how to solve various problem. Then the target here is no longer about the problem-solving process, but to actually find the solution to a task or problem via whatever means possible. So this is where one encounters differential equations etc. that can't be solved analytically, or one ends up with a transcendental equation that requires numerical means to find the solutions. No one is arguing that computers should not be used here. In fact, that's why many schools have classes in computational physics, so that students are equipped to be able to solve these numerical problems.

4. How many schools actually let a students use Mathematica, etc. during their qualifying exams?

So why do you want to depend on a crutch that you can't use when it matters the most?

Zz.
 
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  • #20
dRic2
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I don't want to sound harsh but It seems to me (maybe I'm getting the wrong idea though) that some of you are taking this on a "philosophical" level, also implying that I'll be cheating if I relay on a tool to solve my homework even though I clearly specified that I would use Mathematica only for my own business and not to solve school problems.

Moreover, I think that most of the time it is faster to solve problems by hand than with Mathematica.

I think it is pointless to specify exactly in what scenarios I'll be using Mathematica because everyone seems to have his##^{**}## own point of view on the subject. I really appreciate the discussion and to hear from you all, but, in the end, I realized it is a very "personal" question. The real advise that all of us seem to be sure about is the following: don't get lazy! :biggrin::biggrin:



##^{**}## Just a curiosity: (...) everyone seems to have their / his own point of view (...) Which one is correct? I'm sorry for any mistakes, english is not my main language.
 
  • #21
ZapperZ
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I don't want to sound harsh but It seems to me (maybe I'm getting the wrong idea though) that some of you are taking this on a "philosophical" level, also implying that I'll be cheating if I relay on a tool to solve my homework even though I clearly specified that I would use Mathematica only for my own business and not to solve school problems.

Wait, what? This was your FIRST POST:

Hi, I was wondering if you suggest to use such softwares to handle complicated calculations during your studying. Generally the exercise given by my professors can be handled with pen and paper, but I often run into "complicated" problems in textbooks that require some heavy calculations. For example, when you solve a differential equation or an integral you may have to spend a great amount of time to make the solution "nice and beautiful" so that you can deduce physical insights on the problem more easily. It is not that I'm lazy (because up until now I did everything I can on paper), but, sometimes, a little help with the math could save me a lot of time (and stress! :biggrin:). Again, I like math, it is just to speed things up a little.

Is this another case of "english mistakes"? Where is the "mistake" here?

Furthermore, if this has nothing to do with school work, then it doesn't belong in a forum called "Academic Guidance"!

Zz.
 
  • #22
dRic2
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Maybe I did not express myself correctly. When I'm facing a problem given by a professor of mine I do NOT use Mathematica. But when I study something ON MY OWN (not for the university) if I run into complicated problems (in textbooks) I use Mathematica to speed things up.

Sorry if it wasn't clear.

PS:
dRic2 said:
Generally the exercise given by my professors can be handled with pen and paper, but I often run into "complicated" problems in textbooks that require some heavy calculations.

I didn't say that the "exercises in textbooks" are the one assigned by professors. In fact I didn't even said the subject is the same: usually I study stuff that are not related with my degree.

I thought it was clear, but I'm sorry if it was not. I really didn't want to be mean to you, but I suppose it came out wrong.
 
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  • #23
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Moreover, I think that most of the time it is faster to solve problems by hand than with Mathematica.
My experience is that doing it by hand is faster 90% of the time. But the exceptions are real horror stories where Mathematica/Maple saved the day.
everyone seems to have his##^{**}## own point of view on the subject. I really appreciate the discussion and to hear from you all, but, in the end, I realized it is a very "personal" question.
Right. I am too old to have faced a moral dilemma regarding homework since there was no computer solution when I was taking classes. But many of us have made their decision long ago and have paid the price. You just have to suit yourself.
 
  • #24
PeroK
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Technology is fine, but how are you going to do the work in an exam if you can't do it by hand beforehand. I have no issues with using Matlab or Mathematica but you'll be in a situation where you won't have access to it and be screwed.

That might be a sign that the exam system is out of date. If you are a research physicist or indeed in the non academic world you can use whatever technology is available. That in my view enhances someone's ability to do a job or solve a problem. It's important, of course, to understand what you are doing. Also it could give exam setters more scope to set conceptually more challenging problems as the grunt work of algebra and integrals can be done by computer.
 
  • #25
ZapperZ
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That might be a sign that the exam system is out of date. If you are a research physicist or indeed in the non academic world you can use whatever technology is available. That in my view enhances someone's ability to do a job or solve a problem. It's important, of course, to understand what you are doing. Also it could give exam setters more scope to set conceptually more challenging problems as the grunt work of algebra and integrals can be done by computer.

This is utter fantasy. It is as if I can ask a question that requires that you solve a differential equation, and then, voila! Using some software package, you get an answer by hitting a button! What fantasy research world is this?

Use any finite-element package, such a FEMlab. How long do you think it takes to set up not only the problem that one wish to solve, but also to verify that one is getting the right answer? How long does it take to bench mark a code or routine that has been set up? And you think this is a valid thing to do in an in-class exam that is trying to evaluate the knowledge and ability of a student? Maybe if the exam runs for days continuously.

In advanced undergraduate physics, the ability for the student to work out the mathematics is often PART of the course objective!

Zz.
 

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